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A quantum leap for silicon chips: Spin-photon coupling now a reality - IT, Information, Media - Information science - IT, Network technologies, Information, Media - v.EN, science - studentnews.eu
Quantum theory began to take shape over a century ago and has since been the focus of many studies and observations. Yet, it’s only in recent years that scientists began to envision the use of
quantum mechanics in technology, and more specifically in computing. TU Delft, the university hosting the QC-LAB project, has joined the race to build efficient quantum computers, with significant
The quantum phenomena that allow us to speak of revolutionising the world of computers as we know it are superposition and entanglement. In a classical computer, a bit can have one of two values: a
one or a zero. In a quantum computer, the basic unit of information, known as a quantum bit, or qubit, can be a one, a zero, or both a one and a zero at the same time. This condition of being in
multiple possible states is known as superposition.
As qubits are added to a computer, its power increases exponentially. But, to benefit from this increase in power, qubits need to be linked, even if they are separated by a large distance. This
phenomenon is referred to as quantum entanglement.
The computer of the future
By harnessing phenomena such as superposition and entanglement, tomorrow’s quantum computers will be able to solve problems that would take current mainframe computers countless years to do, such as
factorising large prime numbers or searching extensive unsorted data sets.
However, for a quantum computer to be able to make such useful computations, it would require lots of qubits, and it’s precisely this need for large numbers of qubits that poses a challenge. These
fragile units of quantum information must be able to communicate well if these computers are to be a success.
The promise of silicon
Quantum chips store information in qubits and are made of silicon. Widely used in electronic devices, silicon makes lengthy storage of information possible and therefore holds promise as a quantum
technology material. But, scientists have yet to figure out how to increase the number of
(spin) qubit systems. As described in their paper published in the journal
, the project’s researchers have taken a step towards addressing this issue by showing that a single electron spin and a single microwave
can be coupled on a silicon chip. In the authors’ own words, ‘[t]he electron spin is trapped in a silicon double
quantum dot
and the microwave photon is stored in an on-chip high-impedance superconducting resonator.’ They add: ‘The electric field component of the cavity photon couples directly to the charge dipole of the
electron in the double dot, and indirectly to the electron spin, through a strong local magnetic field gradient from a nearby micromagnet.’ Researchers said that their results provide a route to
realising large networks of quantum dot-based spin qubit registers.
This quantum chip with reliable silicon qubits is an important milestone on the road to achieving scalable quantum calculations. The QC-LAB team’s goal is to develop a 13-qubit circuit that will
demonstrate back-and-forth quantum state transfer between qubits.
For more information, please see: | {"url":"https://science.studentnews.eu/s/3939/76608-IT-Information-Media/4474686-A-quantum-leap-for-silicon-chips-Spin-photon-coupling-now-a-reality.htm?l=25","timestamp":"2024-11-07T22:16:17Z","content_type":"text/html","content_length":"29951","record_id":"<urn:uuid:394416ec-977f-480f-869a-2ae63ec07a6c>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00566.warc.gz"} |
[Solved] A residential wiring circuit is shown in | SolutionInn
Answered step by step
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A residential wiring circuit is shown in the figure. In thismodel, the resistor R 3 is used to model a 250 V appliance(such as an
A residential wiring circuit is shown in the figure. In thismodel, the resistor R3 is used to model a 250 V appliance(such as an electric range), and the resistors R1 andR2 are used to model 125 V
appliances (such as a lamp,toaster, and iron). The branches carrying I1 andI2 are modeling what electricians refer to as thehot conductors in the circuit, and the branch carryingIn is modeling the
neutral conductor. Ourpurpose in analyzing the circuit is to show the importance of theneutral conductor in the satisfactory operation of the circuit. Youare to choose the method for analyzing the
Part A
Open the neutral branch and calculate Ip ifR1=40?, R2=400?, and R3=8?.
Part B
Close the neutral branch and calculate Ip ifR1=40?, R2=400?, and R3=8?.
140 kV + 0.02 02 j0.02 0 125/0 V VR j0.03 0 w RV3 + 0.032 Ideal 125/0 V VR 0.02 0 j0.02 0
There are 3 Steps involved in it
Step: 1
PARTA Open the neural branch and find the currents in secondary s...
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Basic Topological Concepts
4.1 Basic Topological Concepts
This section introduces basic topological concepts that are helpful in understanding configuration spaces. Topology is a challenging subject to understand in depth. The treatment given here provides
only a brief overview and is designed to stimulate further study (see the literature overview at the end of the chapter). To advance further in this chapter, it is not necessary to understand all of
the material of this section; however, the more you understand, the deeper will be your understanding of motion planning in general.
Steven M LaValle 2020-08-14 | {"url":"https://lavalle.pl/planning/node124.html","timestamp":"2024-11-03T05:41:39Z","content_type":"text/html","content_length":"5126","record_id":"<urn:uuid:fbdb3042-7d56-4ccb-8fcd-aefdd6ff3504>","cc-path":"CC-MAIN-2024-46/segments/1730477027772.24/warc/CC-MAIN-20241103053019-20241103083019-00724.warc.gz"} |
Applied Statistics : From Bivariate Through Multivariate Techniques Second Edition | Medicalebooks
Rebecca M. Warner′s Applied Statistics: From Bivariate Through Multivariate Techniques, Second Edition provides a clear introduction to widely used topics in bivariate and multivariate statistics,
including multiple regression, discriminant analysis, MANOVA, factor analysis, and binary logistic regression. The approach is applied and does not require formal mathematics; equations are
accompanied by verbal explanations. Students are asked to think about the meaning of equations. Each chapter presents a complete empirical research example to illustrate the application of a specific
method. Although SPSS examples are used throughout the book, the conceptual material will be helpful for users of different programs. Each chapter has a glossary and comprehension questions.
There are no reviews yet. | {"url":"https://medicalebooks.org/product/applied-statistics-from-bivariate-through-multivariate-techniques-second-edition/","timestamp":"2024-11-01T18:57:45Z","content_type":"text/html","content_length":"67688","record_id":"<urn:uuid:6f6f0a63-e0e9-426b-a9e9-51b2c05d2ce7>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00206.warc.gz"} |
Invited talks since 2005
13/1/05, Philosophy Department, University of Nice, “La Predicativité: problèmes et perspectives”
15/1/05, École Normale Supérieure, Paris, “Recent Developments in the Philosophy of Mathematics”
2/7/05, École Normale Supérieure, Paris, “The varieties of mathematical explanation”
2/8/05, REHSEIS, CNRS, Paris, “Style” in history and philosophy of mathematics
2/21/05, École Normale Supérieure, Paris, “Neurath, Tarski and Kokoszynska on the semantic conception of truth”
3/2/05, Universita’ di Pisa, Dipartimento di Filosofia, “Tarski sui modelli e sul concetto di conseguenza logica”
3/3/05, Universita’ di Pisa, Dipartimento di Filosofia, “Harvard 1940-1941: Carnap, Quine e Tarski sulla fondazione nominalista della matematica e della scienza.”
4/ (5,6,7) /05, (three lectures), Dipartimento di Filosofia, Catholic University of Milan, Aspetti filosofici dell’opera di Tarski
4/8/05, Dipartimento di Filosofia, Universita’ Statale di Milano, “Tarski sui modelli e sul concetto di conseguenza logica”
4/19/05, Colloque “Interpreter la Géométrie de Descartes”, REHSEIS, Paris, “Descartes on geometrical and mechanical curves”
4/27/05, Department of Logic and Philosophy of Science, Universitat de Barcelona, “Logic, mathematics and the finiteness of the world: the discussion between Tarski and Carnap in 1941”
4/28/05, Department of History of Science, Universitat Pompeu Fabra, Barcelona, “Style” in history and philosophy of mathematics
5/23/05, REHSEIS, CNRS, Paris, “Generality and Explanation”
5/25/05, Colloque “La preuve”, Université Lille III, Lille, “Unification and Explanation: a case study from real algebraic geometry.”
9/9/05, U.C. Berkeley, “Harvard, 1940-1941: Tarski, Carnap and Quine on a finitist language for mathematics and science”
3/3/06, Logic in the Humanities, Stanford University, “Empirism and Semantics: Neurath’s critique of Tarski’s theory of truth.”
4/21/06, Center for the Philosophy of Science, University of Pittsburgh, “Unification and Explanation: a case study from real algebraic geometry.”
5/26/06, University of Cagliari, Department of Philosophy, “Tarski sui modelli e sul concetto di conseguenza logica”
6/15/2006, History of Philosophy of Science (HOPOS 2006), Paris, “Empiricism and Semantics: Neurath’s criticism of Tarski’s theory of truth”
8/1/ to 8/5, 2006, Escuela Latinoamericana de Logica Matematica, Oaxaca, Mexico, “Philosophical Aspects of Tarski’s Work” (five lectures)
10/20/06, Princeton University, Department of Philosophy, “Unification and Explanation: a case study from real algebraic geometry.”
11/04/06, PSA Vancouver, “Unification and Explanation: a case study from real algebraic geometry.”
1/10/07, Vrije Universiteit, Amsterdam, (Beth Lecture), “From Harvard to Amersfoort: Quine and Tarski on Nominalism”
1/12/07, Vrije Universiteit, Amsterdam, “On completeness and Categoricity of Deductive Systems”
3/28/07, Bruxelles, International Conference on Philosophy of Mathematical Practices, “Unification and Explanation: a case study from real algebraic geometry.”
3/28/07, Collège de France, Paris, “From the Deductive-Nomological Model to Unification Theories of Explanation”
3/29/07, Collège de France, Paris, “Mathematical Explanation: Why it Matters”
6/20/07, Academia Nacional de Ciencias de Buenos Aires, Argentina, “On Completeness and Categoricity of Deductive Systems”
7/05/07, Instituto Patagónico de Las Artes, General Roca (Rio Negro), Argentina, “Caminos de la revolución cientifica: de la teoría musical a la acústica”
8/02/07, II Encuentro Internacional Sobre Historia y Filosofia de la Matemática, Villa Maria (Cordoba), Argentina, “Mathematical Explanation: Why it Matters”
9/25/07, El Problema de los Fundamentos de la Matemática en la Tradición Analítica, UNAM, Mexico City, “From Harvard to Amersfoort: Quine and Tarski on Nominalism”
9/27/07, Primera Jornadas Tarski, UNAM, Mexico City, “On Completeness and Categoricity of Deductive Systems”
1/14/08, Problemi recenti di filosofia della matematica, Scuola Normale Superiore, Pisa
1/16/08, Representing the invisible in mathematics, Universität Frankfurt am Main, Frankfurt
4/5/08, Logic Colloquium, Group in Logic, U.C. Berkeley, “On Completeness and Categoricity of Deductive Systems”
4/24/08, “On Completeness and Categoricity of Deductive Systems”, Department of Philosophy, Kansas State University at Manhattan
4/25/08, ‘Style’ in history and philosophy of mathematics, Department of Philosophy, Kansas State University at Manhattan
5/22/08, Quine and Tarski on Nominalism, IHPST, CNRS, Paris
5/22/08 to 6/12/08, Kripke’s theory of truth (four lectures), École Normale Superieure, Paris
6/13/08, Understanding, Explanation, and Unification, Congrés “Mathematical Understanding”, Université Denis-Diderot, Paris VII, Paris.
6/17/08, ‘Style’ in history and philosophy of mathematics, Centro de Estudos Clássicos e Centro de História da Ciência, Universidade de Lisboa, Lisbon, Portugal
6/26/08, “On Completeness and Categoricity of Deductive Systems”, Institut d’Études Avancées-Paris, Maison Suger, Paris.
8/29/08, Tarski on Completeness and Categoricity, Two Hundred Years of Analytic Philosophy, University of Riga, Latvia
9/2/08, ‘Style’ in history and philosophy of mathematics, Danish Society for the History of Science, Copenhagen, Denmark
9/4/08, ‘Style’ in history and philosophy of mathematics, Department of Science Studies, Aarhus, Denmark
9/5/08, Mathematical Explanation: Why it Matters, Department of Science Studies, Aarhus, Denmark
9/15 to 9/19/08, Philosophy of Mathematics and Mathematical Practice from Descartes to Bolzano, Summer School, Department of Mathematics, University of Copenhagen.
9/24/08, Mathematical Explanation: Why it Matters, University of Southern Denmark, Department of Mathematics and Computer Science, Odense, Denmark
9/25/08, Tarski on Completeness and Categoricity, IMFUFA Seminar, University of Roskilde, Denmark
10/2/08, Non-Cantorian Notions of Infinity, VIII International Ontology Congress, San Sebastian, Spain.
10/9/08, Mathematical Explanation: Why it Matters, VIII Coloquio Compostelano de Lógica y Filosofía Analítica, Department of Philosophy, Santiago de Compostela, Spain.
11/7/08, ‘Style’ in history and philosophy of mathematics, Departamento de Filosofia, Pontificia Universidade Catolica, Rio de Janeiro, Brazil
11/10/08 La rappresentazione delll’invisibile in matematica, XII Coloquio de filosofia das ciências formais, Universidade Federal de Santa Maria, Brazil
11/13/08, Semantical completeness, categoricity and logical consequence: an unpublished lecture by Tarski (1940), Centro de Logica, Epistemologia e Historia da Ciência, Universidade de Campinas,
11/17/08, Mathematical Explanation: why it matters, Departamento de Filosofia, Universidade de Sao Paulo, Brazil
11/21/08, Quine and Tarski on Nominalism, Departamento de Filosofia, Universidade Federal de Fortaleza, Brazil
1/27/08, “Empiricism and Semantics: Neurath’s critique of Tarski’s theory of truth.”, Universidade Federal de Bahia, Salvador, Brazil
2/9/09, ‘Style’ in history and philosophy of mathematics, Institute for Advanced Study, Princeton.
3/17/09, ‘Style’ in history and philosophy of mathematics, Swarthmore College
4/28/09, Il nominalismo in Quine e Tarski, Dipartimento di Filosofia, Università di Pisa
5/5/09, La misura delle collezioni infinite di naturali: la definizione cantoriana di numero infinito era inevitabile?, Scuola Normale Superiore, Pisa
5/6/09, Alcune conseguenze filosofiche della teoria delle numerosità: riflessioni su Gödel e Kitcher, Centro Ennio de Giorgi, Scuola Normale Superiore, Pisa.
5/8/09, La misura delle collezioni infinite di naturali: la definizione cantoriana di numero infinito era inevitabile?, Dipartimento di Filosofia, Università di Firenze
5/14/09, La misura delle collezioni infinite di naturali: la definizione cantoriana di numero infinito era inevitabile?, Dipartimento di Filosofia, Università Cattolica, Milano.
6/2/09, Measuring the size of infinite collections of natural numbers: was Cantor’s definition of infinite number inevitable?, IHPST, CNRS, Paris
6/26/09, Measuring the size of infinite collections of natural numbers: was Cantor’s definition of infinite number inevitable?, Colloquium on “The Imaginary, the Ideal and the Infinite in
Mathematics”, Pont-à-Mousson, France
8/28/09, Logic Colloquium, Group in Logic, U.C. Berkeley, Measuring the size of infinite collections of natural numbers: was Cantor’s definition of infinite number inevitable?
10/20/09, MSRI, U.C. Berkeley, Some reflections on Logicomix
2/17/10, Department of Logic and Philosophy of Science, UC Irvine, Measuring the size of infinite collections of natural numbers: was Cantor’s definition of infinite number inevitable?
6/2/10, Philosophy and Model Theory Conference, Paris, “Tarski on sematical completeness, categoricity, and logical consequence”
6/14/10, Philosophie de la Logique, Workshop Paris-Berkeley, Paris, Fixed versus variable domain interpretations of Tarski’s account of logical consequence.
1/11/11, On the Relationship between Plane and Solid Geometry, Danish Society for the History of Science, Copenhagen, Denmark
8/5/11, Axiomatics and purity of methods, Vrije Universitet, Amsterdam.
9/2/11, Logic Colloquium, Group in Logic, U.C. Berkeley, Axiomatics and purity of methods.
9/16/11, Ohio University, Athens, Department of Philosophy, On plane and solid geometry.
10/7/11, UC Davis, Department of Philosophy, On plane and solid geometry.
10/26/11, Salvador da Bahia (Brazil), XV Colóquio Conesul de Filosofia das Ciências Formais, On plane and solid geometry.
11/16/11, Mexico City, Coloquio Internacional “Demonstración Matemática”, UNAM, Axiomatics and purity of methods.
12/13/11, The Van Leer Institute, Jerusalem, Conference on “Mathematical Knowledge and its Applications” in honor of Mark Steiner, Axiomatics and purity of methods.
4/15/12, Department of Philosophy, University of Michigan, Ann Arbor, Axiomatics and purity of methods.
4/19/12, Department of Philosophy, UQAM, Montreal, Axiomatics and purity of methods.
5/25/12, McMaster University, Plenary Speaker at conference “Mind,Language and Cognition. Historical Perspectives”, Axiomatics and purity of methods.
6/1/12, Stanford University, First CSLI Workshop on Logic, Rationality and Intelligent Interaction, On plane and solid geometry.
6/13/12, Academia Nacional de Ciencias de Buenos Aires, Buenos Aires, Some Remarks on the Philosophy of Mathematical Practice.
6/19/12, SADAF, Buenos Aires, Axiomatics and Purity of Methods
6/22/12, SADAF, Buenos Aires, Measuring the size of infinite collections of natural numbers: was Cantor’s definition of infinite number inevitable?
6/26/12, Universidad de la Republica, Montevideo, Measuring the size of infinite collections of natural numbers: was Cantor’s definition of infinite number inevitable?
9/23/12, Scuola Normale Superiore, Pisa, Assiomatica e purezza del metodo
9/28/12, Università Cattolica, Milano, Assiomatica e purezza del metodo
6/15/13, Philosophy Faculty, Oxford University, On plane and solid geometry.
9/29/13, Pirenopolis (Brazil), Measuring the size of infinite collections of natural numbers.
10/8/13, Salvador (Brazil), Numerosities and neologicism
10/11/13, Salvador (Brazil), Some reflections on the philosophy of mathematical practice
11/20/13, Milan, Istituto per gli Studi di Politica Internazionale, Round table on “Inside the Zhivago Storm”, “Feltrinelli tra due fuochi: lo Zivago e la censura” [see: http://
11/21/13, Catholic University of Milan, “In Buona Compagnia? Riflessioni sul neologicismo ed il principio di Hume” [In good company? Some reflections on neologicsm and Hume’s principle]
2/28/2014, Oristano, Italy, “The novel about the novel: Pasternak, Feltrinelli and the editorial adventures of Doctor Zhivago”
3/28/2014, University of Groningen, “In Good Company? On the assignment of numbers to infinite concepts.”
3/29/2014, University of Amsterdam, “In Good Company? On the assignment of numbers to infinite concepts.”
4/3/2014, Jagiellonian University, Krakow, “In Good Company? On the assignment of numbers to infinite concepts.”
4//7/2014, Scula Normale Superiore, Pisa, “In Buona Compagnia? Riflessioni sul neologicismo ed il principio di Hume”
4/8/2014, Dipartimento di Filologia, Linguistica e Letterature Straniere, Pisa, “The novel about the novel: Pasternak, Feltrinelli and the editorial adventures of Doctor Zhivago”
4/10/2014, University of Ferrara, “Paradoxes of the Infinite: classic themes and recent results”
4/11/2014, University of Florence, “In Buona Compagnia? Riflessioni sul neologicismo ed il principio di Hume”
4/29/2014, Institute for Advanced Studies, Munich, “Der Roman um den Roman: Pasternak, Feltrinelli and the editorial adventures of Doctor Zhivago”
5/6/2014, Max-Planck-Institut für Wissenschaftsgeschichte, Berlin, Frege’s Grundlagen §64 and the mathematical practice of definitions by abstraction in the nineteenth century
5/7/2014, Humboldt Universität, Berlin, “Paradoxes of the Infinite: classic themes and recent results”
5/8/2014, Ludwig-Maximilians-Universität, Munich Center for Mathematical Philosophy, “In Good Company? On Hume’s Principle and the assignment of numbers to infinite concepts.”
5/15/2014, New York University, “In Good Company? On Hume’s Principle and the assignment of numbers to infinite concepts.”
5/26/2014, Catholic University of Milan, La sezione 64 dei Grundlagen di Frege e la pratica matematica delle definizioni per astrazione nell’ottocento.
6/16/2014, Paris, Frege’s Grundlagen §64 and the mathematical practice of definitions by abstraction in the nineteenth century.
6/16/2014, IHPST, Paris, “In Good Company? On the assignment of numbers to infinite concepts.”
6/23/2014, University of Vienna, “In Good Company? On the assignment of numbers to infinite concepts.”
9/5/2014, Group in Logic, UC Berkeley, “In Good Company? On the assignment of numbers to infinite concepts.”
9/17/2014, Townsend Center for the Humanities, UC Berkeley, “The novel about the novel: Pasternak, Feltrinelli and the editorial adventures of Doctor Zhivago”
10/24/14, Department of Logic and Philosophy of Science, UC Irvine, “In Good Company? On the assignment of numbers to infinite concepts.”
11/11/14, Istituto Italiano di Cultura, San Francisco, “The novel about the novel: Pasternak, Feltrinelli and the publication of Doctor Zhivago”
2/24/15, UC Davis, “Abstraction principles and the nature of abstracta from Grassmann to Weyl. ”
2/25/15, Philosophy Department, UC Berkeley, Work in Progress Series, “Abstraction and Infinity”
3/24/15, Department of Philosophy, Warsaw University, Warsaw, “In Good Company? On the assignment of numbers to infinite concepts.”
3/27/15, Department of Philosophy, Oxford University, Oxford, “In Good Company? On the assignment of numbers to infinite concepts.”
4/2/15, Department of Italian Studies, UC Berkeley, “The novel about the novel: Pasternak, Feltrinelli and the publication of Doctor Zhivago”
4/13/15, Department of Philosophy, UC San Diego, “In Good Company? On the assignment of numbers to infinite concepts.”
6/11/15, Department of Philosophy, Santiago de Compostela, Spain, “Abstraction principles and the nature of abstracta from Grassmann to Weyl. ”
6/12/15, Department of Philosophy, Santiago de Compostela, Spain, “In Good Company? On the assignment of numbers to infinite concepts.”
6/27/15, IHPST, Paris, “Infini, logique, géométrie”
9/28/15, “Censorship and Freedom in the Cold War: Pasternak, Feltrinelli and the Publication of Doctor Zhivago”, Key-note address at the conference “Poetry and Politics in the Twentieth Century:
Boris Pasternak, His Family, and His Novel Doctor Zhivago”, Hoover Institution, Stanford
9/29/15, “Zhivago in England and the source of the CIA (Mouton) edition”, contributed talk to the conference “Poetry and Politics in the Twentieth Century: Boris Pasternak, His Family, and His Novel
Doctor Zhivago”, Stanford University, Stanford.
11/2/15, Third International Conference on the Philosophy of Mathematical Practice, Paris, “Abstraction principles and the nature of abstracta from Grassmann to Weyl. ”
11/6/15, Istituto Italiano di Cultura, Paris, “Il romanzo del romanzo: Pasternak, Feltrinelli e la pubblicazione del Dottor Zivago”
11/13/15, Department of Philosophy, Stanford University, “In Good Company? On the assignment of numbers to infinite concepts.”
4/14/16, Department of Philosophy, Columbia University, “In Good Company? On the assignment of numbers to infinite concepts.”
4/15/16, Department of Philosophy, Princeton University, Some considerations on Burgess’ “Rigor and Structure” (OUP 2015).
6/(6, 9, 13, 14)/16, “Abstraction and Infinity”, four seminars, Université Paul Sabatier. Toulouse
6/7/16, “Le Roman du Roman: Pasternak, Feltrinelli et les aventures éditoriales du Docteur Jivago”, Université Jean Jaurès, Toulouse
6/15/16, “In Good Company? On the assignment of numbers to infinite concepts”, Centre d’Épistémologie et d’Ergologie Comparatives, Aix-Marseille Université/CNRS, Aix-en-Provence.
5/5/17, “A Brief History of the Group in Logic and the Methodology of Science”, Logic at UC Berkeley, UC Berkeley.
5/24/17, “How should we assign ‘sizes’ to infinite sets: some historical and systematic considerations”, Seventh Summer School on Formal Techniques, SRI International, Menlo Park.
6/5/17, “Sol Feferman’s influence on my academic and professional life”, Solomon Feferman Symposium, Stanford University.
6/29/17, “How should we determine the sizes of infinite sets?” Intersem, University of Paris 7-Diderot, Paris
7/10/17, Fondazione Sardegna, Cagliari, “Il romanzo del romanzo: Pasternak, Feltrinelli e la pubblicazione del Dottor Zivago”
7/30/17, Festival “Sette sere, sette piazza, sette libri”, Perdasdefogu, “Il romanzo del romanzo: Pasternak, Feltrinelli e la pubblicazione del Dottor Zivago”
10/2/17, Dipartimento di Filologia, Letteratura e Linguistica, Università di Pisa, I dattiloscritti dello Zivago e la fonte dell’edizione pirata russa della CIA
10/4/17, Dipartimento di Filosofia, Università di Pisa, I paradossi dell’infinito: tematiche antiche e prospettive recenti.
11/6/17 to 12/4/17, State University of Milan, Abstraction and Infinity, a series of five seminars.
11/7/17 to 12/5/17, Catholic University of Milan, Teoria strutturale della dimostrazione, a series of five seminars.
11/8/17, (with Carlo Feltrinelli), EL BORN Centro de la Memoria, Barcelona, “Il romanzo del romanzo: Pasternak, Feltrinelli e la pubblicazione del Dottor Zivago”
11/16/17, Ferrara, Libreria Feltrinelli, A presentation of “Zivago nella Tempesta”, A conversation with Marco Bertozzi.
11/22/17, University of Bergamo, I paradossi dell’infinito: tematiche antichi e prospettive recenti.
11/23/17, University of Bologna, I paradossi dell’infinito: tematiche antichi e prospettive recenti.
11/29/17, Moscow Book Fair (Non-fiction n. 19), Moscow, Round table (with Lazar Fleishman and Elena Vladimirovna Pasternak) for presentation of the Russian translation of my book “Smugglers, Rebels,
Pirates (Azbukovnik, 2017)
12/1/17, House/Museum Boris Pasternak, Peredelkino (Moscow), Olga Ivinskaya and the loss of Pasternak’s “will”.
12/2/17, Moscow Book Fair (Non-fiction n. 19), Moscow, Round table discussion (with Lazar Fleishman and Elena Vladimirovna Pasternak) on recent publications on Pasternak by publisher Azbukovnik.
12/6/17, Scuola Universitaria Superiore IUSS, Pavia, I paradossi dell’infinito: tematiche antichi e prospettive recenti.
12/6/17, (with Stefano Garzonio), Scuola Universitaria Superiore IUSS, Pavia, Il romanzo del romanzo: Pasternak, Feltrinelli e la pubblicazione del Dottor Zivago.
3/9/18, Fèstival literàriu difùndiu “Ananti de sa Ziminera”, Bauladu (Sardinia), Da Pasternak a Feltrinelli: Una storia di censura e libertà.
3/14/18, Dipartimento di Storia, Università di Cagliari, I dattiloscritti dello Zivago e la fonte dell’edizione pirata russa della CIA.
4/7/18, Neo-logicist Foundations: Inconsistent abstraction principles and part-whole, International meeting on “Foundations in Mathematics-Modern Views”, Ludwig-Maximilians-Universität, Munich.
4/12/18, University of Palermo, I paradossi dell’infinito: tematiche antichi e prospettive recenti.
5/10/18, Czech Academy of Sciences, Prague, Neo-logicist Foundations: Inconsistent abstraction principles and part-whole
6/1/18, University of Cagliari, I paradossi dell’infinito: tematiche antichi e prospettive recenti.
8/2/18, University of Vienna, Conference “Varieties of Mathematical Abstraction”, Neo-logicist Foundations: Inconsistent abstraction principles and part-whole
8/6/18, 41st International Wittgenstein Symposium, Plenary Lecture, Neo-logicist Foundations: Inconsistent abstraction principles and part-whole
8/31/2018, Group in Logic, UC Berkeley, Neo-logicist Foundations: Inconsistent abstraction principles and part-whole
10/28/18, 52nd Philosophy Colloquium, Chapel Hill, Neo-logicist Foundations: Inconsistent abstraction principles and part-whole
11/10/18, Conference in honor of Kenneth Manders, University of Pittsburgh, Neo-logicist Foundations: Inconsistent abstraction principles and part-whole
12/5/18, The Calgary Mathematics & Philosophy Lecture, University of Calgary, Paradoxes of the infinite: Ancient themes and recent perspectives,
12/7/18, Department of Philosophy, University of Calgary, Neo-logicist Foundations: Inconsistent abstraction principles and part-whole
2/22/19, Joint APA/ASL Meeting, Denver, Neo-logicist Foundations: Inconsistent abstraction principles and part-whole
3/7/19, Department of Slavic Languages and Literature, Stanford University, Six typescripts in search of a publisher: Pasternak’s Doctor Zhivago and the source of the CIA (Mouton) edition.
4/13/19, Chapman University, The company you keep. Some recent work on neo-logicism and abstraction principles.
6/4/19 École Normale Supérieure, Paris, The company you keep. Some recent work on neo-logicism and abstraction principles.
10/3/19, Institute for European Studies, UC Berkeley, Moscow has Ears Everywhere. Olga Ivinskaya and the loss of Pasternak’s will.
11/21/19, University of Toronto, “Six typescripts in search of a publisher: Pasternak’s Doctor Zhivago and the source of the CIA (Mouton) edition.”, Keynote address at the conference “Editing the
Soviet Underground”.
12/16/19, Scuola Normale Superiore, Pisa, “Inconsistent abstraction principles”.
12/18/19, Dipartimento di Filologia, Letteratura e Linguistica, Università di Pisa, “Mosca ha orecchie dappertutto. Ol’ga Ivinskaja e la scomparsa del ‘testamento’ di Pasternak”.
12/19/19, Dipartimento di Civiltà e Forme del Sapere, Università di Pisa, “The company you keep. Some recent work on neo-logicism and abstraction principles”.
12/20/19, Dipartimento di Filosofia, Università di Firenze, “The company you keep. Some recent work on neo-logicism and abstraction principles”.
4/5/20, Princeton University, “The company you keep. Some recent work on neo-logicism and abstraction principles.” Invited lecture to conference “The ‘end’ of philosophy of mathematics?” [The
conference was canceled on account of the pandemic]
1/14/21, World Logic Day, “I paradossi dell’infinito: tematiche antiche e prospettive recenti.”
2/26/21, University of Connecticut, Storrs, Connecticut Logic Seminar, “The company you keep. Some recent work on neo-logicism and abstraction principles”.
6/28/21, IHPST, Paris, “Infinity: historical, mathematical and philosophical perspectives”
10/13/21, ETH, Zurich, “Paradoxes of infinity: classic themes and contemporary perspectives”.
10/16/21, Universität Bielefeld, “Paradoxes of infinity: classic themes and contemporary perspectives”.
11/17/21, Université Paris-Sorbonne, Eur’ORBEM, “Zhivago’s Secret Journey: from typescript to book.”
12/3/21, Université de Paris 1 Panthéon-Sorbonne, Conférence inaugurale de la Chaire d’excellence internationale Blaise Pascal, “Histoire et philosophie de l’infini mathématique”.
12/5/21, House/Museum Boris Pasternak, Peredelkino (Moscow), “Zhivago’s Secret Journey: from typescript to book.”
1/10/22, SPHERE, Paris, Université de Paris, Journée “Geometry and Logic”, “Mathematical proofs and syllogistic reasoning in Kant”
1/15/22, University of Vienna, Conference “Modern Geometry and its Foundations”, “How many points are in a line segment? From Grosseteste to the theory of numerosities”
1/21/22, Séminaire “Mathématiques de l’Antiquité à l’Age Classique”, SPHERE, Paris, “William of Auvergne on mathematical infinity”
2/21/2022, Oxford Philosophy of Mathematics Seminar, Oxford University, “How many points are in a line segment? From Grosseteste to the theory of numerosities”
2/26/2022, University of Novosibirsk, Russian Federation, “The company you keep. Some recent work on neo-logicism and abstraction principles” [withdrawn]
2/28/2022, Atelier Boris Pasternak, Maison Suger, Paris, “Le Roman du Roman: Pasternak, Feltrinelli et les aventures éditoriales du Docteur Jivago”.
6/1/2022, University of Venice, “How many points are in a line segment? From Grosseteste to the theory of numerosities”.
6/16/22, Fondation Del Duca, Institute de France, Paris, Conference on Formalization, formalism and intuition, “When formal derivations are not optional: some reflections on derivability claims in
first-order vs. second-order theories”
6/28/22, Château de Goutelas, Conference on Computations and Algorithms, “Definitions by abstraction: Historical roots and logical foundations”
7/4/22, Archives Henri Poincaré, Colloque Dialoguer avec Gerhard Heinzmann, “Predicativity: 1906-1960 (with five questions for Gerhard Heinzmann)”.
9/17/22, KU Leuven, Series “Premodern mathematical thought (The Latinate discussion (13th-16th century), “How many points are in a line segment? From Grosseteste to the theory of numerosities”
9/30/22, Ohio State University, Department of Philosophy, “How many points are in a line segment? From Grosseteste to the theory of numerosities”
12/2/22, UC Berkeley, Group in Logic, “How many points are in a line segment? From Grosseteste to the theory of numerosities”
12/16/22, Conférence de clôture de la Chaire Pascal, Paris, IHPST, “The Wilderness of Infinity”
3/29/2023, Università di Tor Vergata, Rome, “La teoria delle numerosità e il suo retroterra storico/filosofico nelle questioni parte/tutto” [Zoom]
5/31/2023, IHPST, Paris, “Totality, regularity and cardinality in probability theory”
7/23/2023, UCA, Buenos Aires, “How many points are in a line segment? From Grosseteste to the theory of numerosities”
7/27/2023, Invited Plenary Lecture, CLMPST, Buenos Aires, “Totality, regularity and cardinality in probability theory”
11/7/2023, Conference in honor of Eberhard Knobloch, Paris, “On a controversial passage on mathematical infinity in Robert Grosseteste’s De Luce”
11/9/2023, SPHERE, Paris, “Three applications of Zermelo’s theorem on part-whole”
12/01/2023, Conference “40 years of neologicism”, IUSS, Scuola Universitaria Superiore, Pavia, “Three applications of Zermelo’s theorem on part-whole” [Zoom]
12/18/23, Università Roma 3, “La teoria delle numerosità e il suo retroterra storico/filosofico nelle questioni parte/tutto”
12/19/23, Università di Bologna, “Tre applicazioni del teorema di Zermelo sulla parte-tutto”
12/20/23, Libreria Pontremoli, Milan, “Itinerari della storia editoriale del ’Dottor Živago’, tra contrabbandieri, ribelli e pirati”
2/1/24, UC Berkeley, Group in Logic, (with Guillaume Massas), “Totality, regularity and cardinality in probability theory”
3/25/24, University of Buenos Aires, “Three applications of Zermelo’s theorem on part-whole”
5/30/24, Università di Cagliari, “Tre applicazioni del teorema di Zermelo sulla parte-tutto”
6/19/24, Meeting of the Association for The Philosophy of Mathematical Practice, Pavia, IUSS, “Euclidean practice and infinite numbers: the case of Robert Grosseteste”
9/11/2024, Centro Ennio de Giorgi, Scuola Normale Superiore, Pisa, “Three applications of Zermelo’s theorem on part-whole” [on Zoom] | {"url":"https://philosophy.berkeley.edu/people/page/7","timestamp":"2024-11-10T17:22:54Z","content_type":"text/html","content_length":"36732","record_id":"<urn:uuid:af7504be-b406-4179-9d01-b16749e60859>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00476.warc.gz"} |
Graphing Other Functions - SAT II Math I
All SAT II Math I Resources
Example Questions
Example Question #1 : Graphing Other Functions
Simplify the following expression:
Correct answer:
To simplify, we must first simplify the absolute values.
Now, combine like terms:
Example Question #1103 : Algebra Ii
Example Question #2 : Graphing Other Functions
Which of the following is an equation for the above parabola?
Correct answer:
The zeros of the parabola are at
each of their signs is reversed to end up with the correct sign in the answer. The coefficient can be found by plugging in any easily-identifiable, non-zero point to the above formula. For example,
we can plug in
Example Question #1 : How To Graph A Function
Which equation best represents the following graph?
Correct answer:
We have the following answer choices.
The first equation is a cubic function, which produces a function similar to the graph. The second equation is quadratic and thus, a parabola. The graph does not look like a prabola, so the 2nd
equation will be incorrect. The third equation describes a line, but the graph is not linear; the third equation is incorrect. The fourth equation is incorrect because it is an exponential, and the
graph is not an exponential. So that leaves the first equation as the best possible choice.
Example Question #2 : Graphing Polynomial Functions
Which of the graphs best represents the following function?
Correct answer:
The highest exponent of the variable term is two (
The graph below will be the answer, as it shows a parabolic curve.
Example Question #5 : Graphing Polynomial Functions
Which of the following is a graph for the following equation:
Correct answer:
The way to figure out this problem is by understanding behavior of polynomials.
The sign that occurs before the
Example Question #2 : Graphing Other Functions
Define a function
Which of the following statements is correct about
Correct answer:
By the Intermediate Value Theorem (IVT), if
Only in the case of
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Indira Gandhi National Open University, Bachelor, Physics.
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Emory University, Bachelor of Science, Mathematics/Economics.
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Density Problems Worksheet With Answers
Density Problems Worksheet With Answers. Want to have a way for students to get instant feedback? Interactive resources you can assign in your digital classroom from TPT. But before we talk about
tips on how to create a math worksheet for kids, let’s have a look at how youngsters be taught math. How much of liquid B does 1 kg of the combination contain?
This useful resource permits you to have the ability to provide your college students with just that! This useful resource will inform students immediately whether their answer was correct or
incorrect. There are 12 completely different problems the place college students will solve for both density, mass or quantity.
Looking for a worksheet that may reinforce how students can calculate density? This density practice issues will remedy all your problems. Students may have 9 apply problems to complete.
H Grade Science Sound Worksheets Printable And Bodily
The mass is in kilograms, however the density is in grams per cubic centimetre. This means that we have to first convert the kilograms into grams before continuing. As a matter of fact, there is a
very good choice on your children to enhance their efficiency in math.
When you are requested to calculate density, make certain your ultimate reply is given in models of mass per quantity . You may be asked to offer a solution in numerous items than you are given.
Studying Line Graphs Worksheets
In this case, you’re asked for a mass, not the density. You might want to rearrange the density equation so that you get mass.
The worksheet shows several squares of varied sizes which symbolize their quantity. The variety of dots contained in the squares represents the mass of the object. Students will reply 12 questions
concerning the squares and the way they relate to mass, quantity, and density.
Mass, Quantity, And Density Math Follow
The two liquids are blended in a sure proportion and the density of the resulting liquid is 850 kg/m3. How much of liquid B does 1 kg of the mixture contain? Assume the quantity of the 2 liquids is
additive when mixed.
It can be simply altered, adapted, or extended. This file comes with eleven issues , a solution key, and a list of densities of the weather which seem within the issues. With this task college
students will obtain immediate suggestions and can save you HOURS of grading!!!
Relative Density
They can simply establish the objects and evaluate it with each other. By evaluating and contrasting, kids will have the flexibility to come out with a clearer idea. This online quiz is meant to give
you further apply in calculating density, mass or volume of over 150 completely different supplies in g/cm3, g/mL or kg/m3.
Density Mass Volume Worksheets, Questions and Revision has been removed out of your saved matters. You can view all of your saved subjects by visitingMy Saved Topics. Density Mass Volume Worksheets,
Questions and Revision has been added to your saved matters.
Students should discover the missing mass, volume or density based on the given data in each query. The densities of materials are true values and the solutions are attached on the end of the doc.
Want to have a way for school kids to get prompt feedback?
It’s a good idea to be acquainted with tips on how to carry out unit conversions when working on these problems. Many teachers are not very impressed after they see the variety of worksheets which
may be being utilized by their children. This is actually very a lot true in the case of elementary colleges.
State Some Practical Functions Of Relative Density
Add highlights, digital manipulatives, and extra. Mass of object is 316 gram, positioned in a container as shown in determine.
The final problem, # 11 is a problem problem requiring college students to resolve for volume, mass and density. In this google forms worksheet students will continue to explore the connection
between mass, quantity, and density without using any math or numbers.
Where acceptable, ignore the small volume contribution of the stabilizer in the calculations. The different thing to observe is the variety of significant figures in your answer. The variety of
important figures will be the similar as the quantity in your least exact value.
To avoid the potential issues of different items, many geologists use specific gravity , explored in problems 8 and 9, beneath. The question is asking about heavier and lighter, which refers to mass
or weight. Therefore, all you care about is the mass in grams and so the 60 g rock in the second drawback is heavierand the 45 g rock is lighter.
Students will use this worksheet to follow calculating densities using the density formula. Some problems require college students to calculate the volume before discovering the density. Some issues
inform the student the mass and quantity and require college students to make use of the formulation to search out the density.
Have students remedy for the mass, volume, or density of an object by using the density triangle. It is given that 10 mL of gasoline stabilizer treats three L of gasoline.
The next set of three issues is fixing for volume utilizing density. The subsequent set of 3 problems is a mix fixing for either mass, volume or density.
I think I’ve mastered density and I am able to take the quiz! Note that the units cancel, so this reply has no units.
Other issues require the coed to make use of a formulation to calculate the amount earlier than discovering the density. A set of 11 density apply issues with a solution key. The first set of four
problems is solving for density.
In this age group, the lecturers typically really feel that the child’s efficiency isn’t good enough and so they cannot simply give out worksheets. This worksheet is a vital a half of a child’s
development. When he or she comes across an incorrect answer, she or he can simply find the best answer by utilizing the assistance of the worksheets.
Learning these topics is necessary because it will help them develop logical reasoning abilities. It can additionally be an advantage for them to know the concept behind all mathematical ideas. When
crammed with water, the bottle has a mass of 55.75 g.
This could be rearranged in order to discover volume or mass depending on which portions you are given and what the question asks you to find. Displaying all worksheets related to – Density Problems
With Answers. Two liquids, A and B, have densities zero.seventy five grams per milliliter and 1.14 grams per milliliter, respectively.
It also provides youngsters a platform to find out about the topic material. They can easily examine and contrast the values of various objects.
He or she may even be ready to work on a problem with out having to refer to the instructor. And most importantly, she or he might be taught the right means of doing the mathematical drawback.
He or she is going to study to arrange a worksheet and manipulate the cells. A strong weighs 1.5kgf in air and zero.9kgf in a liquid of density 1.2×10 3 kg m -3 .calculate relative density of stable.
Introduction to Density Practice Problems is an activity that helps introduce students to the concept of density.
Students apply calculating density, mass and quantity utilizing the “density triangle”. This worksheet forces students to first identify the equation wanted to solve the problem, to plug the given
information into the equation and clear up.
Todd Helmenstine is a science writer and illustrator who has taught physics and math at the school degree. He holds bachelor’s levels in both physics and arithmetic. SC.8.P.eight.3 Explore and
describe the densities of various materials through measurement of their plenty and volumes.
Finally, check to ensure your reply is reasonable. One method to do this is to mentally evaluate your reply in opposition to the density of water . Light substances would float on water, so their
density must be less than that of water.
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Fitness/Health Goals for 2022?
What are your health and fitness goals for 2022?
I feel like we should all have some. I for one and looking to increase the amount of fruit and vegetables I eat on a day to day basis. Right now I only eat them a few times a week which is not
enough. I should be eating them daily.
Same as you, I want to eat healthier. I want to make sure I get all the nutrients my body needs so I can feel healthy again. The last two years have really aged me. I hurt almost every day now. This
is not normal for someone in their 20s!
I am still working on my weight loss goals. I guess my "for now" goal is to be 40 pounds lighter by July. So I will have to lose about 6 pounds a month. I did lose some weight already but I want to
reach my goal in 2022. Also want to be more active in general and I am going to start that in January. Spiritually speaking. I want to read the Bible throughout the year. I have never read it from
cover to cover and since my husband got me a new one for Christmas, I am going to push to do it. I will use the recommended chapters and checklist in the back.
I haven't set anything yet. I usually don't start until after New Year Day and since it is on a weekend, I will be starting Monday if I end up setting up New year's goals for myself in terms of
fitness and health.
I am just going to focus on eating better. I don't really have anything set in stone other than making sure I drink enough water each day. I had been slacking at the end of the year from stress.
5 hours ago, Mila said:
I am just going to focus on eating better. I don't really have anything set in stone other than making sure I drink enough water each day. I had been slacking at the end of the year from stress.
I hear that! I have not started out well though. I already had fast food! I think I will focus on eating healthy Monday-Friday and let myself have some enjoyments at the weekends so I can actually
stick to something. | {"url":"https://www.motivationdistrict.com/forums/topic/1184-fitnesshealth-goals-for-2022/","timestamp":"2024-11-03T07:39:30Z","content_type":"text/html","content_length":"139170","record_id":"<urn:uuid:0bb14f60-939b-40ef-8d0b-4834ad6c8408>","cc-path":"CC-MAIN-2024-46/segments/1730477027772.24/warc/CC-MAIN-20241103053019-20241103083019-00374.warc.gz"} |
87 research outputs found
Euler–Euler two-phase model simulations are usually performed with mesh sizes larger than the smallscale structure size of gas–solid flows in industrial fluidised beds because of computational
resource limitation. Thus, these simulations do not fully account for the particle segregation effect at the small scale and this causes poor prediction of bed hydrodynamics. An appropriate modelling
approach accounting for the influence of unresolved structures needs to be proposed for practical simulations. For this purpose, computational grids are refined to a cell size of a few particle
diameters to obtain mesh-independent results requiring up to 17 million cells in a 3D periodic circulating fluidised bed. These mesh-independent results are filtered by volume averaging and used to
perform a priori analyses on the filtered phase balance equations. Results show that filtered momentum equations can be used for practical simulations but must take account of a drift velocity due to
the sub-grid correlation between the local fluid velocity and the local particle volume fraction, and particle sub-grid stresses due to the filtering of the non-linear convection term. This paper
proposes models for sub-grid drift velocity and particle sub-grid stresses and assesses these models by a priori tests
Gas-particle flows in vertical risers are involved in many industrial scale fluidized bed applications such as catalytic cracking, fossil or biomass combustion. Risers flows are often simulated by
two-fluid model equations coupled with closures developed in the frame the kinetic theory of granular media. However, two-fluid model discretized over coarse mesh with respect to particle clustering
size are performed for large units because of limited computational resources. Now, it is well established that meso-scales cancelled out by coarse mesh simulations have dramatic effect on overall
behaviour of flows. This study proposed a sub-grid modeling approach for effective drag force and particle stresses which accounts for the effects of unresolved structures on the resolved flows
The paper presents numerical simulations of particle-laden fully developed turbulent channel flows per- formed in a stochastic Lagrangian framework. The particle inertia is large in order to neglect
the effect of the turbulent gas motion on the particle dispersion. In contrast the inter-particle collisions are impor- tant and accounted for by using Direct Simulation Monte-Carlo (DSMC) method.
The comparison of the Monte-Carlo results with those obtained by Discrete Particle Simulation (DPS) shows that the stochastic collisions algorithm is able to predict accurately the particle
statistics (number density, mean velocity, second- and third-order velocity moments) in the core flow. More, the paper analyses the number sec- tions needed for accurate predictions. In the very
near-wall region, the Monte-Carlo simulation fails to account for the wall shelter effect due to the wall-normal unbalanced inter-particle collisions influence induced by the presence of the wall.
Then, the paper shows that DSMC permits to assess the closure approximations required in moment approach. In particular, the DSMC results are compared with the corresponding moment closure
assumptions for the third-order correlations of particle velocity, the cor- relations between the drag force and the velocity and the inter-particle collision terms. It is shown that at the opposite
of the standard DSMC, the moment approach can predict the wall shelter effect. Finally, a model for the mean transverse force is proposed for taking into account wall shelter effect in DSMC
In most modelling works on bioreactors, the substrate assimilation is computed from the volume average concentration. The possible occurrence of a competition between the transport of substrate
towards the cell and the assimilation at the cell level is generally overlooked. In order to examine the consequences of such a competition, a diffusion equation for the substrate is coupled with a
specific boundary condition defining the up take rate at the cell liquid interface. Two assimilation laws are investigated, whereas the concentration far from the cell is varied in order to mimic
concentration fluctuations. Both steady and unsteady conditions are investigated. The actual uptake rate computed from the interfacial concentration is compared to the time-averaged uptake rate based
on the mean far-field concentration. Whatever the assimilation law, it is found that the uptake rate can be correlated to the mean far-field concentration, but the actual values of the parameters are
affected in case of transport limitation. Moreover, the structure of the far-field signal influences the substrate assimilation by the microorganism, and the mean interfacial uptake rate depends on
the ratio between the characteristic time of the signal and the diffusional time scale, as well as on the amplitude of the fluctuations around the mean far-field concentration in substrate. The
present work enlightens some experimental results and helps in understanding the differences between the concentration measured and that present in the microenvironment of the cells
Detailed sensitivity numerical studies have shown that the mesh cell-size may have a drastic effect on the modelling of circulating fluidized bed. Typically the cell-size must be of the order of few
particle diameters to predict accurately the dynamical behaviour of a fluidized bed. Then the Euler-Euler numerical simulations of industrial processes are generally performed with grids too coarse
to allow the prediction of the local segregation effects. A filtered approach is developed where the unknown terms, called sub-grid contributions,have to be modelled. Highly resolved simulations are
used to develop the model. They consist of Euler-Euler simulations with grid refinement up to reach a mesh independent solution. Then spatial filters can be applied in order to measure each sub-grid
contribution appearing in the theoretical filtered approach. Such kind of numerical simulation is very expensive and is restricted to very simple configurations. In the present study, highly resolved
simulations are performed to investigate the sub-grid contributions in case of a binary particle mixture in a periodic circulating gas-solid fluidized bed. A budget analysis is carried out in order
to understand and model the effect of sub-grid contribution on the hydrodynamic of polydisperse gas-solid circulating fluidized bed
In dilute gas-solid turbulent flows, as that encountered, for example, in pulverized coal combustion processes, the correct prediction of the non-isothermal/reactive particle-laden turbulent mixture
relies on the accuracy of the modeling of the local and unsteady particle behavior, which affects the hydro-thermodynamic coupling and the heat transfer and transport in and between the phases and at
wall. In very dilute mixtures composed of highly inertial solid particles, such a local and unsteady behavior is the result of the particle interactions with very distant and independent turbulent
eddies, namely with different dynamic and thermal turbulent scales. Such interactions strongly modify the local particle velocity and temperature distributions, changing the local evolution of the
properties of the dispersed phase. Their knowledge is thus crucial when modeling unsteady particle-laden turbulent flows. In this work, the focus is on the particle temperature distribution. Its
characterization is provided by means of an analysis of the two-particle correlation functions in the frame of the direct numerical simulation of non-isothermal homogeneous isotropic, statistically
stationary, turbulent flows
It is well established that small-scale structures have an important effect on the overall hydrodynamic behaviour of dense and circulating fluidized bed. Due to computational constraints, the
numerical simulations of practical applications with Euler-Euler two-phase approach are usually performed with relatively coarse mesh with respect to the local segregation of solid. These simulations
cancel out the small-scale solid structures. All previous studied attempted to take into account the effect of unresolved structures on the drag force in the case where the particulate phase is
monodisperse. This paper is dedicated to analyse the unresolved structures effects on polydisperse gas-solid flow by multi-fluid Eulerian approach. In this study, the binary mixture is conducted by
gas at an ambient condition in a 3D periodic circulating fluidized bed. The aim is first to obtain mesh independent results where further mesh refinement is not necessary. Then these results are used
to investigate the unresolved structures effects on resolved field by following a priori methodology. In particular, the role of small-scale structures on the momentum transfer by inter-particle
collisions is pointed out
3D numerical simulations of dense pressurized fluidized bed are presented. The numerical prediction of the mean vertical solid velocity are compared with experimental data obtained from Positron
Emission Particle Tracking. The results show that in the core of the reactor the numerical simulations are in accordance with the experimental data. The time-averaged particle velocity field exhibits
a large-scale toroidal (donut shape) circulation loop. Two families of boundary conditions for the solid phase are used: rough wall boundary conditions (Johnson and Jackson, 1987 and No-slip) and
smooth wall boundary conditions (Sakiz and Simonin, 1999 and Free-slip). Rough wall boundary conditions may lead to larger values of bed height with flat smooth wall boundary conditions and are in
better agreement with the experimental data in the near-wall region. No-slip or Johnson and Jackson׳s wall boundary conditions, with sufficiently large value of the specularity coefficient (ϕ≥0.1)
(ϕ≥0.1), lead to two counter rotating macroscopic toroidal loops whereas with smooth wall boundary conditions only one large macroscopic loop is observed. The effect of the particle-particle
restitution coefficient on the dynamic behaviour of fluidized bed is analysed. Decreasing the restitution coefficient tends to increase the formation of bubbles and, consequently, to reduce the bed
The aim of the paper is to introduce and validate a Monte-Carlo algorithm for the prediction of an ensemble of colliding solid particles, or coalescing liquid droplets, suspended in a turbulent gas
flow predicted by Reynolds Averaged Navier Stokes approach (RANS). The new algorithm is based on the direct discretization of the collision/coalescence kernel derived in the framework of a joint
fluid–particle pdf approach proposed by Simonin et al. (2002). This approach allows to take into account correlations between colliding inertial particle velocities induced by their interaction with
the fluid turbulence. Validation is performed by comparing the Monte-Carlo predictions with deterministic simulations of discrete solid particles coupled with Direct Numerical Simulation (DPS/DNS),
or Large Eddy Simulation (DPS/LES), where the collision/coalescence effects are treated in a deterministic way. Five cases are investigated: elastic monodisperse particles, non-elastic monodisperse
particles, binary mixture of elastic particles and binary mixture of elastic settling particles in turbulent flow and finally coalescing droplets. The predictions using the new Monte-Carlo algorithm
are in much better agreement with DPS/DNS results than the ones using the standard algorithm
Axial mixture characterization is a wide spread problem in granular particle blending processes such as in an horizontal drum mixer. The homogeneous mixture of particles is obtained by blending the
particles via rotating paddles in a fixed cylindrical drum. This problem, common to many technological devices, is crucial in the manufacture of a broad variety of industrial products, such as
polypropylene. The granular flow behavior in these systems is still poorly understood and the numerical study of such configurations receives increasing academic and industrial attention. In this
paper, a study is conducted to investigate the effects of different aspects of the reactor design on the axial transport of monodisperse, uniform density and spherical polypropylene particles.
Results show that principally the shape of the paddles is the important design consideration to enhance the axial transport of particles | {"url":"https://core.ac.uk/search/?q=author%3A(Fede%2C%20Pascal)","timestamp":"2024-11-02T22:23:43Z","content_type":"text/html","content_length":"189612","record_id":"<urn:uuid:2216d093-1e1a-4c1b-b633-207738e64785>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00176.warc.gz"} |
Turing machines
Turing Machines are the basis of modern computing, but what actually is a Turing Machine? Assistant Professor Mark Jago explains.
A Turing machine is a model of a machine which can mimic any other (known as a universal machine). What we call "computable" is whatever a Turing machine can write down. This video is about how it
was conceived and why it works using physical explaination. | {"url":"https://haltingproblem.org/posts/turing-machines/","timestamp":"2024-11-13T22:47:28Z","content_type":"text/html","content_length":"14906","record_id":"<urn:uuid:afc1ae54-2d77-42d6-ab17-8db57da2babc>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00706.warc.gz"} |
2s And 3s Multiplication Worksheets
Math, specifically multiplication, forms the cornerstone of various academic disciplines and real-world applications. Yet, for several learners, mastering multiplication can posture an obstacle. To
address this difficulty, teachers and moms and dads have actually welcomed an effective device: 2s And 3s Multiplication Worksheets.
Introduction to 2s And 3s Multiplication Worksheets
2s And 3s Multiplication Worksheets
2s And 3s Multiplication Worksheets -
Multiplication by 2s This page is filled with worksheets of multiplying by 2s This is a quiz puzzles skip counting and more Multiplication by 3s Jump to this page if you re working on multiplying
numbers by 3 only Multiplication by 4s Here are some practice worksheets and activities for teaching only the 4s times tables Multiplication
Grade 3 math worksheets on the multiplication tables of 2 3 Practice until instant recall is developed Worksheet 1 Worksheet 2 Worksheet 3 Worksheet 4 Worksheet 5 Worksheet 6 5 More Similar
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Print worksheets for teaching students to multiply single digit numbers by the number 2 This page has printable flash cards practice worksheets math sliders timed tests puzzles and task cards
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Just How to Develop Engaging 2s And 3s Multiplication Worksheets
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Relating multiplication to everyday circumstances includes relevance and functionality to exercises.
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Introduction to Multiplication with Groups Count the number of groups and the number of objects in each group This is a 2 page introductory level worksheet activity 2nd through 4th Grades View PDF
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Grade 3 math worksheets on the multiplication tables of 2 3 Practice until instant recall is developed Worksheet 1 Worksheet 2 Worksheet 3 Worksheet 4 Worksheet 5 Worksheet 6 5 More Similar
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Adding Fractions - Steps, Examples: How to Add Fractions - Grade Potential Kansascity, MO
How to Add Fractions: Steps and Examples
Adding fractions is a usual math problem that children learn in school. It can seem intimidating initially, but it turns easy with a shred of practice.
This blog post will guide the steps of adding two or more fractions and adding mixed fractions. We will ,on top of that, provide examples to show how this is done. Adding fractions is crucial for
several subjects as you move ahead in mathematics and science, so ensure to adopt these skills early!
The Steps of Adding Fractions
Adding fractions is a skill that a lot of kids have difficulty with. Despite that, it is a somewhat easy process once you grasp the basic principles. There are three main steps to adding fractions:
looking for a common denominator, adding the numerators, and streamlining the answer. Let’s carefully analyze each of these steps, and then we’ll look into some examples.
Step 1: Determining a Common Denominator
With these useful points, you’ll be adding fractions like a expert in no time! The first step is to look for a common denominator for the two fractions you are adding. The smallest common denominator
is the lowest number that both fractions will divide uniformly.
If the fractions you want to sum share the same denominator, you can avoid this step. If not, to determine the common denominator, you can list out the factors of respective number as far as you
determine a common one.
For example, let’s say we wish to add the fractions 1/3 and 1/6. The lowest common denominator for these two fractions is six for the reason that both denominators will divide uniformly into that
Here’s a quick tip: if you are uncertain regarding this process, you can multiply both denominators, and you will [[also|subsequently80] get a common denominator, which would be 18.
Step Two: Adding the Numerators
Once you possess the common denominator, the immediate step is to convert each fraction so that it has that denominator.
To turn these into an equivalent fraction with the exact denominator, you will multiply both the denominator and numerator by the identical number necessary to achieve the common denominator.
Subsequently the last example, 6 will become the common denominator. To change the numerators, we will multiply 1/3 by 2 to attain 2/6, while 1/6 will remain the same.
Since both the fractions share common denominators, we can add the numerators collectively to get 3/6, a proper fraction that we will proceed to simplify.
Step Three: Simplifying the Results
The final step is to simplify the fraction. As a result, it means we need to lower the fraction to its minimum terms. To accomplish this, we search for the most common factor of the numerator and
denominator and divide them by it. In our example, the greatest common factor of 3 and 6 is 3. When we divide both numbers by 3, we get the concluding result of 1/2.
You follow the exact steps to add and subtract fractions.
Examples of How to Add Fractions
Now, let’s proceed to add these two fractions:
2/4 + 6/4
By using the steps above, you will see that they share the same denominators. Lucky you, this means you can avoid the initial step. At the moment, all you have to do is add the numerators and leave
the same denominator as it was.
2/4 + 6/4 = 8/4
Now, let’s attempt to simplify the fraction. We can perceive that this is an improper fraction, as the numerator is higher than the denominator. This might indicate that you can simplify the
fraction, but this is not possible when we deal with proper and improper fractions.
In this example, the numerator and denominator can be divided by 4, its most common denominator. You will get a conclusive answer of 2 by dividing the numerator and denominator by 2.
Provided that you follow these steps when dividing two or more fractions, you’ll be a professional at adding fractions in no time.
Adding Fractions with Unlike Denominators
The procedure will require an extra step when you add or subtract fractions with dissimilar denominators. To do these operations with two or more fractions, they must have the exact denominator.
The Steps to Adding Fractions with Unlike Denominators
As we stated above, to add unlike fractions, you must obey all three steps stated above to change these unlike denominators into equivalent fractions
Examples of How to Add Fractions with Unlike Denominators
Here, we will concentrate on another example by adding the following fractions:
As shown, the denominators are different, and the lowest common multiple is 12. Thus, we multiply each fraction by a number to achieve the denominator of 12.
1/6 * 2 = 2/12
2/3 * 4 = 8/12
6/4 * 3 = 18/12
Now that all the fractions have a common denominator, we will go forward to add the numerators:
2/12 + 8/12 + 18/12 = 28/12
We simplify the fraction by splitting the numerator and denominator by 4, coming to the ultimate answer of 7/3.
Adding Mixed Numbers
We have mentioned like and unlike fractions, but presently we will go through mixed fractions. These are fractions followed by whole numbers.
The Steps to Adding Mixed Numbers
To work out addition exercises with mixed numbers, you must start by converting the mixed number into a fraction. Here are the steps and keep reading for an example.
Step 1
Multiply the whole number by the numerator
Step 2
Add that number to the numerator.
Step 3
Take down your answer as a numerator and keep the denominator.
Now, you proceed by summing these unlike fractions as you generally would.
Examples of How to Add Mixed Numbers
As an example, we will work out 1 3/4 + 5/4.
Foremost, let’s change the mixed number into a fraction. You will need to multiply the whole number by the denominator, which is 4. 1 = 4/4
Next, add the whole number represented as a fraction to the other fraction in the mixed number.
4/4 + 3/4 = 7/4
You will be left with this operation:
7/4 + 5/4
By adding the numerators with the same denominator, we will have a ultimate answer of 12/4. We simplify the fraction by dividing both the numerator and denominator by 4, ensuing in 3 as a conclusive
Use Grade Potential to Improve Your Arithmetics Skills Today
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2.2.4.3: Projectile Motion- Very Long Range
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Suppose that a projectile is launched in the horizontal direction (call it \(X\)) from a high tower, with the initial velocity of \(v_x\). The height of the tower is \(H\). Find the equation of the
projectile trajectory, and the spot it hits the ground. It's a standard problem in introductory level physics. The solution is pretty simple: we call the vertical direction the \(Z\) axis, we call
the coordinates of the tower top as \(x=0\) and \(z=0\), and assume that the launching takes place a \(t =0\). So, as there is no force in the \(x\) direction, \(v_x\) does not change, and the \(x\)
coordinate changes with time as \(x(t) = v_xt\). Downwards, there is a motion with acceleration \(g\), so that \(z(t)= gt^2\). These two equations together constitute the so-called “parametric
equations of the trajectory curve''. If one prefers an alternative description of this curve, in the \(z = f(x)\) form, one can readily obtain it, solving the first equation for time: \(t=x/v_x\),
and plugging it into the second, to obtain: \(z = -(g/2v_x^2)x^2\), which is the equation of an inverted parabola. And as far as the spot where the projectile hits the ground is concerned, for this
spot \(z = -H\), so by solving the equation \(-H = -(g/2v_x^2)x^2\), we obtain \(x=v_x\sqrt{2H/g}\).
Earlier in the text, general equations for the free fall (Eqs. 1.20) were presented. For the case discussed above, we need to use only two of them, for \(x\) and \(z\). There is no force in the \(x\)
direction, and in the \(z\) direction the force is \(F_z = -mg\). Therefore, we obtain a set of two differential equations:
\[ dfrac{d^2 x}{dt^2}= 0 \;\;\; {\rm and} \;\;\;dfrac{d^2 z}{dt^2}= -g \]
It can be readily checked by a pretty simple double differentiating that the two parametric solutions for \(x(t)\) and \(z(t)\) obtained above by the “introductory physics method'' indeed do satisfy
both those differential equations.
But will the introductory physics method always work?... Well, note that in such a solving procedure we used an additional “hidden assumption'' -namely, that the Earth is flat. As long as the flight
range of of the projectile is relatively short -say, not beyond the horizon visible from the ground level -the “flat Earth'' is pretty good an approximation because the effects of the Earth curvature
are still very small. But if the projectile can fly far beyond the horizon, the curvature can no longer be neglected. In WW II, the battleships' most powerful artillery pieces could fire on targets
as far away as about 50 km (\)\tilde{30}\)) miles, and at such distance the target is already about 200 m (1/8 mile) below the imaginary “flat Earth level''. And what if we wanted to calculate the
trajectory and the range of a projectile with no propulsion, but with the initial speed sufficient to carry it over distances much, much longer than 50 km?
In such a case there is no other way than to use the general equations. If we put the origin of the \(XZ\) Carthesian system at the Earth center, then the calculation of the force of gravity at any
point above the Earth surface of coordinates \(x\) and \(z\) is straightforward: the distance from the Earth center is \(\sqrt{x^2+z^2}\).
By replacing \(R_{\rm e}\) in the Eq. 2.13 with this distance we get the total force of gravity acting on mass \(m\) at this point:
\[ F(x ,y) = Gdfrac{M_{\rm e}m}{\sqrt{x^2+z^2}^2}. \]
In the equations of motion we need not the total force, but its components in the \(x\) and \(z\) directions. To obtain their values and signs, we have to multiply the total force by, respectively, \
(-\cos\theta\) and \(-\sin\theta\), where \(\theta\) is the angle defined in Fig. XX. From this Figure, one can readily find that:
\[ \cos\theta = dfrac{x}{\sqrt{x^2+z^2}}\;\;\;{\rm and}\;\;\;\sin\theta=dfrac{z}{\sqrt{x^2+z^2}}.\]
By combining Eqs. 1.13, 1.30, and 1.31, we obtain generally valid equations of motion for a projectile launched from an arbitrary point above the surface of \textbf{spherical} Earth:
\[ dfrac{d^2x}{dt^2} = -GM_{\rm e}dfrac{x}{\sqrt{x^2+z^2}^3} \;\;\;{\rm and}\;\;\; dfrac{d^2z}{dt^2} = -GM_{\rm e}dfrac{z}{\sqrt{x^2+z^2}^3}\]
To obtain the trajectory of the projectile, one needs to specify the so-called “initial conditions,'' i.e., the \(x_0\) and \(z_0\) coordinates of the launching point, and the velocity components \
(v_{x0}\) and \(v_{z0}\) at the moment of launching. And then, find the time-dependent
coordinates \(x(t)\) and \(z(t)\), which together constitute a set of parametric equations of the trajectory.
The bad news is that solving these equations using the classical “paper+pencil'' method requires applying sophisticated high-level mathematical techniques. Presenting a step-by-step solution
procedure in this chapter would make no sense. However, the good news is that a highly accurate solution can be obtained by using a relatively simple numerical algorithm which takes even a simple
today's portable computer only a split second to process. This algorithm and a program in the PYTHON language are described in a greater detail in APPENDIX XX. Here, we will only show a few
calculated trajectories in a graphic form in a figure.
The calculations are done for realistic data, i.e., the Earth radius is taken as 6371 km, the Earth's mass as \(5.9722\times 10^{24}\) kg, and \(G = 6.6741\times 10^{-11}\) m\)^3\)kg\)^{-1}\)s\)^{-2}
\). If we wanted to make a plot displaying everything in real proportions, the launching point could not be too low, because the plotted trajectory would “blend'' with the circle representing the
planet's contour. Therefore, the projectile is launched from the altitude of 1000 km -you can either thing of a super-giant tower built at the North Pole, or a spacecraft “hovering'' over the North
Pole at the altitude of 1000 km, and acting as a platform for a horizontal launch. The value of \(g\) at this altitude is markedly lower than at the Earth surface -from the Eq. 2.16, for \(H=1000\)
km one gets \(g(H) = 7.3362\) m/s\)^2\).
So, the initial coordinates of the launching point are: \(x_0 =0\) and \(z_0 = 6371\) km + 1000 km = 7371 000 m. The projectile will always be launched in the horizontal direction, so that always \
(v_{z0}\) -and we will make calculations for several different values of \(v_{x0}\).
In the Fig. 2.1 one can see a trajectory for the initial projectile velocity \(v_{x0} = 6000\) m/s, plotted with black color.^1 The projectile lands at a spot which is about 1/8 of the Earth's
circumference from the base of the “launching tower''. For \(v_{x0} = 6850\) m/s (blue curve) the landing spot is close to the Equator. Now, the range becomes quite sensitive for the initial speed
value: for \(v_{x0} = 7081\) m/s the projectile lands close to the South Pole. And the most interesting trajectory is definitely that for \(v_{x0} = 7353.6\) m/s (red color): the trajectory is a
perfect circle, it never hits the ground -the projectile returns precisely to the spot at the top of the launching tower from which it was launched!
In the next section it is explained what is the significance of the “7353.6 m/s" speed. The trajectories for higher launching velocities have one in common -they all return to the launching spot, but
their shapes get elongated in the “downwards'' direction in the figure (one example plotted with a dashed line is a trajectory for \(v_{x0} = 8000\) m/s). They are no longer circles, but ellipses.
Figure \(\PageIndex{1}\): The shaded circle symbolizes the Eart, and the sphere bar at its top is a 1000 kilometer high tower erected at the North Pole. The black, blue and green curves are
trajectories of projectiles launched horizontally from the tower top with velocities, respectively, 6000, 6850, and 7081 meters per second. They all fall to the ground. But the projectile launched
with a velocity of 7353 m/s (red curve) becomes an artificial satellite of Earth -it travels along a trajectory which is a perfect circle and returns to the tower top. A projectile launched with a
velocity of 8000 m/s travels along an elliptical trajectory (dashed curve).
However, for \(v_{x0} = \sqrt{2}\times 7353.6\) m/s = 10399.6 m/s and higher launching velocities there is yet another change of behavior - the trajectories are no longer closed, but open curves
-meaning that the projectiles never return to the launching site, but they “leave Earth for good''.
In summary, there are four different types of behavior of the projectile. For zero launching speed, which is obvious, it's just a vertical fall. Then, for \(v_{x0} > 0\) the trajectories are first
“ballistic curves'' ending at the Earth surface. Next, the paths become closed orbits, and the projectiles are now Earth's satellites -and finally, for \(v_{x0}\) larger than the so-called “escape
velocity'', the projectile becomes an “artificial asteroid'' and leaves Earth forever.
And it should be stressed that all these four types of behavior have on thing in common - namely, in all cases the \textbf{only} force acting on the projectile is the force of gravity.
Everybody agrees that an appropriate term for a purely vertical drop is “a free fall''. Yet, many students react at the first moment th surprise if the same name is used for a ballistic flight,
satellite motion, or a spacecraft flight. But physicists insist that as long as there is no engine in the moving object, and it is only the gravity which governs its motion, one should rather invoke
the famous “Occam Razor'' and use the same term in each case. One more argument in favor of such thinking is that all types of trajectories are obtained as solutions of the very same set of equations
of motion that are the mathematical form of the Second Newton's Law of Dynamics.
1. 6000 m/s is about 17 times the speed of sound, or about 6 times the speed of a bullet from a powerful military rifle. | {"url":"https://eng.libretexts.org/Sandboxes/jhalpern/Energy_Alternatives/02%3A_General_Remarks/2.02%3A_Forms_of_Energy-_Physicists_View_./2.2.04%3A_Free_Fall_Satellite_Motion_and_the_Mechanism_of_Tides/2.2.4.03%3A_Projectile_Motion-_Very_Long_Range","timestamp":"2024-11-14T01:38:51Z","content_type":"text/html","content_length":"132545","record_id":"<urn:uuid:0bb3394a-bc48-419b-a4ad-cb5b8f952492>","cc-path":"CC-MAIN-2024-46/segments/1730477028516.72/warc/CC-MAIN-20241113235151-20241114025151-00062.warc.gz"} |
ind the number of ways a batsman can score a double century only in terms of 4
Don't learn Mathematics just to prove that you are not a mentaly simple person but learn it to prove that you are intelligent
a man that is poor is very rich because he know the value of zero.
Thanks m4 maths for helping to get placed in several companies. I must recommend this website for placement preparations. | {"url":"https://m4maths.com/22962-find-the-number-of-ways-a-batsman-can-score-a-double-century-only-in-terms-of-4-s-6-s.html","timestamp":"2024-11-12T15:21:43Z","content_type":"text/html","content_length":"80409","record_id":"<urn:uuid:561464ed-8eb4-4a36-919b-680fb14d9052>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.63/warc/CC-MAIN-20241112145015-20241112175015-00076.warc.gz"} |
second moment
What is the second moment in statistics?
The Second Moment
– The second central moment is “Variance”. – It measures the spread of values in the distribution OR how far from the normal. – Variance represents how a set of data points are spread out around
their mean value.
What is the second moment of a function?
In mathematics, the moments of a function are quantitative measures related to the shape of the function’s graph. If the function represents mass density, then the zeroth moment is the total mass,
the first moment (normalized by total mass) is the centre of mass, and the second moment is the moment of inertia.
How do you calculate second moment of data?
In this calculation we perform the following steps:
1. First, calculate the mean of the values.
2. Next, subtract this mean from each value.
3. Then raise each of these differences to the sth power.
4. Now add the numbers from step #3 together.
5. Finally, divide this sum by the number of values we started with.
How do you find the second moment of distribution?
Equate the first sample moment about the origin M 1 = 1 n ∑ i = 1 n X i = X ¯ to the first theoretical moment . Equate the second sample moment about the mean M 2 ∗ = 1 n ∑ i = 1 n ( X i − X ¯ ) 2 to
the second theoretical moment about the mean E [ ( X − μ ) 2 ] .
What is first moment and second moment?
The first moment of area represents the distribution area over a rotational axis. It is used for finding centroid, its unit is a cubic meter. The second moment of area represents the dispersion of
points around an arbitrary axis. The first moment of area is based on the metric space mathematical construct moments.
What do moments in statistics tell us?
Moments in statistics are popularly used to describe the characteristic of a distribution. Measure the location of the central point. Second moment- Standard Deviation (SD, σ(Sigma)): Measure the
spread of values in the distribution OR how far from the normal.
Is second moment equal to variance?
The second moment about the mean is the variance. We can define third, fourth, and higher moments about the mean. Some of these higher moments have useful applications.
What is moment generating function in statistics?
The moment-generating function is the expectation of a function of the random variable, it can be written as: For a discrete probability mass function, For a continuous probability density function,
In the general case: , using the Riemann–Stieltjes integral, and where is the cumulative distribution function.
Is the 2nd moment the variance?
1) The mean, which indicates the central tendency of a distribution. 2) The second moment is the variance, which indicates the width or deviation.
Why moments are important in statistics?
Moments help in finding AM, standard deviation and variance of the population directly, and they help in knowing the graphic shapes of the population. We can call moments as the constants used in
finding the graphic shape, as the graphic shape of the population also help a lot in characterizing a population.
Is the second moment the variance?
What is the use of moments in the study of a frequency distribution?
Moments are popularly used to describe the characteristic of a distribution. They represent a convenient and unifying method for summarizing many of the most commonly used statistical measures such
as measures of tendency, variation, skewness and kurtosis.
What is first and second moment?
Is standard deviation is second central moment?
is therefore equal to the second central moment (i.e., moment about the mean), The sample standard deviation distribution is a slightly complicated, though well-studied and well-understood, function.
How do you use MGF to find expectation?
For the expected value, what we’re looking for specifically is the expected value of the random variable X. In order to find it, we start by taking the first derivative of the MGF. Once we’ve found
the first derivative, we find the expected value of X by setting t equal to 0. Now, we move onto finding the variance.
Is variance The second moment?
How do you explain a moment in statistics?
Moments [of a statistical distribution]
1. The mean, which indicates the central tendency of a distribution.
2. The second moment is the variance, which indicates the width or deviation.
3. The third moment is the skewness, which indicates any asymmetric ‘leaning’ to either left or right.
What is the use of moments in real life?
Moments come into play when forces act on an object that has a fixed point. For example, turning a door handle, sitting on a seesaw or closing a pair of scissors. When forces are applied to these
objects they rotate around their fixed point, also known as the pivot or fulcrum.
What is statistical moment theory?
Statistical moments are parameters that describe the characteristics of the time courses of plasma concentration (area, mean residence time, and variance of residence time) and of the urinary
excretion rate that follow administration of a single dose of a drug.
What are the properties of MGF?
MGF Properties
If two random variables have the same MGF, then they must have the same distribution. That is, if X and Y are random variables that both have MGF M(t) , then X and Y are distributed the same way
(same CDF, etc.). You could say that the MGF determines the distribution.
What is a moment generating function Why is it so called?
What do moments tell you?
The moment of a force depends on the magnitude of the force and the distance from the axis of rotation. The moment of a force about a point is (the magnitude of the force) × (the perpendicular
distance of the line of action of the force from the point).
What is the significance of method of moments in statistics?
The method of moments is a technique for estimating the parameters of a statistical model. It works by finding values of the parameters that result in a match between the sample moments and the
population moments (as implied by the model).
Why we use method of moments?
Due to easy computability, method-of-moments estimates may be used as the first approximation to the solutions of the likelihood equations, and successive improved approximations may then be found by
the Newton–Raphson method. In this way the method of moments can assist in finding maximum likelihood estimates.
What is the importance of moment generating function?
The moment generating function has great practical relevance because: it can be used to easily derive moments; its derivatives at zero are equal to the moments of the random variable; a probability
distribution is uniquely determined by its mgf. | {"url":"https://www.trentonsocial.com/what-is-the-second-moment-in-statistics/","timestamp":"2024-11-02T18:40:33Z","content_type":"text/html","content_length":"64765","record_id":"<urn:uuid:e368226d-8a36-47af-b35c-b31ad3c13b3f>","cc-path":"CC-MAIN-2024-46/segments/1730477027729.26/warc/CC-MAIN-20241102165015-20241102195015-00164.warc.gz"} |
6375 Speed Of A Common Snail to
How many Kilometers Per Second in 6375 Speed Of A Common Snail? How to convert 6375 Speed Of A Common Snail to Kilometers Per Second(km/s) ? What is 6375 Speed Of A Common Snail in Kilometers Per
Second? Convert 6375 Speed Of A Common Snail to km/s. 6375 Speed Of A Common Snail to Kilometers Per Second(km/s) conversion. 6375 Speed Of A Common Snail equals 0.006375 Kilometers Per Second, or
6375 Speed Of A Common Snail = 0.006375 km/s.
The URL of this page is: https://www.unithelper.com/speed/6375-snail-km_s/ | {"url":"https://www.unithelper.com/speed/6375-snail-km_s/","timestamp":"2024-11-02T23:54:21Z","content_type":"text/html","content_length":"8838","record_id":"<urn:uuid:78492a19-8abb-4774-805a-f448d7ee5a97>","cc-path":"CC-MAIN-2024-46/segments/1730477027768.43/warc/CC-MAIN-20241102231001-20241103021001-00114.warc.gz"} |
[8] The convergence of the iterative migration/inversion
Next: The possibility of relative Up: [3] The meaning and Previous: [7] The regularization of
Again, the iterative formula for migration/inversion imaging is The choice of background parameters and the method for linearizing the propagators determine whether the cost function is (or
approaches) a quadratic function. Therefore, the Born approximation should be replaced by De Wolf approximation or other more accurate approximations. On the other hand, to produce the image at the
first iterative step with the so-called true-amplitude imaging approaches will accelerate the convergence of the iterative migration/inversion.
Next: The possibility of relative Up: [3] The meaning and Previous: [7] The regularization of Stanford Exploration Project | {"url":"https://sepwww.stanford.edu/data/media/public/docs/sep123/huazhong1/paper_html/node25.html","timestamp":"2024-11-10T17:46:33Z","content_type":"text/html","content_length":"4543","record_id":"<urn:uuid:0c2e0dbf-11dc-47d5-9780-779ada54e385>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00353.warc.gz"} |
┃ │ Sir Erik Christopher Zeeman ┃
┃ │ ┃
┃ (source) │ (4 Feb 1925 - 13 Feb 2016) ┃
┃ │ ┃
┃ │ ┃
┃ │ ┃
Science Quotes by Sir Erik Christopher Zeeman (5 quotes)
Another of my hobby-horses is the advantage of ignorance, in that it encourages creativity, both in the young and the old.
— Sir Erik Christopher Zeeman
Catastrophe Theory is a new mathematical method for describing the evolution of forms in nature. … It is particularly applicable where gradually changing forces produce sudden effects. We often call
such effects catastrophes, because our intuition about the underlying continuity of the forces makes the very discontinuity of the effects so unexpected, and this has given rise to the name.
— Sir Erik Christopher Zeeman
Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems—general and specific
statements—can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences.
— Sir Erik Christopher Zeeman
Technical skill is mastery of complexity while creativity is mastery of simplicity.
— Sir Erik Christopher Zeeman
The scientist has to take 95 per cent of his subject on trust. He has to because he can't possibly do all the experiments, therefore he has to take on trust the experiments all his colleagues and
predecessors have done. Whereas a mathematician doesn't have to take anything on trust. Any theorem that's proved, he doesn't believe it, really, until he goes through the proof himself, and
therefore he knows his whole subject from scratch. He's absolutely 100 per cent certain of it. And that gives him an extraordinary conviction of certainty, and an arrogance that scientists don't
— Sir Erik Christopher Zeeman
Quotes by others about Sir Erik Christopher Zeeman (1)
An announcement of [Christopher] Zeeman’s lecture at Northwestern University in the spring of 1977 contains a quote describing catastrophe theory as the most important development in mathematics
since the invention of calculus 300 years ago. | {"url":"https://todayinsci.com/Z/Zeeman_Christopher/ZeemanChristopher-Quotations.htm","timestamp":"2024-11-07T07:26:40Z","content_type":"text/html","content_length":"80350","record_id":"<urn:uuid:cf50e574-8ab9-4cde-a5fd-0372759976f8>","cc-path":"CC-MAIN-2024-46/segments/1730477027957.23/warc/CC-MAIN-20241107052447-20241107082447-00377.warc.gz"} |
Heat losses caused by drain
Heat losses caused by drain pipes in the PHPP
Author: Dr. Jürgen Schnieders
Passive House Institute, Rheinstr. 44/46, 64283 Darmstadt, Germany
This article outlines a calculation method for the heat losses caused by waste water or stormwater pipes that are vented through the roof. The upper end of this type of drain pipes is open to the
ambient air, the lower end is connected to the sewer. During the heating period, the air in the pipe is warmer than the ambient air, resulting in a pressure difference (stack effect) that drives air
from the sewer up the drain. Since the air from the sewer is colder than the indoor air, there are heat losses from the room to the drain pipe.
PHPP 9 already contains a calculation method for these heat losses. Particularly for high-rise buildings, this method is overly conservative because it assumes a constant air temperature in the drain
over its whole length. Accounting for the temperature increase in the drain is the main goal of the following considerations.
The calculation method is deliberately kept simple. In order to limit the complexity of data input, certain inaccuracies that will not affect the overall functionality of the building can be
accepted. To compensate for the simplifications, conservative estimates of unknown quantities are preferred.
Heat transfer to pipe
The drain pipe has a specific heat transfer coefficient per unit length that is denoted by Ψ and is given in W/(mK). The temperature of the incoming air at the bottom of the pipe is denoted by T
[sewer]. ṁc[p] is the capacitance rate of the airflow, T[i] is the interior temperature of the building, and l is the total length of the drain pipe inside the thermal envelope.
Then, if T[drain], the (average) temperature of the air inside the drain pipe, is known, the heat flow into the pipe is given by
$$ \Large{Q = \varPsi\cdot l \cdot (T_{i} - T_{drain})} $$
There are two simply derived upper limits to the heat loss from the building to the pipe:
• The air inside the pipe may be assumed to have the sewer temperature over its whole length:
$$ \Large{Q \leq \varPsi\cdot l \cdot (T_{i} - T_{sewer})} $$
• The incoming air may be assumed to be heated to room temperature before it leaves the building:
$$ \Large{Q \leq \dot m c_{l} \cdot (T_{i} - T_{sewer})} $$
A more precise calculation takes the temperature increase over the length of the drain pipe into account. The temperature profile can be calculated from a simple differential equation, resulting in
an exponential temperature increase.
$$ \Large{T(z) = T_{i} - (T_{sewer} -T_{i}) \cdot e^ { \dfrac{-\varPsi}{\dot m c_{p}} \cdot Z}} $$
Where Z is the length in the direction of the pipe, starting at the sewer.
Averaging the temperature profile over the length l leads to the average drain temperature
$$ \Large{\overline{T} = T_{i} - (T_{sewer} -T_{i}) \cdot \dfrac{\dot m c_{p}}{\varPsi l} \cdot (e^ { \dfrac{-\varPsi}{\dot m c_{p}} \cdot l} - 1)} $$
This temperature can be used to calculate the heat flow into the pipe. It always results in a smaller heat flow than the upper limits given above.
Calculation of input data
The formula above requires a few unknown input data. Assumptions for these data are discussed in this section. The validity of these assumptions was checked by an evaluation of temperature and heat
flow measurements on two drain pipes (for stormwater and waste water) in an administrative building [1] and by measurements from a single¬-family home described in [2].
Sewer temperature
The sewer temperature depends mainly on the temperature of the water running in the sewer, whereas heat transfer to the ground and to the ambient air are of minor importance.
Many different configurations are possible, with sewers being located at different depths in the ground, carrying different water volumes, and being used either for pure waste water, pure stormwater,
or a mixture. Sewers that carry only waste water are relatively warm, sewers that carry only stormwater are usually colder.
For most cases, it is a slightly conservative approximation to assume that the incoming air in the drain pipe has the annual average temperature of undisturbed ground.
Air velocity in the pipe
In principle, one could try to calculate the air velocity in the pipe for each individual case, but such a procedure would be overly complicated for the user of the PHPP.
The evaluations described in [1] and [2] resulted in air velocities of approximately 0.5 m/s. The velocity is nearly independent of the building height (additional height adds to both the driving
pressure difference and to the pressure loss), but it may be higher than measured for high-rise buildings with long, straight, vertical pipe runs where horizontal sections, bends, and elbows play a
smaller part. Assuming a fixed velocity of 1 m/s is a solution that is again realistic as well as slightly conservative.
Ψ-value of pipe
The Ψ-value of the pipe can be calculated using the formulae for air ducts in the PHPP. To calculate the interior film coefficient these formulae require the air velocity in the pipe, which was
already estimated above.
Related aspects
Influence of wind
It might be expected that wind is creating a pressure reduction above the upper end of the drain pipe, resulting in increased airflow. However, the measurements revealed that wind does not have a
relevant influence on the air velocity in the pipe.
Cold air entering the pipe from above
Measurements in [2] assured that the airflow in the pipe is upward during the heating period. On rare occasions cold air may enter the pipe from above, so that insulation against condensation is
recommended nevertheless.
For pipes that are closed at the bottom, e.g. chimneys without connection to the room air, a heat tranfer coefficient of 50 W/K per square meter of horizontal opening was estimated in earlier
Water that is running down the pipe can pull air with 30 to 40 times its volume with it. This air causes an additional heat loss, albeit it may not fully be heated to the indoor temperature before it
leaves the thermal envelope. The mechanism exists if the pipe is vented through the roof as well as in cases where an air admittance valve is used. For a family of 5, with a generous 100 l per person
per day, the resulting airflow rate is approximately 1 m³/h, equivalent to a conductance of 0.33 W/K. This is a negligible quantity.
Drain pipes running under suspended floors, in underground car parks, etc.
Drain pipes do not always enter the ground on leaving the thermal envelope. If there is no risk of frost, the pipes may run under a suspended floor or in an unheated basement for a while. This
reduces the temperature of the incoming air at the bottom of the thermal envelope. In principle, this temperature could be calculated with the methodolgy described above. Considering the amount of
additional input data required, including the temperature of the basement, the relatively small possible gain in accuracy did not appear to justify the additional user effort required.
Influence of stormwater
There are temperature drops in stormwater drainpipes whenever cold water is running through the pipes. For the measurements in [1] this effect was already accounted for by using a sewer temperature
of 11 °C, still slightly above the annual average ground temperature in the region of 10 °C. It may be concluded that the additional heat losses due to stormwater are covered by the assumption that
the sewer temperature is equal to the annual average ground temperature.
Multiple pipes that vent through a common opening
Multiple drain pipes are usually connected before they leave the building (or the basement) towards the sewer. It also happens regularly that several vent pipes are connected at the top and are
vented through one common opening. Depending on the details of the installation, such reductions of the cross-section reduce the airflow rate to a different extent.
From an analysis of some examples, the following guideline was derived: if multiple pipes are connected or have varying diameters, the airflow rate can be calculated based on a reduced cross-section,
provided that this cross-section is not exceeded for at least 30% of the pipe length.
It should be noted that this reduction only applies to the airflow rate, i.e. ṁc[p]. The specific heat losses from the building to the pipe, Ψl, still need to account for the whole pipe length, also
of parallel pipes.
Where to insulate
For pipes that are only open at the top, it is common practice to insulate only the upper 3 to 5 m of length against condensation. This is also acceptable with regard to energy efficiency.
Pipes that are open at both ends should be insulated against condensation over the entire length. The more insulation is used, the lower will be the temperatures in the higher parts of the pipes. As
a general rule, it seems appropriate to insulate the whole length of the pipes evenly. Exceptions may be possible in high-rise buildings for central parts of pipes that do not carry stormwater, but
no quantitative assessment is possible as of yet.
Hot climates
If the ambient temperatures are higher than the indoor temperatures, the direction of the airflow is reversed. Hot air will fall into the drain vent and proceed down to the sewer. This air initially
has the ambient air temperature, not the sewer temperature. In principle, the reduction factor that is used for the calculation of Ψ must be 1 in this case, contrary to
$$ \Large{T(z) = \dfrac{T_{i} - T_{drain}}{T_{i} - T_{ambient}}} $$
for the heating case. However, such a distinction would require to provide different Ψ values for each month, or at least for winter and summer. This appears inappropriate with regard to the relative
importance of the effect.
Also, cooling is required not only at ambient temperatures above the setpoint, but also below. This typically results in an average ambient temperature over the cooling period that is very close to
the room temperature. A few experiments for hot climates (Jakarta, Dubai) resulted in average temperatures over the cooling period of less than 29 °C, so that the relevant temperature difference is
Thus, the error occuring for the cooling period due to the overly small reduction factor is acceptable.
The calculation method developed above allows for an appropriate assessment of heat losses to vented drain pipes also for high-rise buildings. With a few evidence-based assumptions, the method is
sufficiently simple to use for practical design applications.
sinfonia/heat_losses_caused_by_drain_pipes_in_the_phpp.txt · Last modified: 2022/02/15 19:32 by admin | {"url":"https://passipedia.org/sinfonia/heat_losses_caused_by_drain_pipes_in_the_phpp?s%5B%5D=pipes","timestamp":"2024-11-12T23:40:59Z","content_type":"text/html","content_length":"41759","record_id":"<urn:uuid:089f2dc4-b314-48ec-90c5-44082a18a6da>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00546.warc.gz"} |
Bounding the bias of tree-like sampling in ip topologies
It is widely believed that the Internet's AS-graph degree distribution obeys a power-law form. However, it was recently argued that since Internet data is collected in a tree-like fashion, it only
produces a sample of the degree distribution, and this sample may be biased. This argument was backed by simulation data and mathematical analysis, which demonstrated that under certain conditions a
tree sampling procedure can produce an artificial power-law in the degree distribution. Thus, although the observed degree distribution of the AS-graph follows a power-law, this phenomenon may be an
artifact of the sampling process. In this work we provide some evidence to the contrary. We show, by analysis and simulation, that when the underlying graph degree distribution obeys a power-law with
an exponent γ > 2, a tree-like sampling process produces a negligible bias in the sampled degree distribution. Furthermore, recent data collected from the DIMES project, which is not based on single
source sampling, indicates that the Internet indeed obeys a power-law degree distribution with an exponent γ > 2. Combining this empirical data with our simulation of traceroute experiments on
DIMES-measured AS-graph as the underlying graph, and with our analysis, we conclude that the bias in the degree distribution calculated from BGP data is negligible.
• Internet topology models
• Network computing
Dive into the research topics of 'Bounding the bias of tree-like sampling in ip topologies'. Together they form a unique fingerprint. | {"url":"https://cris.ariel.ac.il/en/publications/bounding-the-bias-of-tree-like-sampling-in-ip-topologies-3","timestamp":"2024-11-02T15:24:52Z","content_type":"text/html","content_length":"55117","record_id":"<urn:uuid:330ffb0c-4d66-49a8-af26-cd93eae1329e>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00347.warc.gz"} |
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JAVA - Module 04 - Iterative Programming - Complex Loops
You will learn some wonderful complex programs using loops and nested loops
Your Instructor
My name is Saravanan G and I along with my friends Mohan and Nahush passed out of engineering college about 10 years ago.
We started as software engineers in MNC companies and at the same time started teaching computers to students during our free time. We felt that in a world where the future is a lot about Automation,
when the next generation and machines/computers will work together, our system of teaching may not be really helping our children learn, get attracted to and love computers and programming, the way
it should.
Slowly, through experience we found that our doubts are real and also that the students we were teaching with our raw passion, were indeed getting transformed. We started getting busy. Soon, we were
not able to balance the job and our passion and in Jan of 2014, we quit our jobs, invested our savings and started TechSparx to now full time get into our passion, which we have now made it our
We have now created a module and deliver it with the same passion such that 100+ programs we can impart knowledge around programming, such that our students may walk in with a fear or dislike of this
topic but will walkaway having dispelled their fears and most important start loving this subject. Once this class is over, there will be no looking back. We will teach the foundations and then
slowly but surely build interest and knowledge.
We also feel happy that we thus also play a part in nation building as we help create a confident and knowledgeable next generation who will be at ease in the new world where computers and
programming will be required to survive and thrive.
The 2 quotes which inspire us are :
1. "A good teacher can inspire hope, ignite the imagination and instil a love of learning" - Brad Henry
2. "Tell me and I forget. teach me and I remember. Involve me and I learn." - Benjamin Franklin.
Frequently Asked Questions
When does the course start and finish?
The course starts now and never ends! It is a completely self-paced online course - you decide when you start and when you finish.
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How does lifetime access sound? After enrolling, you have unlimited access to this course for as long as you like - across any and all devices you own.
What if I am unhappy with the course?
We would never want you to be unhappy! If you are unsatisfied with your purchase, contact us in the first 30 days and we will give you a full refund. | {"url":"https://techsparx-digital.teachable.com/p/java-module-04-complex-loops","timestamp":"2024-11-09T01:34:19Z","content_type":"text/html","content_length":"134809","record_id":"<urn:uuid:69da1ca4-5c8d-4485-8c0f-c6013cbe0c85>","cc-path":"CC-MAIN-2024-46/segments/1730477028106.80/warc/CC-MAIN-20241108231327-20241109021327-00878.warc.gz"} |
Conservation of Momentum Calculator
Conservation of Momentum Calculator
Conservation of Momentum Calculator
What is a Conservation of Momentum Calculator?
The Conservation of Momentum Calculator is a tool designed to help users determine the movement and interaction between two objects in motion. Specifically, it calculates the momentum before and
after a collision, adhering to the principle of conservation of momentum. This principle states that the total momentum of a closed system remains constant if no external forces act on it.
Applications of This Calculator
This calculator is highly useful in various fields, such as physics, engineering, and automotive safety analysis. Scientists can analyze collisions between particles, while engineers can study
mechanical impacts to design safer vehicles. Sports analysts can use it to study the dynamics of collisions in contact sports, helping improve safety gear and protocols.
How This Calculator is Beneficial
By using this calculator, users can gain critical insights into the dynamics of collisions without the need for complex computations. It aids in understanding how initial conditions translate to
final outcomes, making it an invaluable tool for both educational purposes and practical applications. Students can visualize concepts better, while professionals can make informed decisions based on
accurate data.
Understanding the Calculation Process
The calculator requires the input of initial masses and velocities for two objects, as well as their final velocities after the interaction. The momentum for each object is calculated as the mass
multiplied by the velocity. The principle of conservation of momentum dictates that the total initial momentum (sum of the momenta of both objects before the collision) must be equal to the total
final momentum (sum of the momenta of both objects after the collision).
For example, suppose object 1 has an initial mass of 5 kg and initial velocity of 2 m/s, and object 2 has an initial mass of 3 kg and initial velocity of 1 m/s. After the collision, assume object 1’s
final velocity is 1 m/s and object 2’s final velocity is 2 m/s. The calculator will confirm that the total momentum before and after the collision matches, ensuring the principle is upheld.
Real-Use Cases
Real-life applications of this calculator are extensive. In traffic accident analyses, it helps in reconstructing events to understand the impacts and improve road safety standards. In sports, it is
used to enhance protective gear by studying the collisions athletes experience. The calculator also finds use in astrophysics, where scientists study the interactions between celestial bodies, such
as the gravitational effects leading to collisions.
Key Insights
Using this calculator simplifies the process of understanding complex motion interactions. Users don’t need advanced comprehension of physics equations to employ the principle of conservation of
momentum. This makes high-level analysis accessible, ensuring accurate results with minimal effort.
1. What is the principle of conservation of momentum?
The principle of conservation of momentum states that in a closed system with no external forces, the total momentum remains constant before and after an interaction, such as a collision.
2. How do I use the Conservation of Momentum Calculator?
The calculator requires you to enter the initial masses and velocities of two objects, as well as their final velocities after a collision. It then calculates whether the total momentum before and
after the collision is equal, adhering to the principle of conservation of momentum.
3. What is momentum in physics?
Momentum is the product of an object’s mass and its velocity. It is a vector quantity, which means it has both magnitude and direction.
4. Why is it important to understand momentum in collisions?
Understanding momentum in collisions helps in analyzing and predicting the outcomes of interactions between objects. This knowledge is crucial for applications in fields like automotive safety,
engineering, and physics research.
5. Can this calculator be used for inelastic collisions?
Yes, the calculator can be used for both elastic and inelastic collisions. For inelastic collisions, you only need to input the final velocities to verify the conservation of momentum, even though
kinetic energy is not conserved in this case.
6. How does this tool help in automotive safety analysis?
In automotive safety, this calculator can help reconstruct accident scenarios by analyzing the momentum of vehicles before and after collisions. This analysis can lead to better designs and improved
safety features in vehicles.
7. Is this calculator useful for educational purposes?
Yes, the calculator is an excellent educational tool. It helps students understand the principle of conservation of momentum by allowing them to input different values and observe how changes affect
the system’s momentum.
8. What do I do if the calculated total momentum before and after the collision don’t match?
Should the total momentum before and after the collision not match, re-check the input values for any errors. Ensure you are using consistent units for mass and velocity. If external forces are
acting on the system, the principle of conservation of momentum may not hold.
9. Can I use this calculator for analyzing real-time sports collisions?
Yes, the calculator can help analyze real-time sports collisions by calculating the momentum of athletes or equipment before and after impacts, aiding in the design of better protective gear and
understanding the dynamics of physical interactions.
10. What units should I use for mass and velocity?
Generally, mass is measured in kilograms (kg) and velocity in meters per second (m/s). It is important to use consistent units throughout the calculation to ensure accurate results. | {"url":"https://www.onlycalculators.com/physics/kinematics/conservation-of-momentum-calculator/","timestamp":"2024-11-08T04:48:54Z","content_type":"text/html","content_length":"251046","record_id":"<urn:uuid:572f2b30-4806-484c-83ec-16edf0a5025f>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00377.warc.gz"} |
Transition criterion for the multigrid expectation maximization reconstruction algorithm for PET
The multi-grid expectation maximization algorithm (MGEM), an extension of the maximum likelihood (ML) algorithm, has been applied to the problem of reconstruction in positron emission tomography
(PET). The MGEM algorithm implemented the Expectation Maximization (EM) algorithm on different size image grids. The algorithm is based on the idea that the low frequency image components can be
recovered faster than the high frequency components. The algorithm begins with a coarse grid, where the low frequency components are recovered. After the low frequency components have been recovered,
the solution is projected onto the next finer grid. On the next finer grid, the high frequency components from the previous grid become the low frequency components. The algorithm continues iterating
and switching levels until the finest grid has been reached. This method provides faster convergence than the single grid EM algorithm. An important issue concerning the MGEM algorithm is when to
stop iterating at a particular grid and project to the next grid, or stop at the finest grid. The convergence rate of the MGEM algorithm was used as a grid level transition criterion. A grid level
transition criterion which used the co-occurrence matrix statistics of the reconstructed image is presented. The spatial distribution and dependence among gray levels in a local area of the
reconstructed image can be studied by gray level dependent cooccurrence statistics. The second order histogram represents the probability of occurrence of a pair of gray levels separated by a given
displacement vector. The features computed from the second-order histogram were entropy, contrast, angular second moment, inverse difference moment, correlation, mean, and deviation. The difference
histogram is derived from the second order histogram and represents the probability of occurrence of a difference in gray levels of two pixels separated by a displacement vector. The features
extracted from the difference histogram were entropy, contrast, and angular second moment. The behavior of each of the statistics was compared to the the root mean squared (RMS) error, to evaluate
the potential for use as a transition criterion. An appropriate window was used to average the variance of each statistic. The indication of switching to the next finer grid level, or of stopping at
the finest grid level was provided by a decline in the variance of a statistic. These statistics were computed on an image reconstructed from simulated PET data. Each of the statistics was evaluated
versus the number of iterations at each grid level. The transitions for each level occurred when the variance of one of the statistics decreased sharply. For comparison, the single grid EM algorithm
was allowed to run for the same amount of CPU time as the MGEM algorithm. The RMS error indicates that the MGEM method, using the cooccurrence statistics as a transition criterion, produced a better
reconstruction than the single grid EM algorithm.
All Science Journal Classification (ASJC) codes
• Electronic, Optical and Magnetic Materials
• Condensed Matter Physics
• Computer Science Applications
• Applied Mathematics
• Electrical and Electronic Engineering
• Emission tomography
• Expectation maximization
• Multigrid
Dive into the research topics of 'Transition criterion for the multigrid expectation maximization reconstruction algorithm for PET'. Together they form a unique fingerprint. | {"url":"https://researchwith.njit.edu/en/publications/transition-criterion-for-the-multigrid-expectation-maximization-r-2","timestamp":"2024-11-14T06:46:34Z","content_type":"text/html","content_length":"59399","record_id":"<urn:uuid:78920148-d034-404f-b2db-60d15ba5bf92>","cc-path":"CC-MAIN-2024-46/segments/1730477028545.2/warc/CC-MAIN-20241114062951-20241114092951-00372.warc.gz"} |
Multiplicative Identity Property (Number Multiplied by 1) | Learn and Solve Questions
Overview of Multiplication
Have you ever heard about the answer obtained when any number is multiplied by 1? When any number is multiplied by 1 the product is always the number itself. In the below-discussed article, children
would gain knowledge about the steps involved in solving multiplication problems, which is considered one of the basic and most widely used mathematical and arithmetical operations. Generally, it is
represented using the symbol '×' or '*' in between the two numbers. Now, let us start with our topic here:
What is Multiplication?
Multiplication is a process of calculating the product of two quantities or numbers by multiplying them together. '×' is used to depict the product of two quantities. The number multiplied by the
multiplier is called the multiplicand and the number by which the multiplicand is multiplied is called the multiplier. It can also be stated as a way of adding a number repeatedly to acquire their
Showing Terms Used in the Multiplication of Two Numbers
Steps Involved in Solving Multiplication Queries
The steps required to follow in the multiplication of two numbers are given below:
• Write the given multiplicand and multiplier in the column form by taking into consideration their place values
• Then put the multiplication sign (×) preceding the multiplier
• Start the multiplication from the right-hand side of the multiplier and move to the left side.
• Count the number of digits in multiplier quantity and place the zeroes 1 less than the number of digits in the multiplier from the right side
• Finally, add up all the products respective to each digit of the multiplier.
Multiplication of 8 and 5
Multiplicative Identity Property
Multiplicative identity property states that "Any number multiplied by 1 is the number itself". It means that when any number is multiplied by 1 the answer is always the number. It serves as a user
identity in solving various problems. 1 is the identity of itself i.e. 1 × 1 = 1. It is also called the Identity Property of Multiplication because of the reason, here the identity of a number
remains unaltered.
Showing Identity Property of Multiplication
Solved Examples
Q 1. 12 × 1
Ans: Steps to be followed to calculate the product using Multiplicative Identity
• Align the given numbers in columns or rows to calculate the product
• Multiplying 1 with the given number and noting the result
Thus, we can conclude that when any number is multiplied by 1 the answer is the number itself.
Showing Any Number Multiplied by 1
Q 2. 65 × 31
Ans: Steps to calculate the result of this statement are given below:
• Write the given multiplier and multiplicand in columns format
• Now, using multiplicative identity, any number multiplied by 1 is the number, for multiplying 65 and 1
• Calculate the number of digits of the multiplier and put zeroes one less than the calculated number of digits
• Further, multiplying the tens digit of the multiplier with the multiplicand
• Adding the two obtained partial products i.e. 65 + 1950 = 2015
Hence, the required result of the multiplication of 65 × 31 is 2015.
Showing the Multiplication of Two Digit Number Whose One Digit is 1
Practice Problems
Some practice problems based on the concept, any number multiplied by 1 is the number itself are given below. These should be solved by the children on their own for a better understanding of the
Q 1. 59 × 1
Ans: 59
Q 2. 84 × 1
Ans: 84
Q 3. 1 × 18
Ans: 18
Q 4. 34 × 1
Ans: 34
Q 5. 1 × 32
Ans: 32
To wrap up here with the topic of number multiplication. The main motive of this article is to impart knowledge of multiplication by covering every topic including, what is multiplication, the steps
involved in solving mathematics problems, whether any number multiplied by 1 is the number, etc. It is formed using the solved examples and images which makes learning interesting and exciting.
Hoping the writing helped you in capturing the concept of multiplication and you enjoyed reading it. Feel comfortable to ask about your problems.
FAQs on Multiplicative Identity Property (Number Multiplied by 1)
1. What is the general use of multiplication?
The most general use of multiplication is when we need to calculate a large number of things for a given small amount. Multiplication is nothing but a less time taking process of repetitive addition.
So it takes less time to calculate the sum. The multiplication rule is also used to calculate the probability of occurrence of two events.
2. Can the multiplier and multiplicand be the same?
Yes, a multiplier and multiplicand can be the same in a multiplication problem. There is no such rule in maths that these both should be different. When a number is multiplied by its own, the result
is always the square of the given number. For example 2 × 2 = 2² = 4, 13 × 13 = 13² = 169, etc.
3. What happens when one is multiplied by zero?
When 1 is multiplied by 0, the answer is always zero. However, we know that when any number is multiplied by 1 the product is the number itself, similarly we know that any number multiplied by zero
results in zero. | {"url":"https://www.vedantu.com/maths/multiplicative-identity-property","timestamp":"2024-11-07T23:44:31Z","content_type":"text/html","content_length":"241794","record_id":"<urn:uuid:02fc0a67-0130-45fc-9ae2-4c038fe88c59>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00597.warc.gz"} |
Online Undergraduate Research Seminar - Prof. Peter McGrath (NCSU) and Mathew Kushelman - Department of Mathematics
Online Undergraduate Research Seminar – Prof. Peter McGrath (NCSU) and Mathew Kushelman
October 10, 2023 @ 3:00 pm - 4:00 pm
On Liouville’s theorem for conformal maps
Abstract. A theorem of Liouville asserts that the simplest conformal transformations on Euclidean space—translations, dilations, reflections, and inversions—generate all conformal transformations
when the dimension is at least 3. I will describe a new proof of this theorem which is shorter and more elementary than the argument, due to Nevanlinna, found in most modern textbooks.
Related Events | {"url":"https://math.unc.edu/event/online-undergraduate-research-seminar-prof-peter-mcgrath-ncsu-and-mathew-kushelman/","timestamp":"2024-11-05T16:17:57Z","content_type":"text/html","content_length":"114297","record_id":"<urn:uuid:c8cca626-8bef-4748-95b8-0dd8492212d2>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00414.warc.gz"} |
Calculate Electrical Resistance With Ease | Step By Step - Last Updated: Monday, May 01, 2023
Last updated: Monday, May 01, 2023
Electric resistance is a measure of how difficult it is for electric current to flow through a material. Ohm's law states that the electric current flowing through a material is directly proportional
to the voltage applied across the material and inversely proportional to the resistance of the material. This means that if the voltage applied across a material is increased, the electric current
flowing through the material will also increase, as long as the resistance of the material remains constant.
The unit of electric resistance is the ohm (Ω). Resistance is determined by the material's physical properties, such as its length, cross-sectional area, and resistivity. Materials with higher
resistivity have higher resistance, while materials with lower resistivity have lower resistance. Electrical engineers and physicists use the concept of electric resistance in the design and analysis
of electrical circuits, electronic devices, and power transmission systems.
Ohm's law and the concept of electric resistance have many real-world applications. For example, electricians use this law to determine the amount of current that will flow through a circuit given a
certain voltage and resistance. It is also used in the design of electrical wiring for buildings and homes, as well as in the design of electronic devices such as computers and smartphones. Power
companies use the concept of resistance to design power transmission lines with minimal power loss due to resistance.
The formula for determining the electric resistance can be derived from Ohm's law:
\(V\) \(=\) \(I\) \(\cdot\) \(R\)
\(R\): the electric resistance
\(V\): the electric potential
\(I\): the electric current
The SI unit of electric resistance is: \(ohm\text{ }(\Omega)\)
Find R
Use this calculator to determine the resistance in an electric circuit using Ohm's Law
Bookmark this page or risk going on a digital treasure hunt again | {"url":"https://www.smartconversion.com/electric-resistance-calculator","timestamp":"2024-11-15T02:32:06Z","content_type":"text/html","content_length":"38954","record_id":"<urn:uuid:5c1cfcb2-c933-4069-979c-1de6eb7f8bfa>","cc-path":"CC-MAIN-2024-46/segments/1730477400050.97/warc/CC-MAIN-20241115021900-20241115051900-00330.warc.gz"} |
The marketing manager of a firm that produces laundry products
decides to test market a new...
The marketing manager of a firm that produces laundry products decides to test market a new...
The marketing manager of a firm that produces laundry products decides to test market a new laundry product in each of the firm's two sales regions. He wants to determine whether there will be a
difference in mean sales per market per month between the two regions. A random sample of 17 supermarkets from Region 1 had mean sales of 86.2 with a standard deviation of 8. A random sample of 13
supermarkets from Region 2 had a mean sales of 82.2 with a standard deviation of 7.3. Does the test marketing reveal a difference in potential mean sales per market in Region 2? Let μ1 be the mean
sales per market in Region 1 and μ2 be the mean sales per market in Region 2. Use a significance level of α=0.1 for the test. Assume that the population variances are not equal and that the two
populations are normally distributed.
Step 2 of 4: Compute the value of the t test statistic. Round your answer to three decimal places.
Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0. Round your answer to three decimal places.
Step 4 of 4: State the test's conclusion. | {"url":"https://justaaa.com/statistics-and-probability/176352-the-marketing-manager-of-a-firm-that-produces","timestamp":"2024-11-03T23:34:47Z","content_type":"text/html","content_length":"42220","record_id":"<urn:uuid:992175df-8ca2-4098-8bc9-f5a160f2d22e>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00031.warc.gz"} |
Test-of-Time Award
Test-of-Time Award
The ESA Test-of-Time Award recognizes papers from ESA proceedings from 19-21 years prior that have best met the “test of time”. The winner is selected by a committee of three members appointed by the
ESA Steering Committee. The prize may be shared by more than one paper, and the Award Committee reserves the right to declare no winner at all.
ESA Test-of-Time Award 2023
The award committee selected the following papers for the ESA ToTA 2023. The papers stand out for their impact in the algorithms field that also inspired important follow-up work, and by their
significant citation record which shows that the papers are still relevant today.
Raphael Yuster, Uri Zwick: Fast Sparse Matrix Multiplication. In ESA 2004, pp. 604-615. Also, in ACM Transactions on Algorithms 1(1):2-13, 2005.
The paper studies the fundamental problem of computing the product of two n x n sparse matrices over a ring R, where each matrix contains at most m non-zero elements. It presents a new algorithm
that, for certain values of m, multiplies the two matrices using an almost optimal or faster number of algebraic operations over R compared to best-known algorithms. The paper introduces a new way of
partitioning the matrices into a dense and a sparse part that influenced subsequent work and can be used to improve the bounds of multiplying more than just two matrices.
Giovanni Manzini, Paolo Ferragina: Engineering a Lightweight Suffix Array Construction Algorithm. In ESA 2002, pp. 698-710. Also, in Algorithmica 40:33–50, 2004.
The paper provides a new algorithm for computing the suffix array of a string (lexicographically sorting all the suffixes of the given string). The new algorithm is lightweight (uses very small
additional space to that required by the suffix array) and is based on a new deep–shallow sorting method that uses a “shallow” sorter for suffixes with a short common prefix, and a “deep” sorter for
suffixes with a long common prefix. This new key idea allowed to overcome the drawbacks of previous approaches that either required a large amount of space or were inefficient when the input string
contained many repeated substrings. The work included an extensive experimental study that demonstrated the practicality of the new approach. It constitutes a significant step forward towards (i) the
efficient solution of an important practical problem, (ii) bridging the gap between theory and practice, and (iii) influencing subsequent work.
Award Committee: Christos Zaroliagis, Andrew Goldberg, Susanne Albers
ESA Test-of-Time Award 2022
The award committee selected the following papers for the ESA ToTA 2022. The papers stand out for their impact in the algorithms field that also inspired significant follow-up work, and by their
excellent citation record which shows that the papers are still relevant today.
Marianne Durand, Philippe Flajolet: Loglog Counting of Large Cardinalities (Extended Abstract). In ESA 2003, pp. 605-617.
The paper studies the problem of approximately counting the number (cardinality) of distinct elements in a large dataset. It presents a very efficient probabilistic approach that computes an estimate
with a small relative error via a single pass over the input that uses very little auxiliary memory (a small number of words of log log N bits each, where N is the maximum possible cardinality).
Since this is the size needed to represent the answer, this asymptotic dependence is optimal. The work included an empirical evaluation that demonstrates the practicality of the new approach. The
paper introduced key new ideas that laid the foundations to subsequent research work on double-logarithmic size sketches and to implementations with a profound impact and widespread use in industry.
Ulrik Brandes, Marco Gaertler, Dorothea Wagner: Experiments on Graph Clustering Algorithms. In ESA 2003, pp. 568-579.
The paper provides a thorough analysis of indices that formalize the relation between the number of intra- and inter-cluster edges for measuring the quality of graph clustering, for which there was
no conclusive algorithmic evaluation. The paper proposed a new heuristic and experimentally evaluated it against two other theoretically grounded algorithms, making a significant step forward towards
the efficient solution of an important practical problem, as well as bridging the gap between theory and practice. Beyond its particular contribution, this paper influenced subsequent work by
broadening the scope and refining the methodology of modern experimental evaluation of algorithms.
Award Committee: Edith Cohen, Christos Zaroliagis, Andrew Goldberg
ESA Test-of-Time Award 2021
The award committee selected the following two papers for the ESA ToTA 2021.
Andrew Goldberg, Jason Hartline:
Competitive Auctions for Multiple Digital Goods
Proceedings ESA’01
The paper is part of a foundational line of work by the authors on designing auctions for digital goods, which are goods such as software, music, and videos that are in unlimited supply. The work
focuses on competitive auctions that encourage consumers to bid their utility values by providing yield revenue within a constant factor of the optimal fixed pricing. The paper initiates a study of
the important case of multiple digital goods and extends on prior work focused on a single digital good.
Giuseppe Lancia, Vineet Bafna, Sorin Istrail, Ross Lippert, and Russell Schwartz:
SNPs Problems, Complexity, and Algorithms
Proceedings ESA’01
This paper contributed to foundational work of understanding emerging problems in genetics through the computational lens. Single nucleotide polymorphisms (SNPs) are the most frequent form of human
genetic variation. They are of fundamental importance in medical diagnostic, drug design, and are a fingerprint of disease genes. This work studied problems related to computational SNPs validation
based on genome assemblies of diploid organisms (those with two copies of each chromosome) and presented both hardness results and efficient algorithms, using graph modeling.
Award Committee: Samir Khuller, Edith Cohen, Christos Zaroliagis
ESA Test-of-Time Award 2020
The ESA Test-of-Time Award (ToTA) recognizes excellent papers in algorithms research that were published in the ESA proceedings 19-21 years ago and which are still influential and stimulating for the
field today. For the 2019 Award, papers from ESA 1999 to ESA 2001 were considered. Because WAE merged in with ESA, the Steering Committee decided that the papers from WAE 1999 to WAE 2001 were also
to be considered.
The award committee selected the following paper for the ESA ToTA 2020. The paper stands out for its rare combination of simplicity and elegance and has become a textbook classic with significant
followup work and practical use.
Rasmus Pagh, Flemming Friche Rodler
Cuckoo Hashing
Proceedings of ESA 2001, pp. 121-133
Appeared also in J. Algorithms 41(2): 122-144 (2004)
The paper on Cuckoo Hashing by Rasmus Pagh and Flemming Friche Rodler addresses the fundamental problem of designing an efficient data structure that supports key lookups under insertions and
deletions. The Cuckoo Hashing design facilitates lookup and deletion of keys in worst-case constant time and insertions of keys in expected constant time. With its rare combination of simplicity and
elegance, the work has been highly influential both in theory and in practice. In the two decades since its introduction in ESA 2001, the data structure has become a textbook classic and initiated
significant followup work with well over a thousand citations. Cuckoo hashing and its variations are broadly implemented and used in critical applications that require small worst-case lookup times,
such as computation on Graphic Processing Units (GPUs) or internet routing.
Award Committee: Uri Zwick, Samir Khuller, Edith Cohen
ESA Test-of-Time Award 2019
The ESA Test-of-Time Award (ToTA) recognizes excellent papers in algorithms research that were published in the ESA proceedings 19-21 years ago and which are still influential and stimulating for the
field today. For the 2019 Award, papers from ESA 1998 to ESA 2000 were considered. Because WAE merged in with ESA, the Steering Committee decided that the papers from WAE 1998 to WAE 2000 were also
to be considered.
The award committee selected the following paper for the ESA ToTA 2019. The paper stands for its impact in the design of efficient parallel algorithms for shortest path problems.
Ulrich Meyer, Peter Sanders
Delta-Stepping: A Parallel Single Source Shortest Path Algorithm.
Proceedings of ESA 1998, pp. 393-404.
Appeared also in J. Algorithms 49(1): 114-152 (2003)
The paper presents an ingenious algorithm, dubbed Delta-stepping, for the Single-Source Shortest Path Problem (SSSP). This problem is well understood in the sequential setting (i.e., Dijkstra’s
algorithm) but its ubiquitous applications call for efficient parallelizations. Most of the sequential SSSP algorithms are based either on label-setting or on label-correcting methods. Label-setting
algorithms, like Dijkstra’s algorithm, settle at each iteration the distance label of one vertex. Label-correcting algorithms work instead by relaxing edges incident to unsettled vertices: all labels
are temporary until the final step, when they all become permanent. In spite of the great practical performance of label-correcting methods, label-setting algorithms have been known to be
asymptotically superior. In their paper, Meyer and Sanders show how to fill this gap by presenting Delta-stepping, a new label-correcting algorithm for SSSP which runs in optimal linear time with
high probability for a large class of graphs with random edge weights. They further provide an efficient parallel implementation of their Delta-stepping algorithm, which has been a reference method
and has inspired much subsequent work in parallel algorithms for many years.
Award Committee: Giuseppe F. Italiano, Uri Zwick, Samir Khuller
ESA Test-of-Time Award 2018
The ESA Test-of-Time Award (ToTA) recognizes excellent papers in algorithms research that were published in the ESA proceedings 19-21 years ago and which are still influential and stimulating for the
field today. For the 2018 award, papers from ESA’97 to ESA’99 were considered. Because WAE merged in with ESA, the Steering Committee decided that the papers from WAE’97 to WAE’99 were also to be
The award committee selected the following paper for the ESA ToTA 2018. The paper stands out as a classic in efficient data structure design and provides what is still an essential building block in
the fastest-possible deterministic comparison-based minimum spanning tree algorithm.
Bernard Chazelle
Car-Pooling as a Data Structuring Device: The Soft Heap
Proceedings ESA’98, pp. 35-42, also in: Journal of the ACM 47(6): 1012-1027 (2000)
The paper presents an ingenious data structure, the soft heap, which realizes an intricate compromise between what is possible (speed) and what is useful (accuracy). The soft heap is an approximate
priority queue, in the sense that the items it returns are not necessarily items of minimum key. A soft heap is allowed to increase the keys of some, but not too many, of its items, to facilitate
what Chazelle calls the “car-pooling equivalent of data structures”. All soft heap operations take constant amortized time, given a desired level of accuracy. Soft heaps were devised by Chazelle to
obtain a deterministic, comparison-based O(mα(m,n))-time algorithm for the fundamental minimum spanning tree problem. Twenty years on, this is still the fastest algorithm of its kind. Soft heaps were
also used by Pettie and Ramachandran (2002) to obtain an optimal algorithm for the problem, i.e., with algorithmic complexity equal to its decision-tree complexity, albeit with an as yet unknown
running time. The soft heaps paper has not aged over the years and continues to inspire as a fundamental achievement.
Award Committee: Giuseppe F. Italiano (Rome), Jan van Leeuwen (Utrecht), Uri Zwick (Tel Aviv)
ESA Test-of-Time Award 2017
The ESA Test-of-Time Award (ToTA) recognizes excellent papers in algorithms research that were published in the ESA proceedings 19-21 years ago and which are still influential and stimulating for the
field today. For the 2017 award, papers from ESA’96 to ESA’98 were considered.
The award committee selected the following paper for the ESA ToTA 2017. The paper stands out as a classic in the algorithms field and continues to be cited as an exemplary study in its field.
James Abello, Adam L. Buchsbaum, and Jeffery R. Westbrook
A Functional Approach to External Graph Algorithms
Proceedings ESA’98, pp. 332-343, also in: Algorithmica 32 (2002) 437-458
The paper deals with the design of algorithms that operate on massive data sets in external memory. Building on the well-known I/O model of complexity by Aggarwal and Vitter, the authors introduce a
novel design principle for external algorithms based purely on functional transformations of the data, which facilitates standard checkpointing and program optimization techniques. Illustrated on a
variety of graph problems, their approach is proved to be elegant and versatile in the design of both deterministic and randomized external algorithms while the resulting I/O complexities remain
competitive. Functional algorithms are also designed for semi-external problems, in which the nodes fit in main memory but the connecting edges are abundant and only available in external memory. The
paper is an excellent illustration of how general principles of functional program design and model-based complexity can remain in harmony in the field of external algorithms.
Award Committee: Giuseppe F. Italiano (Rome), Mike Paterson (Warwick), Jan van Leeuwen (Utrecht)
ESA Test-of-Time Award 2016
The ESA Test-of-Time Award (ESA ToTA) recognizes excellent papers in algorithms research that were published in the ESA proceedings 19-21 years ago and which are still influential and stimulating for
the field today. In this second year in which the award is given, papers from ESA’95 to ESA’97 were considered.
The award committee selected the following paper for the ESA ToTA 2016. The paper stands out as a classic in the algorithms field and by its excellent citation record still relevant today.
From ESA 95-97:
Boris V. Cherkassky, Andrew V. Goldberg:
Negative-cycle detection algorithms
Proceedings ESA’96, also in: Mathematical Programming 85:2 (1999) 277-311
The paper by Cherkassky and Goldberg deals with the problem of finding a negative-length cycle in a network or proving that there is none. Algorithms for this are a combination of a shortest-path
algorithm and a negative-cycle detection strategy. The authors analyse known algorithms and some new ones and determine the best combinations. Novel instance generators are used in this study. The
paper is a model experimental paper in algorithms. Award Committee: Kurt Mehlhorn (Saarbrucken), Mike Paterson (Warwick), and Jan van Leeuwen (Utrecht)
ESA Test-of-Time Award 2015
The ESA Test-of-Time Award (ESA ToTA) recognizes outstanding papers in algorithms research that were published in the ESA proceedings 19-21 years ago and which are still influential and stimulating
for the field today. Exceptionally, in this first year in which award is given, the ESA ToTA 2015 committee was asked to consider all qualifying papers from ESA 93-95 and ESA 94-96, respectively.
The award committee selected the following two papers for the ESA ToTA 2015. The papers stand out for their impact and wide use in the algorithms field, and for their excellent citation records up to
the present day.
From ESA 93-95:
Mechthild Stoer, Frank Wagner:
A Simple Min Cut Algorithm
Proceedings ESA’94, also in: JACM 44:4 (1997) 585-591
The minimum cut problem in graphs is a basic problem in network analysis and is needed, for example, as the separation routine in branch-and-cut algorithms for the Traveling Salesman problem. Stoer
and Wagner gave an elegant and efficient algorithm for the problem that avoids the computation of maximum flows, building upon previous work by Nagamochi and Ibaraki. The same algorithm was
independently found by Frank. The algorithm continues to be taught because of its elegance and used because of its efficiency and ease of implementation.
From ESA 94-96:
Sudipto Guha, Samir Khuller:
Approximation Algorithms for Connected Dominating Sets
Proceedings ESA’96, also in: Algorithmica 20:4 (1998) 374-387
It is natural to require connectedness as an additional constraint for a dominating set, for example, in ad hoc wireless networks. Domination guarantees coverage and connectedness guarantees
communication between the selected nodes. Guha and Khuller gave polynomial algorithms for a logarithmic-factor approximation to its solution. Under the usual assumptions, this is the best possible.
Their much-cited work has stimulated similar research for connected variants of many other graph problems. Award Committee: Jan van Leeuwen, Kurt Mehlhorn and Mike Paterson
Guidelines for the ESA Test-of-Time Award
The ESA Test-of-Time Award would like to recognize paper(s) from ESA Procs. from 19-21 years prior (i.e., in year X papers from Procs. ESA X-21, ESA X-20, ESA X-19 are considered) that have best met
the “test of time”. Only for the first year, the ESA Test-of-Time Award 2015 considered papers from Procs. ESA 1993, ESA 1994, ESA 1995, ESA 1996.
The winner of the ESA Test-of-Time Award is selected by a committee of three members, appointed by the ESA Steering Committee. The prize may be shared by more than one paper, and the Award Committee
reserves the right to declare no winner at all.
All papers from given years are eligible for the award, except those that are authored or co-authored by members of the Awards Committee. Although the Award Committee is encouraged to consult with
the theoretical computer science community at large, the Award Committee is solely responsible for the selection of the winner of the award. All matters relating to the selection process that are not
specified here are left to the discretion of the Award Committee. | {"url":"https://algo-conference.org/esa/test-of-time-award/","timestamp":"2024-11-09T12:06:43Z","content_type":"text/html","content_length":"50555","record_id":"<urn:uuid:eda416e3-92d4-4476-9ae6-08a70db95783>","cc-path":"CC-MAIN-2024-46/segments/1730477028118.93/warc/CC-MAIN-20241109120425-20241109150425-00232.warc.gz"} |
Convert 6371 KM to Meters: Easy Conversion Techniques
Table of Contents :
Converting distances from kilometers to meters is a fundamental skill that can come in handy in a variety of situations, whether you are working on a school project, planning a hike, or simply
satisfying your curiosity about how far away something is. In this blog post, we will explore how to convert 6371 kilometers into meters easily and accurately, along with some techniques and tips
that will make conversions a breeze. 🌍✨
Understanding the Basics of Kilometers and Meters
Before we dive into the conversion process, let's first clarify what kilometers and meters are.
• Kilometer (km): A kilometer is a unit of length that is equal to 1,000 meters. It is commonly used to measure long distances, such as the distance between cities.
• Meter (m): The meter is the base unit of length in the International System of Units (SI). It is used in various fields such as science, engineering, and everyday life.
The Conversion Formula
To convert kilometers to meters, we can use the following simple formula:
Meters = Kilometers × 1,000
Using this formula, we can easily convert any distance in kilometers to meters.
Step-by-Step Conversion of 6371 KM to Meters
Now, let’s apply the conversion formula to convert 6371 kilometers into meters.
1. Write down the distance in kilometers:
2. Apply the conversion formula: [ \text{Meters} = \text{Kilometers} \times 1,000 ]
3. Plug in the value: [ \text{Meters} = 6371 , \text{km} \times 1,000 ]
4. Calculate the result: [ \text{Meters} = 6,371,000 , \text{m} ]
Thus, 6371 kilometers is equal to 6,371,000 meters. 📏
Visualization of the Conversion Process
To make it easier to understand, here’s a simple table summarizing the conversion:
Kilometers (km) Meters (m)
1 km 1,000 m
5 km 5,000 m
10 km 10,000 m
6371 km 6,371,000 m
Why Convert Kilometers to Meters?
Knowing how to convert kilometers to meters is crucial for several reasons:
• Scientific Calculations: In science, precise measurements are crucial. Converting kilometers to meters ensures that calculations are accurate, especially in fields like physics and engineering.
• Travel Planning: When planning a trip or hike, knowing distances in meters can help you gauge how far you will be traveling. 🚶♀️🗺️
• Educational Purposes: Students often need to convert between metric units for assignments, making this skill valuable in academic settings.
Common Mistakes to Avoid
While converting kilometers to meters is relatively straightforward, some common mistakes can lead to errors in calculations:
• Forgetting the multiplier: Remember that 1 kilometer equals 1,000 meters. Skipping this step can lead to underestimating or overestimating distances.
• Mixing up units: Ensure you’re consistently using kilometers when you start the conversion and that your final answer is in meters.
Practical Applications of Distance Conversion
Understanding how to convert kilometers to meters has numerous practical applications in various fields. Here are some examples:
1. Transportation and Navigation: Knowing the distance in meters can help with navigation systems that often display data in metric units. 🚗🛰️
2. Sports and Athletics: Runners often train using kilometers, but may want to track their speed in meters per second.
3. Land Measurement: In real estate, distances are often measured in meters for property boundaries and land use.
Important Notes
Remember: The metric system is based on multiples of ten, which makes calculations more straightforward than some other measurement systems. Take advantage of this simplicity!
Summary of Techniques for Conversion
To ensure that you can convert kilometers to meters effectively, here are a few additional tips and techniques:
• Use a calculator: For larger numbers, using a calculator can save time and reduce errors.
• Practice frequently: Regularly practice converting different values to reinforce your understanding and speed.
• Visual aids: Create flashcards or charts to visualize the relationships between different metric units.
Converting 6371 kilometers to meters is a simple process that can be tackled easily with the right formula and understanding. By grasping the concept of metric conversions, you empower yourself to
navigate distances with confidence, whether you are working on academic tasks, planning adventures, or simply indulging in curiosity about the world around you. The metric system offers a structured
approach to measurements, making it accessible and efficient.
Whether you’re a student, traveler, or just someone keen to learn, mastering distance conversion from kilometers to meters is a valuable skill. 🏆 Keep practicing, and soon it will become second | {"url":"https://tek-lin-pop.tekniq.com/projects/convert-6371-km-to-meters-easy-conversion-techniques","timestamp":"2024-11-08T10:24:24Z","content_type":"text/html","content_length":"85813","record_id":"<urn:uuid:2737f785-4021-4e19-ba87-131886a2d3bc>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00220.warc.gz"} |
The New Math Wars: Humans vs. AI
I’m sure many of us remember or are familiar with the “Math Wars.” Two divergent schools of thought vehemently clashing over how mathematics should be taught in schools: procedural fluency vs.
conceptual understanding. And in some ways the battle rumbles on, despite most teaching materials and methods these days being an approximation of “a bit of both.” However, recent advances in widely
available commercial AI software have rendered this battle completely moot.
There has been a succession of products, “photomath” and now several AI programs that allow anyone with a subscription to drop in a screenshot of any math problem, and within a few seconds, produce
an absolutely perfect response. On one level, this renders all math homework somewhat irrelevant, but on another level it raises serious questions about the role of humans and the learning of
mathematics. Math class has long felt pretty irrelevant to many students, and the old Math Teachers’ adage of “you won’t always have a calculator in your hand” is now so outdated it’s tragic. Not
only will today’s students likely always have a calculator in their hands, they will also have a tool that can solve any word problem and give them perfect answers. In this scenario, really, what’s
the point of learning math?
About now, it has become clear that the old math wars are over. As I discussed in an earlier blog, “My Daughter Doesn’t Need My Mother’s Math Education,” it was already obvious that learning
procedures for the sake of procedural fluency were a dead end—despite the protests of “but that’s how I learned it.” Now, with the power of commercially available AI, the details of any symbolic or
math word problem can almost immediately be laid bare.
So what does have value anymore? What is the role of humans alongside AI? And what the heck are we supposed to teach the kids?
I’d like to look at two math problems, both concerning fractions at the upper elementary level.
Problem A is a released item from the SBAC Common Core testing consortium
Problem B comes from youcubed.org
First, let’s ask this question, “Which of these problems is more difficult for students?”
While there may be some difference of opinion on this, most teachers are likely to say that A is more difficult because it’s a word problem. This would match my experience both in and out of the
classroom at the Los Angeles Unified School District during the first decade of this century.
Now let’s ask a different question, “Which of these problems is more difficult for an AI?”
Hmm, neither of them is difficult? A is more difficult? B? This question intrigued me, so I bought a subscription to an AI math solver and decided to try some experiments. Will it solve, I asked
The AI took about 0.3 seconds to answer with complete perfection, spelling out in detail the correct method for word problem A, converting 3/10 to 30/100, and told me with unerring accuracy that C
was the answer. For the record, it did exactly the same with a Calculus word problem involving partial differential equations. The complexity of the math was no match for it.
So then I dropped in B. At first, I was stunned by what I was reading. It was so good. I’m paraphrasing, but it said, “First we need to determine the total number of squares in a grid. Each grid is a
10 by 10 square with 100 squares.” This is excellent, I thought, and it followed it up with statements of immense certainty, “In the first grid there are 4 vertical stripes each consisting of 10
squares, so 40/100 are shaded which can be reduced to ⅖.” Nice…
What? The eagle-eyed among you may want to look at the picture again. 4 vertical strips? I don’t think so; there are three. It also only found answers (and wrong ones at that); it made no mention of
the strategy you’d likely want to emerge from a class discussion with students that although the first three are different patterns, you can see that in each one there are always three shaded squares
in each column and three in each row, so you don’t have to count the squares, once you realize the pattern you can tell it’s 3/10 for each one. And there’s a dog!
So this got me really thinking. I wonder how well the AI is trained in visual problem solving, especially given that for the last 15 years, I have designed visual math games and interactive learning
experiences for a living. So I threw in an ST Math puzzle, Alien Bridge, which is also about fractions, to see what it would make of that.
For those of you unfamiliar with ST Math, it’s a game-based learning system that has students use Spatial Temporal (ST) reasoning to solve visual puzzles, helping a penguin, JiJi, across the screen.
In the above puzzle, the question being asked, visually, is we have an alien spaceship that is shaded with ½ + another shaded with ¼. The students have to manipulate the area model below the
spaceships to create an amount equivalent to this sum; in this case, they would build 6/8. And here’s where the AI really started to lose the plot. It told me in no uncertain terms that the answer
was 3 + 5 = 8. At first, I thought maybe it was seeing something connected to the denominator being 8?
And then I realized what it was actually likely doing. It is so desperate to see language and symbols, it was interpreting the half shaded square on the left spaceship as a 3—can you see it?—and then
the quarter-shaded square on the right spaceship as a slightly weirdly drawn 5. The AI loves language and symbols, and I’m sure its ability to see symbols in badly written text is awesome, but in
this context, it’s trying to see what’s not even there. It really struggles to make ANY sense of visual mathematics.
OK, now I’m ready to throw the AI the ultimate test. An ST Math problem that is pure spatial reasoning that we give to Kinder and First grade students but has literally no symbols at all: Upright
In this game, students have to choose a series of 3 rotational moves to get JiJi the penguin from the current position (legs pointing out of the screen, beak to the left, etc.), to an upright
position ready to walk off as seen in ghostly form on the right. What would the AI make of this?
I could not have been more shocked. It did find some symbols on the screen after all—the dummy demo account student name, “I. Newton”. It loved that. It spat out a brilliant summary of the life and
achievements of Isaac Newton:
So this was fascinating. The more accessible we make the mathematics and the thinking to students (humans) by making it visual, challenging, and maybe even interactive, the LESS accessible we make to
AI, trained on a diet of language and symbols to be the ultimate in math homework cheat codes.
Now it’s clearer than ever: the math wars are so long done. The role of humans in learning mathematics is what it always should have been—it is rigorous training in a system of thought about patterns
and problem-solving. Fluency within this system still has massive value. We can talk another time about the need to reduce working memory load within the process of solving non-routine problems, but
procedural fluency is no longer useful as the sole objective of math class—the goal is your ability to show how human you are and develop your creative reasoning, your productive struggle, and your
problem-solving skills.
To all the Math teachers, especially those in Middle and High School grappling with kids using apps to do their homework: assign more visual tasks. Having a student explain and discuss with others
how they solved 1 good, interesting puzzle is worth 100 textbook repetitions of the same question over and over again with different numbers. And to make sure you really throw the AI off the scent,
maybe just add the name “Isaac Newton” somewhere on the page and see what happens. | {"url":"https://blog.mindresearch.org/blog/the-new-math-wars-humans-vs.-ai","timestamp":"2024-11-02T14:07:43Z","content_type":"text/html","content_length":"121631","record_id":"<urn:uuid:88cfd12e-7bab-409a-afeb-b8ad673f29a0>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00048.warc.gz"} |
Introduction to Deep Learning
What’s in this documentation?
This documentation is an introduction to deep learning.
It’s dedicated to people who want to discover the neural networks and the world around it.
This isn’t a tutorial, this is a course whose purpose is to provide the knowledge needed to start any deep learning framework tutorial.
The purpose is to be more familiar with the neural network environment, concepts and vocabularies.
You’ll find here a description of deep learning, how to create the neural network that corresponds to your needs, and few code examples written in Python using Keras.
Keras is an open source neural network library running on top of other neural network libraries. Here, we will use Keras on top on Tensorflow.
What’s deep learning
Before to talk about deep learning, let’s talk a bit about artificial intelligence and machine learning.
Personally, I would define Artificial Intelligence as the set of theories and techniques, mathematical and algorithmic implemented to simulate human intelligence.
That’s not very far from the Cambridge definition: “The study of how to produce machines that have some of the qualities that the human mind has, such as the ability to understand language, recognize
pictures, solve problems, and learn”.
We can find many definitions of A.I, but all of them describe the same concept:Â the capability of a machine to imitate intelligent human behavior.
The purpose is to make the machine able to successfully achieve its goals as a human would do.
There are several ways to perform this approach, one of them is to allow a machine or a system to learn and improve from experience without being explicitly programmed: that’s machine learning.
Machine learning is an application of A.I.
Finally, there are some ways to do it, and one of them, a subcategory of machine learning, is inspired by the human brain and the way it thinks.
Directly inspired from the biological neural networks, the machine learning method we are going to talk about is the method using artificial neural networks. That’s what we call the Deep Learning
Not far either from the Cambridge definition: “AÂ type of artificial intelligence that uses algorithms (= sets of mathematical instructions or rules) based on the way the human brain operates”.
Actually, it’s quite of hard to define because it has changed decades after decades since 1980.
We can define it by a machine learning using neural networks with a large number of parameters and layers, belonging to one of the fundamentals network architectures :
• Multilayers Perceptrons (MLP)
• Convolutional Neural Networks (CNN)
• Recurrent Neural Networks (RNN)
Historically, the first perceptron model was invented by Frank Rosenblatt in 1957, inspired by the cognitives theories of Friedrich Hayek and Donald Hebb.
That’s in 1974 that Paul Werbos proposed the first neural network model using multilayer perceptrons, then developed and perfected by David Rumelhart in 1986.
This is the first type of model we will talk about.
What can we do with it
Before to explain how it works and how to use it, it may be useful to know what need it meets.
From my experience and what I did with them, I would sum up the purpose of neural networks by “predict an output from an input, according to a training data set”. This is what we call supervised
Let’s explain this sentence by a simple example. You’re walking on the street, and you see a cat. The interesting thing to notice is that you obviously know that’s a cat, but you’ve never
seen it before. If we were talking about an animal, or anything you’ve already seen before it would seem normal that you’re able to recognize it, but when you see something that looks like
something else you already know, you don’t recognize it. You figure it out. Have you ever wondered why you are able to figure out so many thing you see every day, even though you’ve never seen
them before?
The answer is simple: your brain is trained. When you see something, the picture of your sight is sent to your brain, your neural network is processing the information to guess what you’re seeing.
You learn, an then you’re trained. Real biological functioning is of course much more complicated, but this explanation is sufficient to understand what the first deep learning researchers were
inspired by.
We can say that the picture your brain received is the input sent to your neural network, and the guess the output.
Following this logic, if we’re able to create an artificial neural network, we would be able to recognize something it never saw before, according to a training data set you sent to it, exactly
like your brain do.
It’s not hard to imagine that the possibilities are infinite.
You want to recognize hand-written letters? Build your neural network model correctly, give a huge amount of hand-written letters to it, and then try to make it able to recognize a letter it never
saw before. If you built properly your model and if you have enough data for the training, you will succeed.
That’s using this method that the robots are currently able to read printed texts easily. By feeding as many fonts and handwritten letters as possible into a neural network, it will be easy to
figure out text from an image.
That’s the same thing if you want to recognize faces, cars, or anything.
This method can of course be applied to any kind of data, but it’s interesting to know that today we have much better results using neural networks than classic images processing to recognize
patterns in images.
If we go farther, the data prediction isn’t that far to the recognition. If I say “2, 4, 6, 8, and?”, you will answer “10”. That’s also thanks to your trained brain that you were able to
figure out the following of this logical sequence.
Okay, but what’s a neural network? What it looks like? Is it easy to implement?
Multilayer Perceptrons (MLP)
Build your model: shapes recognition
Let’s start by the most classic type of model and the easier to understand, the Multilayer Perceptrons.
Here’s what a MLP looks like:
This is a 5-layers Multilayer Perceptron. It has 25 neurons in its input layer, 5 neurons in its output layer, and 3 intermediate layers. The intermediate layers are called hidden layers.
So this model is built to figure out an answer among 5 possibilities via a data that we can describe in 25 parts.
For example, we will use this model to recognize simple 5x5 shapes among 5 different shapes.
Here’s what the shapes would look like:
Build this model with Keras
1 model = Sequential()
2 model.add(Dense(25, activation='relu', input_shape=(25,)))
3 model.add(Dropout(0.2))
4 model.add(Dense(20, activation='relu'))
5 model.add(Dropout(0.2))
6 model.add(Dense(15, activation='relu'))
7 model.add(Dropout(0.2))
8 model.add(Dense(10, activation='relu'))
9 model.add(Dropout(0.2))
10 model.add(Dense(5, activation='softmax'))
12 model.summary()
14 model.compile(loss='categorical_crossentropy',
15 Â Â optimizer=SGD(lr=0.01, clipnorm=1.),
16 Â Â metrics=['accuracy'])
We can see here the 5 layers declarations, with the good amount of neurons for each of them. The activation function, dropout, loss, cross entropy, optimizer and accuracy concepts will be explained
in the part dedicated to the explanation how how the neural networks really work.
Now, in order to make the neural network able to recognize them later, let’s see how to use these shapes to train your model.
Train your model
Obviously, our neural network won’t understand the symbols we used to draw our shapes, we have to give to it numeric values.
If we now convert these shapes into numeric data, we have this :
To make them fit into the neural network, we will vectorize them:
Finally, as it’s a training dataset, we have to indicate the expected result. To write it in a neural network format, we have to use the one-hot encoding.
That just means that we write 5 bits, one by possible output. The expected output for the input line is set to 1, and the others to 0. So “1 0 0 0 0” means “the first output neuron” and “0
0 0 1 0” means “he fourth output neuron”.
If you want now to write a training file with our vectorized shapes, it will look like this:
Once the neural network is trained with this dataset, if we now give to it one of our shapes like the rhombus, it will recognize it.
But it’s cheating, because this exact vector describing the rhombus had already be seen by the neural network, it belong to the training dataset, so of course the model can recognize it.
But, as you probably expect now, this trained model is now able to figure out, among shapes it never seen before, what shape does it make him think.
Train this model with Keras
1 train = pd.read_csv('training_file.dat', sep=" ", header=None)
3 x_train = (train.ix[:,:train.shape[1]-5-1].values).astype('float32')Â Â #Â - 5 => nb classes
4 labels = (train.ix[:,25:train.shape[1]-1].values).astype('int32')Â Â Â #Â 25 => nb inputs
6 history = model.fit(x_train, labels,
7 Â Â batch_size=1,
8 Â Â epochs=20,
9 Â Â verbose=1)
Test your model
Let’s try now with this broken square:
We pass the vector in the first layer:
The neural network figured it out, thanks to its training.
To be clear, this example is very simple to be as understandable as possible. The model is very light, and the training file is very weak.
We had here only one line by shape to train, for a real use case it wouldn’t be enough.
Test this model with Keras
1 test = pd.read_csv('shapes_test.dat', sep=" ", header=None)Â Â Â # shapes_test.dat => e.g:Â 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0
2 x_test = (test.ix[:,:test.shape[1]-1].values).astype('float32')
3 outputs = model.predict(x_test)
5 prediction = {}
6 prediction['confidence'] = float(max(outputs[0]))
7 df = pd.DataFrame(data=outputs)
8 prediction['class'] = df.values[0].tolist().index(prediction['confidence'])
10 print(df)
11 print(prediction)
1 0Â Â Â 1Â Â Â Â 2Â Â Â Â 3Â Â Â Â 4
2 0.016649 0.929342 0.020666 0.001302 0.032041
3 {'class': 1, 'confidence': 0.9293420314788818}
Character recognition
Let’s go then to a real example, which is a logical follow-up from this one: characters recognition. This use-case is more common and there are many neural network models created to do it today in
With the example we just talked about, it shouldn’t be hard now to understand this one:
This model takes 2500 neurons as input, so we will now give to it 50x50 images for each character.
It still has 5 layers, and now 26 neurons as output, one by alphabetical character.
We will now use a more consequent data set, we will give 25 images by character:
These images will be converted in one training file, as you’ve already seen before, in order to train the model.
To be more accurate, instead of passing binary data, we will convert the images in normalized vectors. The first step is to get for each pixel the greyscale value (between 0 and 255), and then
normalize them to have only values between 0 and 1.
When we have our 26x25 vectors (25 images for each alphabetical character) with the one-hot encoding for each line, our training file is ready.
If now we draw another letter, and automatically do the same operations (vectorization + normalization) before to give it as input of the neural network, it will be able to recognize the letter.
Okay, but how does it really works? A neural network is of course not magical, let’s see how it works behind.
The next part is more theoretical.
Its purpose is to:
• Explain how the neural networks really work behind
• Introduce you to the common neural network vocabulary and concepts
You can read it quickly and pass directly to the convolutional neural networks (another kind of neural network) if you’re not interested in the mathematical part, but in order to understand the
purpose of this other kind of neural network, you’ll need to understand some basics concepts like accuracy, cross entropy loss, or overfitting.
Keras code
You can find the whole sample source code here:
How a neural network really works
Degrees of freedom and activation function
When you pass the vector as input of the neural network, a neuron does always the same thing:
• It does the weighted sum of all of its inputs,
• Adds an additional value (called the “bias”)
• Then it passes the value into a mathematical function called an “activation function”
It gives us the following formula for one neuron output: L = activation(X.W + b)
• activation(): the activation function
• X: the vector of inputs
• W: the vector of weights
• b: the bias
We have then, for each neuron, 2 degrees of freedom:
• The bias
• The weights of the weighted sum
There can be many functions to use as activation function, but the function must fulfill 2 conditions:
• It must not be linear
• It must be continuous between 0 and 1
Historically, the activation function has almost always been the sigmoid function, but these last years we recently discovered that the activation of a biological neuron looks more like a relu
function than a sigmoid function. After many tests, the researchers in biology discovered that from a certain level, the neurons pass to an activation proportional to the size of the input signals.
That’s why today the relu function is the most used, allowing the model to converge to a more accurate output.
Sigmoid function
Relu function
That’s what each neuron do, layer after layer.
There’s however an exception for the output layer. We almost always use the softmax function instead of the relu as activation function for the output layer. The softmax is just an exponential
function, so after the output neurons has done their weighted sum, they raise the result exponentially, and then we normalize them to have only values between 0 and 1.
This method is used to improve the convergence of the neural network, it widens the gaps between all of the output results. The purpose is to have only values close to 0 (+- 0.1) for every neurons
expect for one neuron close to 1 (+- 0.9). We can then interpret it as a probability: the neuron with the output value closest to 1 is the result provided by the neural network.
That’s why it’s called “softmax”, it it highlights the maximum, but without destroying the information. It’s still “soft”.
In our previous example with the characters recognition model, if we have all output neurons with output close to 0 but the second one close to 1, that means that the neural network figured out that
the input we passed to it corresponds to the letter “B”.
The first intermediate layer does the weighted sum of the inputs, the layer below does the weighted sum of the previous weighted sums, the outputs of the previous layer, etc…
We can have this result because the neural network was able to converge to the good output, and it was able to do it because the weights and the biases were well chosen.
Okay, but how to chose them? how to direct the weights and the biases in the good direction?
How to direct the degrees of freedom
Accuracy and cross-entropy loss
The entire capacity of a neural network to produce good predictions is based on this.
As we saw earlier, in order to make the neural network able to do a prediction from an input, we need to train it.
The training consists to pass as many inputs as possible in our neural network (like the shapes or the characters in the previous example), and to define an error function, because we already the
know the results. Each input is passed with its own one-hot encoded expected input. For each input passed, we set arbitrarily a vector of weights and a bias for each neuron. The result is therefore
the output of the last layer with the highest probability. Then we compare this result with the expected result, and we know if the weights and biases were good enough to make the neural network able
to do good prediction. That will allow us to establish the error function, and the purpose will to minimize this error function. We call this error function the cross-entropy loss.
This error function is defined by the distance between the output vector (all output neurons values), and the one-hot encoded expected output vector. We could use any distance method, like the
Euclidean distance, but the distance that works best today is the cross-entropy distance. That’s why we call our error function the cross-entropy loss.
The cross-entropy consists to multiplying value by value the one-hot encoded expected outputs by the logarithm of the outputs computed by the neural network, and then to do the sum.
Here’s the cross-entropy formula:Â
That makes us able to compute the accuracy of the neural network, we call that the evaluation.
The cross-entropy loss decrease and the accuracy increase as the training progresses.
The weights and the biases change in a direction that make the error function decrease.
So now in order to direct the values to the good direction, we need to use an optimizer.
The optimizers
One of the most used is the Gradient Descent Optimizer.
The optimizer will take the error function and compute its partial derivatives in relation to all the weights and the biases of the system.
This involves a huge amount of partial derivative calculation.
Once the calculations are completed, we obtain a vector of partial derivatives.
It’s this vector that we call the gradient.
This gradient points towards the extremum. As we want to minimize cross-entropy, we make it negative, and it then tells us where to direct the values. This then tells us which small delta to add to
weights and biases in order to get closer to a value where the error function will be lower.
Finally, when we train a neural network, the whole input dataset won’t be passed only once. It will train again, then again, many times.
We consider that when we train the neural network with the dataset one time, the neural network trained in one epoch. The number of epochs is the number of times you continue to train with the same
dataset. So it’s up to us, doing calculations and experiments, to figure out the best number of layers for the neural network, as well as the number of epochs.
These numbers change from a specific need to another.
For a generic use, the number of layers is generally between 3 and 5 for most needs, but some complex neural networks can exceed 80 layers.
For the number of layers as well as the number of epochs, we often find it empirically.
But we have to be very careful when we chose them, it would be a huge mistake to think “more layers and epochs I use, more accurate my model will be. In any case, it can’t make things worse”,
because it’s totally wrong. If you use too many layers or if you train your neural network too much (in too many epochs), we will lose the convergence, as well as the accuracy.
This is a common phenomenon, called overfitting.
Vanishing gradient
Now that we have explained what the gradient is, we can understand the problem of the Sigmoid: it has two flat zones on the edges, so having derivatives at these places that tend towards 0. Since the
direction we give to weights and biases comes from the gradient, itself composed of partial derivatives, if these derivatives are zero, we no longer have any direction to direct our degrees of
That’s what we call the vanishing gradient.
This is a phenomenon that occurs when you start stacking layers, which is a problem because stacking layers is part of the machine learning concept.
The Relu function was therefore able to overcome this problem.
But that’s not all there is to say about training yet. Thanks to these methods we were able to make the neural network converge, but we still need to improve the accuracy.
Learning Rate Decay
The first idea to do that is to reduce the step, the delta we use to make the weights and biases progress in the good direction. That will allow the neural network to be more accurate, but this will
also make the training slower.
To avoid this inconvenience, we will use the Learning Rate Decay.
This method consists to start very quickly and slow down gradually.
That will allow the deltas to stop varying too much from one direction to another.
Then, we have to take care of the overfitting, and find a way to reduce it.
In order to reduce the overfitting, we will do that we call the regularization, to correct the parts of our calculations that can mislead us.
Regularization and dropout
A very famous regularization method is the dropout, and it’s very simple to understand: we will kill randomly a certain amount of neuron from the neural network (e.g 25%) before to do the training.
Then we put all the neurons back in the model, and do the evaluation. We do it again and again, many times. Each time, we restart the operation from the full model.
By killing a neuron, we mean put its value to 0, and slightly raise the other neuron values, to rebalance the average of the vectors.
The reason we’re doing this to regulate the neural network is that a neural network has too much degrees of freedom. Sometimes, some weights and biases can progress in the wrong direction, but if
they are significantly outnumbered, the other neurons correct it and keep the convergence. We could say that’s fine while there’s enough neurons to correct, but that also means that we could have a
better accuracy. The problem is that we can’t locate the bad neurons and the neurons which correct them.
The dropout method is a simple a very effective method because as at each time we train the neural network there’s a probability for the neurons that corrected the bad neurons to not be there
anymore, there’s less chances for the bad neurons to be corrected.
We have now optimized our accuracy and our cross-entropy loss.
For some cases we would have reached the maximum optimization (approximately), but for our example (shapes or characters recognition), we definitely can’t.
Why? Because we did a very brutal operation at the very beginning: we had images/matrix in 2D, and we flatted them. This isn’t really smart, because we lost a huge information: the 2D shape of the
But we hadn’t the choice, out MLP can take only vectors as input, so what can we do?
The answer is that our type of model is simply not adapted. We need a model that can take a 2D matrix as input.
That’s exactly why the convolutional neural networks were created.
Convolutional Neural Network (CNN)
From 1D to 2D
This time, here’s what our model looks like (still for the characters recognition, 50x50 images):
The basis of the principle is the same, but with some differences:
• We keep the 2D input information
• For a neuron, we don’t do the weighted sum of the entire previous layer anymore
• We introduce the concept of channel
Batches and channels
For a MLP, if you remember, each neuron has as input the entire vector of the previous layer outputs, but not this time.
This time, each neuron will have only a patch of the previous layer (4x4 for example) as inputs. We still do the weighted sum of these inputs and we still add a bias, but only with this patch as
We continue patch after patch, building another 2D layer of neurons.
Very important: we keep the same weights and the same bias for the all of the patches through the same layer.
With this method, we keep the 2D information, but we don’t have enough degrees of freedom anymore. That’s why we build another layer at the same layer level of this one, but with another weights
and bias. It’s like “another version” of this layer.
That’s the concept of channel: the hidden layers won’t be alone anymore, each of them will have a certain amount of another versions of themselves.
Here’s a representation of the inputs for each neurons, patch by patch (here we draw the 2 channels instead of to write “X2”):
If we zoom a little, that would look like this:
In this example, the same 4x4 weight matrix and the same bias will be used for the whole layer, and the we use another weight matrix and another bias for the second channel.
Using 2D layers and patches allow us to keep every important information, every detail of the shape contained in the image/matrix: pieces of curves, lines, etc…
It’s of course up to us to define the size of the patch (4x4, 5x5, 6x6, …)
If we do this, as we can see above, no matter what number of channel we use, we will generate output layers with the same size as the input layers (it’s logic).
But the purpose of a neural network to converge. To do that, we will simply move the patch not everypixel, but every two pixels (the patch step goes from 1 to 2), we will then obtain output layers
twice smaller than the input layer.
We continue to decrease the size of our layers and increase the number of channels, until we’re ready to generate the last hidden layer, a no-convolutional one, fully connected. We are then ready
to generate the last output layer whose result will give our prediction. (Cf. our first CNN schema).
The last hidden layer is fully connected, that means that every neuron output of this layer will be the input of every neuron of the output layer, so as a MLP, each neuron has his own weight vector
and bias.
If the neural network meets issues to converge (overfitting), that probably means that it doesn’t have enough degrees of freedom. The solution is to use more channels for each layers.
Also, as the MLPs models, adding dropout will help a lot, but only in the fully connected layer. There’s not enough degrees of freedom in the convolutional networks to do that, it would be too
And that’s it! We’re now able to do predictions from 2D inputs with the maximum theoretical accuracy and minimum cross-entropy loss.
Before to finish with the CNNs, it’s good to know that recently we discovered a new method to do a regularization called the batch normalization.
Batch normalization
It consists to divide the whole training dataset in batches, and ensure that the values are in the same scale of values, and that the curves are centered and uncorrelated.
We will be able to compute some statistics for each batch.
For each batch, we will take the output of a neural network layer. For a 100 matrix batch, we sill have 100 output values.
For all of these values, we will compute the average and the standard deviation, and we will modify each layer outputs before to use the activation function.
The modification consists to subtracting the average and to divide by the standard deviation.
For x the initial output computed and xĚ‚ the new output normalized, we can have this formula:Â
To ensure that we won’t break the outputs that the layer computed, we will add 2 parameters to our new output, so here’s the batch normalization before to use the activation function: BN(x) = αxĚ‚
+ β
If the neural networks figures out that it would be a bad idea to transform the output value subtracting the average and dividing by the standard deviation, the parameters α and β will allow us to
rewind our calculation. That add 2 degrees of freedom by neuron for our neural network.
As we can cancel each batch normalization, we can ensure that our neural network will be at least as good with the batch normalization as without.
Keras code
The way to build this model with Keras is similar to the MLPs, but this time we take in account the 2D shape of the layers as well as the channels.
Build this model with Keras
1 # Image Size
2 IMG_SIZE = 50
3 # Number of classes (Number of Persons in Database)
4 NB_CLASSES = 26
6 model = Sequential()
7 model.add(Conv2D(32, kernel_size=(12, 12),activation='linear',padding='same',input_shape=(IMG_SIZE,IMG_SIZE,1)))
8 model.add(LeakyReLU(alpha=0.1))
9 model.add(MaxPooling2D((2, 2),padding='same'))
10 model.add(Dropout(0.25))
11 model.add(Conv2D(64, (6, 6), activation='linear',padding='same'))
12 model.add(LeakyReLU(alpha=0.1))
13 model.add(MaxPooling2D(pool_size=(2, 2),padding='same'))
14 model.add(Dropout(0.25))
15 model.add(Conv2D(128, (3, 3), activation='linear',padding='same'))
16 model.add(LeakyReLU(alpha=0.1))
17 model.add(MaxPooling2D(pool_size=(2, 2),padding='same'))
18 model.add(Dropout(0.4))
19 model.add(Flatten())
20 model.add(Dense(128, activation='linear'))
21 model.add(LeakyReLU(alpha=0.1))
22 model.add(Dropout(0.3))
23 model.add(Dense(NB_CLASSES, activation='softmax'))
25 model.compile(loss=keras.losses.categorical_crossentropy,
26 optimizer=keras.optimizers.Adam(),metrics=['accuracy'])
As the CNNs are made to take matrix instead of vectors as input, the inputs are often images.
In order to be able to train and use the neural network with images, here are some functions to convert the images into the matrix we will give to the neural network:
Preparation functions in Python
1 # Set the labels vocabulary for the dictionary. The part before the "_" in the file name will be the label for this image
2 def label_vocabulary(train_dir):
3 Â Â labels_dict = {}
4 Â Â i = 0
5 Â Â for img in os.listdir(train_dir):
6 Â Â Â Â label = img.split('_')[0]
7 Â Â Â Â if label not in labels_dict:
8 Â Â Â Â Â Â labels_dict[label] = i
9 Â Â Â Â Â Â i=i+1
10 Â Â return labels_dict
12 # Invert keys_values map
13 def inv_map(map):
14 Â Â return {v: k for k, v in map.iteritems()}
16 # Create training data for the images directory
17 def create_train_data(train_dir):
18 Â Â X = []
19 Â Â Y = []
20 Â Â for img in os.listdir(train_dir):
21 Â Â Â Â Â word_label = img.split('_')[0]
22 Â Â Â Â label = labels_dict[word_label]
23 Â Â Â Â path = os.path.join(train_dir, img)
24 Â Â Â Â img = cv2.imread(path,cv2.IMREAD_GRAYSCALE)
25 Â Â Â Â img = cv2.resize(img, (IMG_SIZE, IMG_SIZE))
26 Â Â Â Â X.append(np.array(img))
27 Â Â Â Â Y.append(label)
28 Â Â return X,Y
30 # Resize the input image and preprocess it
31 def prepare_image(image, target):
32 Â Â Â Â image = cv2.resize(image, target)
33 Â Â Â Â image = np.array(image).reshape(-1, 50, 50, 1)
34 Â Â Â Â image = image.astype('float32')
35 Â Â Â Â image = image / 255.
36 Â Â Â Â
37 Â Â Â Â return image
Train this model with Keras
1 # Train directory containing the images
2 train_dir = 'letters'
4 # Create the dictionary of labels
5 labels_dict = label_vocabulary(train_dir)
7 # Create train data
8 train_X,train_Y = create_train_data(train_dir)
9 train_X = np.array(train_X).reshape(-1, IMG_SIZE,IMG_SIZE, 1)
10 train_X = train_X.astype('float32')
11 train_X = train_X / 255.
13 # Change the labels from categorical to one-hot encoding
14 train_Y_one_hot = to_categorical(train_Y)
16 # Split the training set in validation and training data
17 train_X,valid_X,train_label,valid_label = train_test_split(train_X, train_Y_one_hot,  test_size=0.2, random_state=13)
19 model.fit(train_X, train_label, batch_size=64, epochs=60, verbose=1, validation_data=(valid_X, valid_label))
Test this model with Keras
1 prediction = {}
2 prediction['confidence'] = float(max(outputs[0]))
3 df = pd.DataFrame(data=outputs)
4 index = df.values[0].tolist().index(prediction['confidence'])
5 labels_dict_inv = inv_map(labels_dict)
6 prediction['class'] = labels_dict_inv.get(index)
1 {'confidence': 0.9999970197677612, 'class': '0001'}
So here the class ‘0001’ was recognized, that corresponds to the letter ‘A’
You can find the whole sample source code here:
Beyond this blog article
There are many other types of neural network, such as recurrent neural networks (RNN / LSTM) or generative neural networks. Well enough to make this blog post a hundred times longer, but I hope that
with this explanation of neural networks via MLPs and CNNs you now have some basics to explore the rest!
All neural network drawings were designed by my own graphic library: BYONND
I also made a neural network studio based on this library: Deep Learning studio
Thanks for reading! | {"url":"https://blog.kimi.ovh/p/introduction-to-deep-learning/","timestamp":"2024-11-08T08:35:05Z","content_type":"text/html","content_length":"95246","record_id":"<urn:uuid:5cbea507-fe6b-476c-9196-86bd75b478f8>","cc-path":"CC-MAIN-2024-46/segments/1730477028032.87/warc/CC-MAIN-20241108070606-20241108100606-00240.warc.gz"} |
Dynamical system definition
A dynamical system is a system whose state evolves with time over a state space according to a fixed rule.
For an introduction into the concepts behind a dynamical system, see the idea of a dynamical system.
Formal definition of dynamical system
A dynamical system is formally defined as a state space $X$, a set of times $T$, and a rule $R$ that specifies how the state evolves with time. The rule $R$ is a function whose domain is $X \times T$
(confused?) and whose codomain is $X$, i.e., $R : X \times T \to X$ (confused?). The rule function $R$ means that the $R$ takes two inputs, $R=R(\vc{x},t)$, where $\vc{x} \in X$ (confused?) is the
initial state (at time $t=0$, for example) and $t \in T$ is a future time. In other words, $R(\vc{x},t)$ gives the state at time $t$ given that the initial state was $\vc{x}$. | {"url":"https://mathinsight.org/definition/dynamical_system","timestamp":"2024-11-10T07:46:58Z","content_type":"text/html","content_length":"12964","record_id":"<urn:uuid:eab9ffe3-6535-45c7-8b11-9e489b29f6f6>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00459.warc.gz"} |
CBSE Class 9 Maths Lab Manual - Quadrilateral Formed by Joining Mid-points - CBSE Sample Papers
CBSE Class 9 Maths Lab Manual – Quadrilateral Formed by Joining Mid-points of Sides of a Quadrilateral
To show that the quadrilateral formed by joining the mid-points of the adjacent sides of a quadrilateral is a parallelogram by paper folding.
Prerequisite Knowledge
1. Concept of finding mid-point of a line segment by performing paper folding activity.
2. Properties of a parallelogram.
Materials Required
Glazed papers, pencil, a pair of scissors, gluestick and tracing paper.
1. Take any coloured glazed paper.
2. Draw a quadrilateral of any dimensions on glazed paper and name it as ABCD.
3. Cut that quadrilateral from the glazed paper.
4. Now, find the mid-point of each side AB, BC, CD, DA by paper folding and name them E, F, G, H respectively as shown infig. (i).
5. Now, fold the figure along EF, GF, GH and EH. Press it and then unfold it as shown in fig. (ii).
6. We will get creases along EF, GF, GH, HE.
7. Make a replica (true copy) of EFGH (say PQRS) by using a tracing paper [fig.(iii)].
8. Cut the quadrilateral PQRS along any diagonal (say RP) [fig.(iv)].
9. We will get two triangles ∆PSR and ∆PQR.
10. Now, overlap these two triangles. Two triangles coincide with each other [fig.(v)] such that side PS overlaps with QR and PQ with SR.
We observe that two triangles coincide with each other which means two triangles are congruent to each other. In a quadrilateral, two triangles cover each other completelv along any diagonal, then
the quadrilateral will be a parallelogram.
∴ ∆PQR = ∆PSR
i.e., ar (∆PQR) = ar(∆PSR)
∴ PQRS is a parallelogram.
As the replica of ∆PQR exactly covers the replica of ∆PSR
∴ PQ = RS, QR=SP
∴ PQRS is a parallelogram.
Learning Outcome
We have verified by paper folding that the quadrilateral formed by joining the mid-points of adjacent sides of a quadrilateral will be a parallelogram. We also learnt that a diagonal always divides
the parallelogram into two triangles of equal areas.
Activity Time
What type of figures do you obtain?
• If you join mid-points of the sides of a rectangle (Do it by paper folding).
• If you join the mid-points of thesidesof a square (Do it by paper folding).
Viva Voce
Question 1.
What do you mean by a quadrilateral ?
A quadrilateral is a plane closed figure bounded by four line segments.
Question 2.
What are two main properties of a quadrilateral ?
• Sum of four angles is 360°.
• It has 4 sides.
Question 3.
Is a parallelogram a quadrilateral ?
Question 4.
Write two main properties of a parallelogram.
• Diagonals bisect each other.
• Opposite sides are equal.
Question 5.
In a parallelogram, if one angle is 90°, then what type of parallelogram you will get ?
Question 6.
Do you know any difference between a parallelogram and a trapezium ?
In a parallelogram, two pairs of opposite sides are parallel. In a trapezium, one pair of opposite sides is parallel.
Question 7.
What is the area of a parallelogram ?
Base x corresponding altitude.
Question 8.
If base and altitude of a parallelogram are same, then what will be area of parallelogram ?
Base x altitude.
Question 9.
If base and altitude of a parallelogram are same, then what type of parallelogram will be obtained ?
Question 10.
What do you mean by a parallelogram ?
A parallelogram is a quadrilateral in which opposite sides are equal and parallel.
Question 11.
Write the name of different kinds of parallelograms.
Rectangle, square and rhombus.
Question 12.
If you join the mid-points of consecutive sides of a quadrilateral, what shape will you obtain ?
Question 13.
Which theorem is used in this activity ?
Mid-point theorem.
Question 14.
If you join the mid-points of consecutive sides of a rectangle, what figure will you obtain ?
Question 15.
If you join the mid-points of consecutive sides of a rhombus, what figure will you obtain ?
Multiple Choice Questions
Question 1.
Name the quadrilateral formed by joining the mid¬points of the consecutive sides of a square:
(i) rectangle
(ii) square
(iii) rhombus
(iv) none of these
Question 2.
The four triangles formed by joining the mid-points of three sides of a triangle are:
(i) congruent
(ii) non-congruent
(iii) similar
(iv) none of these
Question 3.
In the given figure ABCD, if P, Q, R and S are the mid-points of sides AB, BC, CD and DA respectively, then:
(i) SR = \(\frac { 1 }{ 2 }\) AC
(ii) SR = AC
(iii) SR = \(\frac { 1 }{ 3 }\) AC
(iv) none of these
Question 4.
In ∆ABC, if E is the mid-point of AC, F lies on BC and EF // AB then:
(i) EF = \(\frac { 1 }{ 3 }\) AB
(ii) EF = \(\frac { 1 }{ 2 }\) AB
(iii) EF = AB
(iv) none of these
Question 5.
In a parallelogram, the figure formed by joining the mid-points of consecutive sides is :
(i) a rectangle
(ii) a rhombus
(iii) a square
(iv) none of these.
Question 6.
In a rhombus, diagonals bisect each other at an angle of:
(i) 45° and 135°
(ii) 60° and 120°
(iii) 90°
(iv) none of these
Question 7.
In a rectangle, diagonals are:
(i) equal
(ii) not equal
(iii) half of each other
(iv) none of these
Question 8.
The straight line joining the mid-points of the non¬parallel sides of a trapezium is parallel to:
(i) parallel sides
(ii) non-parallel sides
(iii) one non-parallel side
(iv) none of these
Question 9.
The triangle formed by joining the mid-points of the sides of a right triangle is :
(i) a right triangle
(ii) an obtuse-angled triangle
(iii) an isosceles triangle
(iv) none of these
Question 10.
The triangle formed by joing the mid-points of the sides of an isosceles triangle is:
(i) an equilateral triangle
(ii) an isosceles triangle
(iii) a right-angled triangle
(iv) none of these
1. (ii)
2. (i)
3. (i)
4. (ii)
5. (iv)
6. (iii)
7. (i)
8. (i)
9. (i)
10. (ii)
Math Lab ManualMath Labs with ActivityMath LabsScience LabsScience Practical Skills | {"url":"https://www.cbsesamplepapers.info/cbse/cbse-class-9-maths-lab-manual-quadrilateral-formed-by-joining-mid-points","timestamp":"2024-11-05T02:23:44Z","content_type":"text/html","content_length":"150690","record_id":"<urn:uuid:2fc0a12d-6dcb-45dc-9ff6-06ffd0740e2e>","cc-path":"CC-MAIN-2024-46/segments/1730477027870.7/warc/CC-MAIN-20241105021014-20241105051014-00599.warc.gz"} |
Accuracy of GPS digital coords?
In google maps the lat/long references are given to six decimal places
e.g. 52.398609, 0.263875
My sat nav only accepts five decimal places.
Is there any appreciable difference between the five- and six-figure references?
Just trying to decide if I should be rounding up/down, or just ignoring the final digit.
For what purpose? The difference is about 3 feet in latitude and 2 and a bit in longitude.
At the equator, 360 degrees corresponds to 25,000 miles of longitudinal distance, so 1 degree = 69.4 miles. That means 0.000001 degree corresponds to 0.367 feet. GPS receivers typically self-report
accuracies of a few feet, so entering coordinates to more than 5 decimal places is probably pointless.
Just a data point, but my geocache software on my phone reports to three decimals of minutes and self reports and accuracy of 16 feet. It’s enough to get one close but not so close that you don’t
have to search for the cache.
Up/down rounding is more accurate. Errors just add together, (that is two errors cannot be assumed to cancel out !)
Just ignoring the final digit means wiping 9 off ?
0-4 means 0, which you ignore .
5 - 9, means add one to the column to the left (with carry as appropriate)
In this case, the maximum error introduces is 5… half that of if you just drop the last digit.
An even better method (even though only slightly better I’m nitpicking here) is to round down 0-4, round up 6-9, and to use a random algorithm to decide what to do with 5. Always rounding up fives
introduces a slight upward bias, meaning that over the long run you will round up more than you round down, so errors won’t cancel out. A typical random algorithm would be to say that you always
round to the even figure. So 47.5 would be rounded up to 48 (because the 8 is even, the 7 is not), whereas 42.5 would be rounded down to 42. This preserves symmetry; over the long run, you round down
just as much as you round up. | {"url":"https://boards.straightdope.com/t/accuracy-of-gps-digital-coords/676153","timestamp":"2024-11-10T19:14:42Z","content_type":"text/html","content_length":"34057","record_id":"<urn:uuid:9410db34-d250-43e5-8f86-257d70b274fd>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00705.warc.gz"} |
Hyperbola: Formulas, Equations, Properties & Examples
What is a hyperbola?
A hyperbola can be defined as the set of all points such that the ratio of the length to a single focal point divided by the distance to a line (the directrix) is greater than one.
Which application uses the hyperbolic curve?
Cooling towers, water channels use hyperbolic curves as their design.
What is the difference between parabola and hyperbola?
The main difference is that for a parabola, eccentricity is equal to 1, and for hyperbola, eccentricity is greater than 1. A parabola is represented as a set of points in a plane that are equidistant
from a straight line called the directrix and focus. On the other hand, hyperbola can be described as the difference of distances between a set of points, which are present in a plane.
What are the four conic sections?
The four conic sections are: circle, ellipse, parabola and hyperbola.
Where can I apply hyperbolas?
Hyperbolas have applications to several different systems and problems including sundials, trilateration, lens, monitors, optical glasses and more. | {"url":"https://testbook.com/maths/hyperbola","timestamp":"2024-11-06T17:00:05Z","content_type":"text/html","content_length":"869926","record_id":"<urn:uuid:baae5fe7-069f-4913-b76c-956e4362f69f>","cc-path":"CC-MAIN-2024-46/segments/1730477027933.5/warc/CC-MAIN-20241106163535-20241106193535-00089.warc.gz"} |
Some recent papers by group members
Nina Kamčev, Anita Liebenau, Nick Wormald. Asymptotic enumeration of hypergraphs by degree sequence. Adv. Comb. 2022.
Graham Farr. The history of Tutte–Whitney polynomials. In: Handbook of the Tutte Polynomial and Related Topics, Chapman and Hall, 2022.
Ian M. Wanless, David R. Wood. A general framework for hypergraph coloring. SIAM J. Discrete Math. 2022.
Alexander Cant, Heiko Dietrich, Bettina Eick, Tobias Moede. Galois trees in the graph of p-groups of maximal class. J. Algebra 2022.
Tao Feng, Daniel Horsley, Xiaomiao Wang. Novák’s conjecture on cyclic Steiner triple systems and its generalization. J. Combin. Theory Ser. A, 2021.
Norman Do, Danilo Lewański. On the Goulden-Jackson-Vakil conjecture for double Hurwitz numbers. Adv. Math. 2022.
Kevin Hendrey. Sergey Norin, David R. Wood. Extremal functions for sparse minors. Adv. Comb. 2022.
Chun-Hung Liu, David R. Wood. Clustered variants of Hajós’ conjecture. J. Combin. Theory Ser. B, 2022.
Mikhail Isaev, Angus Southwell, Maksim Zhukovskii. Distribution of tree parameters by martingale approach. Combin. Probab. Comput. 2022. | {"url":"https://blogs.monash.edu/discretemaths/2022/09/13/some-recent-papers-by-group-members/","timestamp":"2024-11-12T12:14:29Z","content_type":"application/xhtml+xml","content_length":"22194","record_id":"<urn:uuid:f64006b7-84ad-4f5d-9cc8-ff5d848fe4e8>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.45/warc/CC-MAIN-20241112113320-20241112143320-00252.warc.gz"} |
2018.09 KCI 등재 구독 인증기관 무료, 개인회원 유료
2017.09 KCI 등재 구독 인증기관 무료, 개인회원 유료
The objective of this study is to estimate the mechanical characteristics and nonlinear behaviors on the geometric nonlinear analysis of curved cable-membrane roof systems for long span lightweight
roof structures. The weight of a cable-membrane roof dramatically can reduce, but the single layer cable-membrane roof systems are too flexible and difficult to achieve the required structural
stiffness. A curved cable roof system with reverse curvature works more effectively as a load bearing system, the pretension of cables can easily increase the structural stiffness. The curved cable
roof system can transmit vertical loads in up and downward direction, and work effectively as a load bearing structure to resists self-weights, snow and wind loads. The nonlinear behavior and
mechanical characteristics of a cable roof system has greatly an affect by the sag and pretension. This paper is carried out analyzing and comparing the tensile forces and deflection of curved roof
systems by vertical loads. The elements for analysis uses a tension only cable element and a triangular membrane element with 3 degree of freedom in each node. The authors will show that the curved
cable-membrane roof system with reverse curvature is a very lightweight and small deformation roof for external loads.
2002.09 KCI 등재 구독 인증기관 무료, 개인회원 유료
It is often hard to obtain analytical solutions of boundary value problems of shells. Introducing some approximations into the governing equations may allow us to get analytical solutions of boundary
value problems. Instead of an analytical procedure, we can apply a numerical method to the governing equations. Since the governing equations of shells of revolution under symmetric load are
expressed by ordinary differential equations, a numerical solution of ordinary differential equations is applicable to solve the equations. In this paper, the governing equations of orthotropic
spherical shells under symmetric load are derived from the classical theory based on differential geometry, and the analysis is numerically carried out by computer program of Runge-Kutta methods. The
numerical results are compared to the solutions of a commercial analysis program, SAP2000, and show good agreement.
2002.09 KCI 등재 구독 인증기관 무료, 개인회원 유료
The purpose of this paper is to study the buckling characteristics of elliptical latticed domes under conservative loading conditions. The latticed domes are usually designed in geometrically
spherical shape. For this type of latticed domes, many researchers have researched and even the simplified estimation codes for the buckling load level have been available. However, geometrically
elliptical latticed domes have been often constructed, and show different buckling characteristics following with geometrical parameters as rise-to-span ratio and so on. Therefore, it is necessary to
investigate the general tendency of buckling characteristics of the elliptical latticed domes. In this paper, to find out some buckling characteristics of elliptical latticed domes, height, boundary
configuration and gap are used as the shape coefficients. For each model with different parameters, the eigen values and the buckling loads are evaluated.
2002.06 KCI 등재 구독 인증기관 무료, 개인회원 유료
The basic systems of spatial structures such as shells, membranes, cable-nets and tensegrity structures have been developed to create the large spaces without column. But there are some difficulties
concerning structural stability, surface formation and construction method. Tensegrity systems are flexible structures which are reticulated spatial structures composed of compressive members and
cables. The rigidification of tensegrity systems is related to selfstress states which can be achieved only when geometrical and mechanical requirements are simultaneously satisfied. In this paper,
the force density method allowing form-finding for tensegrity systems is presented. And various modules of unit-structures are investigated and discussed using the force density method. Also, a model
of double-layered single curvature arch with quadruplex using supplementary cable is presented.
2001.12 KCI 등재 구독 인증기관 무료, 개인회원 유료
The structural behaviors of anisotropic laminated shells are quite different from that of isotropic shells, Also, the classical theory of shells based on neglecting transverse shear deformation is
invalid for laminated shells. Thus, to obtain the more exact behavior of laminated shells, effects of shear deformation should be considered in the analysis. As the length of x-axis or y-axis is
increase, the effects of transverse shear deformation are decrease because the stiffness for the axis according to the increasing of length is large gradually. In this paper, the governing equations
for anisotropic laminated shallow shell including the effects of shear deformation are derived. And then, by using Navier's solutions for shallow shells having simple supported boundary, extensive
numerical studies for anisotropic laminated shallow shells were made to investigate the effects of shear deformation for 3 typical shells. Also, static analysis is carried out for cross-ply laminated
shells considering the effects of various geometrical parameters, e,g., the shallowness ratio, the thickness ratio and the ratio of a(length of x-axis)-to-b(length of y-axis). The results are
compared with existed one and show good agreement. | {"url":"https://db.koreascholar.com/Search/Result?field=a&query=%EA%B6%8C%EC%9D%B5%EB%85%B8","timestamp":"2024-11-10T16:04:24Z","content_type":"text/html","content_length":"40307","record_id":"<urn:uuid:0a319782-2165-4f2b-9e17-749f3e1ccd87>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.60/warc/CC-MAIN-20241110134821-20241110164821-00188.warc.gz"} |
What is the zero method in Clojure numbers?
We use the zero method to test if a number is zero.
(zero? number)
Syntax for zero method
The zero method accepts just one parameter, the number itself, as illustrated in the syntax section.
Return value
The zero method returns true if the number is 0 and false if the number is greater or less than 0.
We use the zero method to ensure that the calculations we are making does not include a zero. Thus, we use the zero method to test the number. Let's look at the example below:
(ns clojure.examples.hello
;; This program displays Hello World
(defn zerro []
(def x (zero? 0))
(println x)
(def x (zero? -1))
(println x)
(def x (zero? 9))
(println x))
From the code above:
• Line 5: We define a function zerro.
• Line 6: We pass in 0 into the zero method.
• Line 7: We print the output, notice that the output we get is true because 0 is 0 .
• Line 9: We pass in -1 into the zero method.
• Line 10: We print the output, notice that the output we get is false because -1 is not 0 .
• Line 12: We pass in 9 into the zero method.
• Line 13: We print the output, notice that the output we get is false because 9 is an odd number and not 0.
• Line 14: We call our zerro function to execute the code. | {"url":"https://www.educative.io/answers/what-is-the-zero-method-in-clojure-numbers","timestamp":"2024-11-03T01:18:28Z","content_type":"text/html","content_length":"137658","record_id":"<urn:uuid:27dc636e-8a1c-421b-8572-fb48e12ecac0>","cc-path":"CC-MAIN-2024-46/segments/1730477027768.43/warc/CC-MAIN-20241102231001-20241103021001-00188.warc.gz"} |
Notes - Shunting Yard Algorithm
The shunting yard algorithm is an algorithm to take an infix expression and convert it to reverse polish notation. This way we can then use a stack to process the expression and make evaluation much
I've written this algorithm before but usually I take what is on wikipedia and translate it. I'm hoping that writing it down this time will help intuit what is going on with the stack juggling and
taking an infix expression and converting it.
I also want to extend this algorithm to handle functions, array subscripts and string subscripts for BASIC specifically.
My main resources are the wikipedia pages for the Shunting Yard Algorithm and the Operator Precedence page.
This was much simpler to write and reason about once I wrote my stack implementation.
The first step is to set up two stacks. The first stack will be our output stack, this is what will hold the final reverse polish notation. The second stack is the operator stack. This is where
operators will move in an out of.
DIM OUT.STACK(STACK.SIZE)
MAT OUT.STACK = ''
DIM OP.STACK(STACK.SIZE)
MAT OP.STACK = ''
PARSE.TOKENS.LEN = DCOUNT(EXPRESSION,@AM)
Now that we have everything set up, we can then loop through a list of tokens and process them. The first thing we need to do is get the current token and check if it is an operator or a regular
value. If it is a regular value, we will push it on to the output stack. If it's an operator we will push it to the operator stack.
LOCATE(PARSE.TOKEN,OPERATORS,1;OP.POS) ELSE
CALL STACK.PUSH(MAT OUT.STACK,STACK.SIZE,PARSE.TOKEN)
This is for illustration purposes, the full code is more involved and is below. This get's point across though. If the token isn't an operator, then we add it to the output stack.
Now if the token is an operator we have something to do. We will add the token to the operator stack. However before we do, we'll check if there are any operators in the stack that have a higher
precedence than the token we are currently processing. If there is a token with a higher precedence, we will move it to the output stack. We will keep doing this until we get to a token with a lower
Once we have a token left on the operator stack that is lower than the new token, we will then add the new token to the operator stack.
That is the core of the shunting yard algorithm.
IF OP.STACK(1) > 1 THEN
CALL STACK.PEEK(MAT OP.STACK,STACK.SIZE,VALUE)
CURRENT.PRECEDENCE = VALUE<1,2>
END ELSE
CURRENT.PRECEDENCE = 0
IF NEW.ASSOC = RIGHT THEN
POP.FLAG = CURRENT.PRECEDENCE <= NEW.PRECEDENCE
END ELSE
POP.FLAG = CURRENT.PRECEDENCE < NEW.PRECEDENCE
UNTIL POP.FLAG DO
CALL STACK.POP(MAT OP.STACK,STACK.SIZE,VALUE)
CALL STACK.PUSH(MAT OUT.STACK,STACK.SIZE,VALUE<1,1>)
VALUE = PARSE.TOKEN : @VM : NEW.PRECEDENCE
CALL STACK.PUSH(MAT OP.STACK,STACK.SIZE,VALUE)
Here we loop over the operator stack and move an operator if it has a higher precedence than the new token we are adding.
We also have some logic to check the associativity. If it is right associative like exponents, we want to move the operator if it equal precedence, if it's left associative then we want it to be when
the operator precedence is less than the new token we are adding.
We follow this logic for all the tokens in the expression. At the end we will have an output stack and an operator stack.
The final step is to move everything in the operator stack to the output stack.
FOR OP.STACK.CTR = OP.STACK(1) TO 2 STEP -1
CALL STACK.POP(MAT OP.STACK,STACK.SIZE,VALUE)
CALL STACK.PUSH(MAT OUT.STACK,STACK.SIZE,VALUE<1,1>)
NEXT OP.CTR
Voila! With that the infix expression is now made into a postfix expression that will be easier to evaluate.
The full code is below and this handles the [] substring operator, <> the array operator and the () function operators. This is better than my previous attempt at parsing and evaluating expressions
as this moves the logic into the postfix notation rather than having more parsing logic deeper down in the evaluate function.
EQU DEBUG.STACK TO 1
EQU TRUE TO 1
EQU FALSE TO 0
EQU LEFT TO 0
EQU RIGHT TO 1
FUNCTION.PRECEDENCE = 15
OPERATORS = ''
OPERATORS<1> = '+ - * / ** [] <>'
OPERATORS<2> = '12 12 13 13 14 15 15'
OPERATORS<3> = '0 0 0 0 1 0'
CONVERT ' ' TO @VM IN OPERATORS<1>
CONVERT ' ' TO @VM IN OPERATORS<2>
CONVERT ' ' TO @VM IN OPERATORS<3>
EQU STACK.SIZE TO 15
EXPRESSION = ''
EXPRESSION<-1> = '3'
EXPRESSION<-1> = '+'
EXPRESSION<-1> = '4'
EXPRESSION<-1> = '*'
EXPRESSION<-1> = '2'
EXPRESSION<-1> = '/'
EXPRESSION<-1> = '('
EXPRESSION<-1> = '1'
EXPRESSION<-1> = '-'
EXPRESSION<-1> = '5'
EXPRESSION<-1> = ')'
EXPRESSION<-1> = '**'
EXPRESSION<-1> = '2'
EXPRESSION<-1> = '**'
EXPRESSION<-1> = '3'
PRINT 'Expression: ' : EXPRESSION
CALL PRINT.STACK(MAT OUT.STACK,STACK.SIZE)
********************* S U B R O U T I N E *********************
DIM OUT.STACK(STACK.SIZE)
MAT OUT.STACK = ''
DIM OP.STACK(STACK.SIZE)
MAT OP.STACK = ''
PARSE.TOKENS.LEN = DCOUNT(EXPRESSION,@AM)
FOR PARSE.CTR = 1 TO PARSE.TOKENS.LEN
IF DEBUG.STACK THEN
PRINT 'Output:' :
CALL PRINT.STACK(MAT OUT.STACK,STACK.SIZE)
PRINT 'Operator:' :
CALL PRINT.STACK(MAT OP.STACK,STACK.SIZE)
PARSE.TOKEN = EXPRESSION<PARSE.CTR>
NEXT.TOKEN = EXPRESSION<PARSE.CTR+1>
IF PARSE.TOKEN = ',' THEN
IF PARSE.TOKEN = '(' THEN
CALL STACK.PUSH(MAT OP.STACK,STACK.SIZE,PARSE.TOKEN)
IF PARSE.TOKEN = ')' THEN
CALL STACK.POP(MAT OP.STACK,STACK.SIZE,VALUE)
UNTIL VALUE<1,1> = '(' DO
CALL STACK.PUSH(MAT OUT.STACK,STACK.SIZE,VALUE<1,1>)
IF PARSE.TOKEN = '[' THEN
VALUE = PARSE.TOKEN : @VM : 0
CALL STACK.PUSH(MAT OP.STACK,STACK.SIZE,VALUE)
IF PARSE.TOKEN = ']' THEN
CALL STACK.POP(MAT OP.STACK,STACK.SIZE,VALUE)
UNTIL VALUE<1,1> = '[' DO
CALL STACK.PUSH(MAT OUT.STACK,STACK.SIZE,VALUE<1,1>)
CALL STACK.PUSH(MAT OUT.STACK,STACK.SIZE,'[]')
IF PARSE.TOKEN = '<' THEN
VALUE = PARSE.TOKEN : @VM : 0
CALL STACK.PUSH(MAT OP.STACK,STACK.SIZE,VALUE)
IF PARSE.TOKEN = '>' THEN
CALL STACK.POP(MAT OP.STACK,STACK.SIZE,VALUE)
UNTIL VALUE<1,1> = '<' DO
CALL STACK.PUSH(MAT OUT.STACK,STACK.SIZE,VALUE<1,1>)
CALL STACK.PUSH(MAT OUT.STACK,STACK.SIZE,'<>')
LOCATE(PARSE.TOKEN,OPERATORS,1;OP.POS) ELSE
IS.FUNCTION = FALSE
IF NEXT.TOKEN = '(' THEN
IS.FUNCTION = TRUE
IF IS.FUNCTION THEN
VALUE = PARSE.TOKEN : @VM : FUNCTION.PRECEDENCE
CALL STACK.PUSH(MAT OP.STACK,STACK.SIZE,VALUE)
END ELSE
CALL STACK.PUSH(MAT OUT.STACK,STACK.SIZE,PARSE.TOKEN)
NEW.PRECEDENCE = OPERATORS<2,OP.POS>
NEW.ASSOC = OPERATORS<3,OP.POS>
IF OP.STACK(1) > 1 THEN
CALL STACK.PEEK(MAT OP.STACK,STACK.SIZE,VALUE)
CURRENT.PRECEDENCE = VALUE<1,2>
END ELSE
CURRENT.PRECEDENCE = 0
IF NEW.ASSOC = RIGHT THEN
POP.FLAG = CURRENT.PRECEDENCE <= NEW.PRECEDENCE
END ELSE
POP.FLAG = CURRENT.PRECEDENCE < NEW.PRECEDENCE
UNTIL POP.FLAG DO
CALL STACK.POP(MAT OP.STACK,STACK.SIZE,VALUE)
CALL STACK.PUSH(MAT OUT.STACK,STACK.SIZE,VALUE<1,1>)
VALUE = PARSE.TOKEN : @VM : NEW.PRECEDENCE
CALL STACK.PUSH(MAT OP.STACK,STACK.SIZE,VALUE)
NEXT PARSE.CTR
FOR OP.STACK.CTR = OP.STACK(1) TO 2 STEP -1
CALL STACK.POP(MAT OP.STACK,STACK.SIZE,VALUE)
CALL STACK.PUSH(MAT OUT.STACK,STACK.SIZE,VALUE<1,1>)
NEXT OP.CTR
* END OF PROGRAM | {"url":"https://nivethan.dev/devlog/notes---shunting-yard-algorithm.html","timestamp":"2024-11-11T21:40:55Z","content_type":"text/html","content_length":"19719","record_id":"<urn:uuid:1457b802-21ab-4dc1-9662-e0c3d1928062>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00487.warc.gz"} |
11+ State Diagram Digital Logic | Robhosking Diagram11+ State Diagram Digital Logic
11+ State Diagram Digital Logic
11+ State Diagram Digital Logic. Digital logic is the basis of electronic systems, such as. Guy even and moti medina.
multiplexer – Help building Digital Logic Circuit (from … from i.stack.imgur.com
These states are labelled inside the circles as shown in figure, there are two parts present in moore state machine. Realizing logical expressions using different logic gates and comparing their
performance. In this case we see that there are 4 possible transitions.
Logic diagrams have several applications in investigations, and are most often developed in an iterative fashion.
11+ State Diagram Digital Logic. The book covers the material of an introductory course in digital logic design including an introduction to we use the simplied timing diagrams from the notes of
litman 9. Logic diagrams have several applications in investigations, and are most often developed in an iterative fashion. Digital logic and state machine design. The digital systems which are based
on two voltage values • drawings, diagrams and pictures: | {"url":"https://robhosking.com/11-state-diagram-digital-logic/","timestamp":"2024-11-06T04:10:03Z","content_type":"text/html","content_length":"64925","record_id":"<urn:uuid:5829613d-b398-44aa-82cc-d0d831803a08>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00083.warc.gz"} |
7 Examples of the Spacing Effect
The spacing effect is the tendency for long-term memory to be increased when learning events are spaced in time. This has broad implications for education, communication and marketing. The following
are illustrative examples of the spacing effect.
Spaced Practice
Spaced practice is the process of learning the same information in separate sessions over several days or weeks. This is thought to improve long-term retention of knowledge. For example, studying a
vocabulary list for 10 minutes every day for a week may result in permanent memorization of the vocabulary where studying the list for 70 minutes consecutively may only result in short term
memorization of the list.
Cramming is the process of trying to remember or learn a great deal of information in a short period of time, usually in preparation for a pending test, job interview or task. This is discouraged by
educators as it is thought to result in shallow learning that isn't retained or useful. It is a commonly adopted principle of communication that it is better to overcommunicate than under
communicate. People do remember things that they hear many times but can be remarkably good at filtering any message that feels uninteresting. If it takes 4 repetitions for people to remember a
communication and they only listen 25% of the time then it may take 16 communications for them to remember your message.The spacing effect is well known to marketers who can directly measure this
with conversion testing whereby consumers are more likely to respond to promotions that they have seen several times over a few hours or days. Marketers use both spaced repetition and massed
repetition to increase the results of campaigns. For example, you might see the same promotion multiple times on the same page and then continue to see it on a device for several days in a row.
Brand Recognition
Brand recognition is the ability for consumers to recognize a brand by its name and visual symbols. People tend to prefer products that they recognize, even if they have no actual information about
the brand. As such, firms may produce advertising that does nothing more than feature brand symbols in a positive context. Due to the spacing effect, consumers may not develop brand recognition until
they have seen many such commercials over a period of time.
Testing Effect
The testing effect is the tendency for people to remember information when they are asked to recall it. For example, using flashcards to quiz yourself on something you're trying to remember. The
testing effect is often used in combination with the spacing effect to enhance learning productivity.
Memory Reinforcement
After you have learned something, it is helpful to recall it again to reinforce the memory. For example, you will quickly lose vocabulary in a second language if you aren't exposed to that language
for months or years. Memory reinforcement can occur with extremely infrequent learning events such as a word you heard once a year.
The theory that learning efficiency and long term retention of knowledge increases as you space out learning into multiple sessions over many days. Next: Learning Curve | {"url":"https://simplicable.com/edu/spacing-effect","timestamp":"2024-11-04T14:35:57Z","content_type":"text/html","content_length":"75381","record_id":"<urn:uuid:96ba61cb-ab2e-43a0-bb3a-776e9cc22a6e>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00817.warc.gz"} |
[GiF] A possible model of an impossible cube of M.C. Escher
30648 Views
4 Replies
41 Total Likes
[GiF] A possible model of an impossible cube of M.C. Escher
Imagine you would like to 3D print an impossible cube of M.C. Escher, how would you do this? Take a look at the image below, but don't scroll down yet to see how it is made. It is real 3D graphics
built upon only possible geometries, so there should be a trick to it. Try to notice some details that will give it out. The image is not perfectly constructed, so look for betraying inconsistencies.
The cube was invented by M.C. Escher for Belvedere, a lithograph in which a boy seated at the foot of the building holds an impossible cube (below is a fragment). The impossible cube draws upon the
ambiguity present in a Necker cube illustration; an impossible cube is usually rendered as a Necker cube in which the edges are apparently solid beams.
Designing a good optical illusion requires polishing little things. In this particular method of constructing one would need to know a bit about:
• plane curves in 3D space
• varying thickness of a spline
• controlling the reflection of light
There are alternative ways to construct it, for instance, cutting the edges:
but here I will follow a different trick illustrated below, which I saw originally in Pierpaolo Andraghetti's video.
I start from simply drawing a cube from built-in data:
v = PolyhedronData["Cube", "VertexCoordinates"];
i = PolyhedronData["Cube", "EdgeIndices"];
Graphics3D[{Orange, Specularity[White, 20], GraphicsComplex[2 v, Tube[i, .1]]}, Boxed -> False]
We used Tube and Specularity, which greatly increase 3D depth perception, especially for seemingly crossing edges. To replace a cube's edge with a illusion-curve I need an easy way to make it. I
suggest making a very simple 2D spline:
pts = {{-1, -1}, {2.5, -2}, {2.5, -1}, {-1, 1}};
{PointSize[.1], Red, Point[{1, -1}]},
{BSplineCurve[pts], Green, Line[pts], Red, Point[pts]}}, Frame -> True]
which as you can see "hugs" the red dot, - a mark for $(-1,1)$ coordinate. This visually guarantees the curve extends well enough beyond other perpendicular edge to create an impossible crossover
illusion. Next we add an extra coordinate to all points and place this 2D spline into 3D:
pts3D = Transpose[Transpose[pts]~Join~{ConstantArray[-1, 4]}];
{{BSplineCurve[pts3D], Green, Line[pts3D], Red, Point[pts3D]},
{Orange, Specularity[White, 20], GraphicsComplex[2 v, Tube[i, .1]]}},
Boxed -> False, SphericalRegion -> True]
Next I apply rotation around the "illusion" edge:
{{Thick, Rotate[BSplineCurve[pts3D], a Degree, {0, 1, 0}, {-1, -1, -1}]},
{Orange, Specularity[White, 20], GraphicsComplex[2 v, Tube[i, .1]]}},
Boxed -> False, SphericalRegion -> True, PlotRange -> 2]
, {{a, -65, "angle"}, 0, -90}]
We finally make a first model:
{{Orange, Specularity[White, 20],
Rotate[Tube[BSplineCurve[pts3D], .09], -65 Degree, {0, 1, 0}, {-1, -1, -1}]},
{Orange, Specularity[White, 20], GraphicsComplex[2 v, Tube[Delete[i, 2], .09]]}},
Boxed -> False, SphericalRegion -> True]
As you can see it is not good. Too much light reflection pinpoints curvature of the "illusion"-edge. Also it should be slightly less thick because it should be most remote, but in reality it is of
course is very close to viewer in the middle. The thickness can be fixed with variable spline thickness. For our example we need a tiny unnoticeable thickness variation, so here is an example for
Graphics3D[{Red, CapForm["Round"],
Tube[BSplineCurve[{{0, 0, 0}, {1, 1, 0}, {1.2, 2, 0}, {.6, 1.8, 0},
{0, 1.3, 0}, {-.6, 1.8, 0}, {-1.2, 2, 0}, {-1, 1, 0}, {0, 0,0}}],
{.1, .1, .1, .1, .3, .1, .1, .1, .1}]}]
And the light is fixed by removing Specularity and providing a few sources to uniformly illuminate the "illusion"-edge:
{{Rotate[Tube[BSplineCurve[pts3D],{.09,.06,.06,.09}],-65 Degree,{0,1,0},{-1,-1,-1}]},
And this is much better, but once you know the trick you can notice light variations that betray curvature. There is a lot of room for improvement of course, feel free to post your ideas. I would
need to take a better care of corner junctions bending the spline as Pierpaolo Andraghetti did. The original by Pierpaolo Andraghetti is exquisitely crafted, a beautiful work, nevertheless you still
can see imperfections. For example, his beam, is rectangular as contrasted with mine which is round. If you look carefully along Pierpaolo's "illusion"-edge you can notice that sharp edge is getting
vague, relative to other vertical edges. Constructing this in real life perfectly is a challenge, lighting is subtle. I think the best would be to give little lighting to allow the brain to "guess"
and imagine the rest. This and other code for making GiFs is in the attached notebook.
4 Replies
I was inspired by the "Impossible Cube" and wanted to apply similar ideas to a chair model I had previously been working on. This resulted in the tentative making of an "Impossible Chair."
I enjoyed that post of your very much, @Erik (actually I enjoyed all of your post:-) ). Yes, the idea with mirrors is excellent. I, indeed, should try to 3D print and take some photos.
Very interesting! Reminded me of my past contributions on "ambiguous rings etc..." Was rightly coined as "shape shifting" by the Moderation Team. If your Escher-like cube would be 3D printed, you
could demonstrate using two perpendicular mirrors as I demonstrated here. This will split the shapes of the cube as seen from two different viewpoints. This way, one mirror will show a the intended
Escher-cube while the other mirror will clearly unveil the optical illusion!
Be respectful. Review our Community Guidelines to understand your role and responsibilities. Community Terms of Use | {"url":"https://community.wolfram.com/groups/-/m/t/875044?sortMsg=Recent","timestamp":"2024-11-04T22:22:59Z","content_type":"text/html","content_length":"118257","record_id":"<urn:uuid:6ff769bd-6893-4a30-b1b7-f47e87811817>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.16/warc/CC-MAIN-20241104194528-20241104224528-00161.warc.gz"} |
Courses - Institute for Advanced Physical Studies
Lecturer: Vesselin Gueorguiev, Vladimir Gerdjikov, Stoyan Mishev
This doctoral level lecture course is intended to audience interested in theoretical physics and mathematics. Its purpose is to introduce the theory of semisimple Lie algebras so that the student
could master their Cartan-Weyl basis, as well as to become familiar with important basic structures such as the root and weight systems, which are needed for constructing finite-dimensional
irreducible representations. The final goal is the construction of the graded Lie algebras and the related Kac-Moody algebras. These are basic tools in contemporary theoretical and mathematical
physics. They are fundamental tools for the infinite-dimensional completely integrable Hamiltonian systems and to a number of problems in quantum mechanics, statistical physics and others. | {"url":"http://iaps.institute/courses/","timestamp":"2024-11-13T08:27:35Z","content_type":"text/html","content_length":"46452","record_id":"<urn:uuid:3e53f718-ba22-45e4-b59b-ac43fb1eaefa>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00719.warc.gz"} |
Angles of Polygons In this section, we review the names of polygons based on the number of sides, and learn about the interior and exterior angles of a polygon. Specifically, we explore the sum of
the interior angles and the sum of the exterior angles of convex polygons. Polygon Investigation Alternatively, watch the video below [...] | {"url":"https://systry.com/tag/polygons/","timestamp":"2024-11-04T02:41:54Z","content_type":"text/html","content_length":"23595","record_id":"<urn:uuid:481b3769-0d4d-4f4b-934c-b706c2114482>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00323.warc.gz"} |
Asif Rahman
Nowcasting: Maintaining real time estimates of infrequently observed time series
Time series analysis appears in every disciple from physiology to retail pricing. A time series variable is typically measured sequentially at fixed intervals of time (often equispaced but not
necessarily). Variables may be measured less frequently than theoretically possible for reasons of cost, effort, or convention. With local level linear trend models we can maintain realtime measures
of infrequently measured values (see Predicting the Present with Bayesian Structural Time Series). The problem has been referred to as nowcasting because the goal is to maintain a current estimate of
the value of a time series by forecasting the current value instead of the future value. The term itself is not very important as the task is essentially a standard forecasting problem.
Consider a measurement like US weekly initial claims for unemployment (ICNSA), which is a recession leading indicator. Can we learn this week’s number before it is released? To answer this question
we would need a real time signal correlated with the outcome (ICNSA numbers). We can use Google Correlate to extract the top 100 search terms that are most correlated with the ICNSA signal. Google
Correlate finds search terms that vary in a similar way to your own time series, ICNSA signal in our case. The 100 search term time series signals are our explanatory (also caled exogenous) variables
that can be included as regressors to improve the ICNSA forecast performance. The idea is that contemporaneous signals (exogenous variables) are correlated in time with the unobserved signal (
endogenous variable) we are trying to estimate and by regressing on these features can improve our forecast. The temporal structure in these observed signals can be exploited to infer the behaviour
of an unobserved signal. Here we will explore using structural time series models that decompose a signal into additive components consisting a linear trend and a mean level.
US weekly initial claims for unemployment (ICNSA)
Brief description of structural time series models
The general approach to time series analysis is to first remove or model the parts that change through time to get a stationary series (a time series is stationary if its statistical properties, like
variance, don’t change through time). Next, we use a time series model to capture the correlation in the stationary series. A series can be decomposed into:
• trend components (long-term change in the mean level)
• seasonality component (variation in mean that is periodic in nature and you generally know the period beforehand)
• cycles (variation that oscillates but not according to some known or fixed period)
• exogenous variables that have some correlation with the endogenous variable
• noise
The various components can be combined additively to model the endogenous variable \(y\) at time \(t\). Such additive models are desirable because we can interpret each term, progressively increase
model complexity, and easily diagnose model performance. More concretely a typical model will be written as:
\[ y_t=\mu_t+\gamma_t+\beta^Tx_t+\epsilon_t \]
where \(y_t\) is the endogenous variable we want to forecast, \(\mu_t\) captures changes in the mean level over time, \(\gamma_t\) models the periodic nature of the signal, \(\beta^T\boldsymbol{x}_t
\) is a regression term with exogenous variables and \(\epsilon_t\) is the noise term.
The local linear trend model decomposes the time series into a local level component and a trend component.
\[ \mu_t = \mu_{t-1}+\delta_{t-1}+u_t \]
\[ \delta_t = \delta_{t-1}+v_t \]
The current level of the trend is \(\mu_t\), the current “slope” of the trend is \(\delta_t\), and the noise terms are \(u_t\) and \(v_t\).
This kind of model is referred to as UnobservedComponents in statsmodels.
from statsmodels.tsa.statespace.structural import UnobservedComponents
# train on all time points before this and forecast time points after
interventionidx = 200
# df: dataframe with ICNSA and exogenous variables
# regression_columns: exogenous variables
intervention = df.index[interventionidx]
model = UnobservedComponents(
df.loc[:intervention, 'ICNSA'].values,
exog = df.loc[:intervention, regression_columns].values,
level = 'local linear trend'
fit = model.fit(maxiter=1000)
We can compare a few models: without exogenous variables from Google Correlate, with the top 10 most correlated search terms, and with the bottom 10 least correlated search terms. The figures below
show the ICNSA values in blue and the model predictions in red. The model is trained on observations until 2008 (vertical dashed line) and forecasts are made for the unobserved time after 2008. 95%
confidence intervals are in grey.
It’s clear that adding additional features to the model improves both the fit to the observed data and the forecast. But adding uncorrelated data can have undesired effects on your forecasts. The
unobserved components model in statsmodels is unable to pick the best features since it does not have any kind of regularization. Ideally, we want to select only those correlated search terms that
gives the best model fit and forecast. The original paper on Bayesian Structural Time Series model provides a methodology for feature selection.
In addition to applications in forecasting, state space models like the one described above can be used to infer the effect of an intervention, like an ad campaign, for counterfactual inference (see
Inferring Causal Impact from Bayesian Structural Time-Series Models by Kay Brodersen et. al. (2015))
Useful references: | {"url":"https://asifr.com/nowcasting","timestamp":"2024-11-06T08:54:06Z","content_type":"text/html","content_length":"12589","record_id":"<urn:uuid:a32b1c80-d8ec-4133-b306-63363a7f8047>","cc-path":"CC-MAIN-2024-46/segments/1730477027910.12/warc/CC-MAIN-20241106065928-20241106095928-00002.warc.gz"} |
RLE :: Computational Prototyping Group
This page contains journal papers as well as conference papers. Alumni theses can be found in the alumni section.
Papers in Refereed Journal
1. J. White, F. Odeh, A.S. Vincentelli, and A. Ruehli, "Waveform Relaxation: Theory and Practice," Trans. Of the Society for Computer Simulation, vol. 2, no. 2, June 1985, pp. 95-133.
2. K. Kundert, J. White, A. Sangiovanni-Vincentelli, "A Mixed Frequency-Time Approach for Distortion Analysis of Switching Filter Circuits." IEEE Journal of Solid State Circuits, vol. 24, No. 2,
April 1989, pp. 443-451.
3. R. Saleh, J. White, "Accelerating Relaxation Algorithms for Circuit Simulation Using Waveform-Newton and Step-Size Refinement," IEEE Transactions on Computer-Aided Design, vol.9, no. 9, Sept.
1990, pp. 951-958.
4. J. White and S. Leeb, "An Envelope-Following Approach to Switching Power Converter Simulation," IEEE Transactions on Power Electronics, vol. 6, No.2, April 1991, pp. 303-308.**
5. K. Nabors and J. White, "Fast-Cap: A Multipole-Accelerated 3-D Capacitance Extraction Program," IEEE Transactions on Computer-Aided Design, vol.10, no. 10, November 1991, p. 1447-1459.
6. J. White and F. Odeh, "Connecting Waveform Relaxation Convergence Properties to the A-stability of Multitirate Integration Methods," COM-PEL, vol. 10, no. 4, December, 1991, pp. 497-508.
7. S. Devadas, K. Keutzer, J. White, "Estimation of Power Dissipation in CMOS Combinational Circuits Using Boolean Function Manipulation," IEEE Transactions on Comp. Aided Design, vol. 11, , no. 3,
March 1992, p. 373-383.
8. S.D. Senturia, R.M. Harris, B.P. Johnson, S. Kim, K. Nabors, M. A. Shulman, and J.K. White, "A Computer-Aided Design System for Microelectromechanical Systems (MEMCAD)," IEEE Journal of
Microelectromechanical Systems, March 1992, vol. 1, no. 1, p.3-13.**
9. H. Neto, L. Miguel Silveira, J. White, L.M. Vidigal, "On Exponential Fitting for Circuit Simulation," IEEE Transactions on Computer-Aided Design, May 1992, vol. 11, vol. 5, p. 566-574.**
10. K. Nabors, S. Kim and J. White, "Fast Capacitance Extraction of General Three-Dimensional Structures," IEEE Trans. On Microwave Theory and Techniques, July 1992, vol.40, no.7, p. 1496-1507.
11. K. Rahmat, J. White, and D. Anotoniadis, "Computation of Drain and Substrate Currents in Ultra-Short-Channel nMOSFET's Using the Hydrodynamic Model," IEEE Trans. on Computer-Aided Design, June
1993, vol. 12, no.6 p. 817- 825.
12. K. Nabors, and J. White, "Multipole-Accelerated Capacitance Extraction Algorithms for 3-D Structures with Multiple Dielectrics," IEEE Trans. on Circuits and Systems, November 1992, vol. 39 no.11,
p. 946-954.**
13. A. Lumsdaine, L.M. Silveira, and J. White, "Massively Parallel Simulation Algorithms for Grid-Based Analog Signal Processors," IEEE Trans. on Computer-Aided Design, November 1993, vol. 12, no.
11, p. 1665-1679.
14. J.R. Phillips, H. Van der Zant, J. White, and T. Orlando, "Influence of Induced Magnetic Fields on the Static Properties of Josephson-Junction Arrays," Physical Review B, vol. 47, 1993, p.
15. K. Nabors, F.T. Korsmeyer, F.T. Leighton, and J. White, "Multipole Accelerated Preconditioned Iterative Methods for Three-Dimensional Potenetial Integral Equations of the first Kind," SIAM J. on
Sci. and Stat. Comp., May 1994, vol.15, no.3, p. 713-735.**
16. X. Cai, P. Osterberg, H. Yie, J. Gilbert, S. Senturia and J. White, "Self-Consistent Electromechanical Analysis of Complex 3-D Microelectromechanical Structures using a Relaxation/Multipole
Method," To Appear, International Journal of Sensors and Materials.**
17. A. Lumsdaine and J. White, "Accelerating Waveform Relaxation Methods with Application to Parallel Semiconductor Device Simulation," Numerical Functional Analysis and Optimization, vol. 16 no.3-4,
p.395-414, Marcel Dekker, 1995.**
18. M. Kamon, M. J. Tsuk and J. White, "FASTHENRY: A Multipole-Accelerated 3-D Inductance Extraction Program," IEEE Trans. on Microwave Theory and Techniques, September 1994, vol. 42, no.9, p.
19. L.M. Silviera, I. Elfadel, J. White, M. Chilukura and K. Kundert, "Efficient Frequency-Domain Modeling and Circuit Simulation of Transmission Lines," IEEE on Components, Hybrids, and
Manufacturing Technology-Part B: Advanced Packaging, special issue on Electrical Performance of Electrical Packaging, vol. 17, no. 11, pp. 505-513, November 1994.**
20. M. Reichelt, J. White, J. Allen, "Optimal Convolution SOR Acceleration of Waveform Relaxation with Application to Parallel Simulation of Semiconductor Devices" SIAM J. on Scientific Computing,
vol. 16, no.5, pp. 1137-1158, September 1995. **
21. J.R. Phillips, H.S. J. van der Zant, J. White, and T.P. Orlando, "Influence of Induced Magnetic Fields on Shapiro Steps in Josephson-Junction Arrays," Physical Review B, vol. 50, 1994,
22. L. Miguel Silveira, Mattan Kamon and Jacob White, "Algorithms for Coupled Transient Simulation of Circuits and Complicated 3-D Packaging," IEEE Transactions on Components, Hybrids, and
Manufacturing Technology-Part B: Advanced Packaging, special issue on the Electrical Performance of Electronic Packaging, vol. 18, no.1, pp. 92-98, February, 1995.
23. L. Miguel Silveira, Mattan Kamon and Jacob K. White, "Efficient Reduced-Order Modeling of Frequency -Dependent Coupling Inductances associated with 3-D Interconnect Structures," IEEE Transactions
on Components, Packaging and Manufacturing Technology-Part B: Advanced Packaging, vol. 19, no. 2, pp. 283-288, May 1996.**
24. A. Lumsdaine, M. Reichelt an J. White, "Accelerated Waveform Methods for Parallel Transient Simulation of Semiconductor Devices," IEEE Trans. on Computer-Aided Design, July 1996, vol. 15, no. 7,
p. 716-726.**
25. K. Rahmat, J. White, D. Antoniadis, "Simulation of Semiconductor Devices using a Galerkin/Spherical Harmonics Expansion Approach to Solving the Coupled Poisson/Boltzmann System," IEEE Trans. On
Computer-Aided Design, October 1996, vol. 15, no. 10, p.1181-1196.
26. J. Monteiro, S. Devadas, A. Ghosh, K. Keutzer and J. White, "Estimation of Average Switching Activity in Combinational Logic Circuits Using Symbolic Simulation'', IEEE Transactions on
Computer-Aided Design of Integrated Circuits and Systems, Volume 16, Issue 1, Jan. 1997, pp. 121 -127.
27. S. Senturia, N. Aluru, and J. White, "Simulating the Behavior of MEMS Devices: Computational 3-D Structures," IEEE Computational Science and Engineering, Jan.-March 1997, vol. 16, no.10, p.
28. J.R. Phillips and J. K. White, "A Precorrected-FFT method for Electrostatic Analysis of Complicated 3-D Structures," IEEE Trans. on Computer-Aided Design, October 1997, vol. 16, no.10,
29. M. Chou and J.K. White, "Efficient Formulation and Model-Order Reduction for the Transient Simulation of Three-dimensional VLSI Interconnect," IEEE Trans. on Computer-Aided Design, December 1997,
vol.16, no. 12, p. 1454-1476.
30. J. Tausch and J. White, "Boundary Integral Solution of Laplace's Equation with Highly Varying Coefficients. Numerical Treatment of Multi-scale Problems," (Kiel, 1997), 156--167, Notes Numer.
Fluid Mech., 70, Vieweg, Braunschweig, 1999.
31. J. Tausch and J. White, "Second-Kind Integral Formulations for the Capacitance Problem," Adv. In Comput. Math. 1998, vol. 9, p. 217-232.
32. J. Tausch and J. White, "Capacitance Extraction of 3-D Conductor Systems in Dielectric Media with high Permittivity Ratios," IEEE Trans. Microwave Tech., January 1999, vol. 47, no.1, p.18-26.
33. L.M. Silveira, I. Elfadel, M. Kamon and J. White, "A Coordinate-Transformed Arnoldi Algorithm for Generating Guaranteed Stable Reduced-Order Models of RLC Circuits," Special Issue of Comp.
Methods in Appl. Mech. And Eng. On Advances in Comp. Methods in Electromagnetics, February 1999, vol. 169/3-4, p. 377-389.
34. M. Kamon, N. Marques, L.M. Silviera and J. White, "Automatic generation of Accurate Circuit Models of 3-D Interconnect," IEEE Transactions on Components, Packaging, and Manufacturing
Technology-Part B. Advanced Packaging , August, 1998, vol. 21.no.3, pp. 225-240.
35. L. Daniel, C. R. Sullivan and S. R. Sanders. “Design of Microfabricated Inductors”, IEEE Transactions on Power Electronics, Vol. 14, No. 4, July 1999
36. N. R. Aluru and J. White, "A Multilevel Newton Method for Mixed-energy Domain Simulation of MEMS," IEEE Journal of Microelectromechanical Systems, Volume 8, Issue 3, Sept. 1999, Page(s): 299
37. D. Ramaswamy, W. Ye, X. Wang and J. White, "Fast Algorithms for 3-D Simulation," Journal of Modeling and Simulation Microsystems, vol. 1, no. 1 p. 77-82, December, 1999.
38. M. Kamon, F. Wang and J. White, "Generating Nearly Optimally Compact Models from Krylov Subspace Basedreduced-order Models," IEEE Transactions on Circuits and Systems II: Analog and Digital
Signal Processing, Volume 47, No. 4, April 2000.
39. D. Kring, T. Korsmeyer, J. Singer, and J. White, "Analyzing mobile offshore bases using accelerated boundary-element methods'' Marine Structure (Elsevier Science), volume 13(4-5), 2000, pp. 301
-- 313
40. T. Mukherjee, G. Fedder and J. White, "Emerging Simulation Approaches For Micromachined Devices'', IEEE Trans. on Computer Aided Design, December, 2000.
41. J. Tausch, J. Wang and J. White, "Improved Integral Formulations for Fast 3-D Method-of-Moment Solvers," IEEE Transactions of Computer-Aided Design of Integrated Circuits and Systems, vol. 20,
no. 12, December 2001, p. 1398-1405.
42. K. Willcox, J. Peraire J. and J. White, "An Arnoldi Approach for Generation of Reduced-order Models for Turbomachinery'', Computers and Fluids, Vol. 31, No. 3, pp 369-89, March 2002.
43. J. Li and J. White, "Reduction of Large Circuit Models via Low Rank Approximate Gramians'', International Journal of Applied Mathematics and Computer Science,Vol. 11, No. 5, pp. 101--121, 2001.
44. J. Tausch and J. White, "Multiscale Bases for the Sparse Representation of Boundary Integral Operators on Complex Geometry.'' To appear, SIAM J. Sci Comp.
45. J. Li and J. White, "Low Rank Solution of Lyapunov Equations," SIAM J. Matrix Anal. Appl. 24 (2002), no. 1, 260--280 (electronic).
46. Y. Massoud, S. Majors, J. Kawa, T. Bustami, D. MacMillen, and J. White, "Managing On-chip Inductive Effects," IEEE Transactions on Very Large Scale Integration (VLSI) Systems, Vol. 10, No. 6, pp.
789--798, December 2002.
47. Y. Massoud and J. White, "Simulation and Modeling of the Effect of Substrate Conductivity on Coupling Inductance and Circuit Crosstalk,'' IEEE Transactions on Very Large Scale Integration (VLSI)
Systems, Vol. 1, No. 3, pp. 286-291, June 2002.
48. M. Rewienski and J. White, "A Trajectory Piecewise-linear Approach to Model Order Reduction and Fast Simulation of Nonlinear Circuits and Micromachined devices," IEEE Transactions on
Computer-Aided Design of Integrated Circuits and Systems, Vol. 22, No. 2, pp. 155--170, Feb. 2003.
49. W. Ye, X. Wang, W. Hemmert, D. M. Freeman, and J. White, “Air damping in laterally oscillating microresonator: a numerical and experimental study,” IEEE Journal of Microelectromechanical Systems
, vol. 12, no. 5, pp. 557-566, 2003.
50. J. Phillips, L. Daniel, L. M. Silveira, "Guaranteed Passive Balancing Transformations for Model Order Reduction", IEEE Transaction on Computer Aided Design of Integrated Circuits and Systems, Vol
22, No 8, Aug 2003.
51. L. Daniel, O. C. Siong, L. S. Chay, K. H. Lee, and J. White, “A multiparameter moment matching model reduction approach for generating geometrically parameterized interconnect performance
models,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems , vol. 23, no. 5, May, pp. 678-693, 2004.
52. N. Marques, M. Kamon, L. M. Silveira, and J. White, “Generating compact, guaranteed passive, reduced-order models of 3D RLC interconnects,” IEEE Transactions on Advanced Packaging , vol. 27, no.
4, Nov., pp. 569-580, 2004.
53. J. Li and J. White, “Low-rank solution of lyapunov equations,” Selected for Republication in SIAM Review , vol. 46, no. 4, p. 693-713, 2004.
54. M. Rewienski and J. White, "Model order reduction for nonlinear dynamical systems based on trajectory piecewise-linear approximations", Linear Algebra and its Applications, (2005)
55. Z. Zhu, B. Song, J. White, "Algorithms in FastImp: A fast and wideband impedance extraction program for complicated 3D geometries”, Accepted for publication in TCAD. (2005).
56. D. Vasilyev, M. Rewienski, and J. White, "Macromodel generation for BioMEMS components using a stabilized Balanced Truncation plus Trajectory Piecewise Linear Approach," IEEE Transactions on
Computer-Aided Design of Integrated Circuits and Systems, (Special BioChips Issue) Volume 25, Issue 2, Feb. 2006,Page(s):285 - 293.
57. X.Wang, J. Kanapka, W. Ye, N. Aluru, and J. White, "Algorithms in FastStokes and its application to micromachined device simulation,'' IEEE Transactions on Computer-Aided Design of Integrated
Circuits and Systems, (Special BioChips Issue) Volume 25, Issue 2, Feb. 2006 Page(s):248 - 257.
58. M. D. Altman, J. Bardhan, B. Tidor and J. White, "FFTSVD: A Fast Multiscale Boundary Element Method Solver Suitable for BioMEMS and Biomolecule Simulation,'' IEEE Transactions on Computer-Aided
Design of Integrated Circuits and Systems, (Special BioChips Issue) Volume 25, Issue 2, Feb. 2006 Page(s):274 - 284.
59. M. Rewienski and J. White, "Model Order Reduction for Nonlinear Dynamical Systems based on Trajectory Piecewise-linear Approximations,'' Linear Algebra and its Applications, Volume 415, (2006),
Pages 426-454.
60. B. N. Bond, L. Daniel, "A Piecewise-Linear Moment-Matching Approach to Parameterized Model-Order Reduction for Highly Nonlinear Systems", IEEE Transactions on Computer-Aided Design of Integrated
Circuits and Systems, Vol: 26 , Issue: 12, page(s): 2116 - 2129, Dec. 2007.
61. O. Nastov, R. Telichevesky, K. Kundert, J. White, "Fundamentals of Fast Simulation Algorithms for RF Circuits,'' Invited paper to Appear, Proceedings of the IEEE Special Issue on Tools for Mixed
Signal Design.
62. K. C. Sou, A. Megretski and L. Daniel, “A quasi-convex optimization approach to parameterized model order reduction,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and
Systems, vol. 27, no. 3, pp. 456-469, March 2008
63. S.-H. Kuo, B. Tidor and J. White, “A meshless, spectrally accurate, integral equation solver for molecular surface electrostatics”, ACM Journal on Emerging Technologies in Computing Systems, vol.
4, no. 2, April 2008.
64. B. N. Bond and L. Daniel, “Stable reduced models for nonlinear descriptor systems through piecewise-linear approximation and projection,” IEEE Transactions on Computer-Aided Design of Integrated
Circuits and Systems vol. 28, no.10, pp.1467-1480, Oct. 2009
65. A. K. Wilkins, B. Tidor, J. White and P. I. Barton, “Sensitivity analysis for oscillating dynamical systems,” SIAM Journal of Scientific Computing, vol. 31, no. 4, pp. 2706-2732, 2009
66. M. D. Altman, J. P. Bardhan, J. K. White and B. Tidor, “Accurate solution of multi-region continuum biomolecule electrostatic problems using the linearized Poisson-Boltzmann equation with curved
boundary elements,” Journal of Computational Chemistry, vol. 30, no.1, pp.132-153, Jan. 2009
67. B. Bond, Z. Mahmood, Y. Li, R. Sredojevic, A. Megretski, V. Stojanovic, Y. Avniel and L. Daniel, “Compact modeling of nonlinear analog circuits using system identification via semidefinite
programming and incremental stability certification,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 29, no. 8, pp. 1149-1162, Aug. 2010
68. T. El-Moselhy, I. M. Elfadel and L. Daniel, “A Markov chain based hierarchical algorithm for fabric-aware capacitance extraction”, IEEE Transactions on Advanced Packaging, vol. 33, no. 4, pp.818,
Nov.2010. (Invited Paper)
69. L. Zhang, J. H. Lee, A. Oskooi, A. Hochma, J. White and S. G. Johnson, “A novel boundary element method using surface conductive absorbers for full-wave analysis of 3-D nanophotonics,” IEEE
Journal of Lightwave Technology, vol. 29, no.7, pp. 949 – 959, July 2011
70. M. Jafarpoor, J. Li, J. K. White and S. B. Rutkove, “Optimizing electrode configuration for electrical impedance measurements of muscle via the finite element method,” IEEE Transactions on
Biomedical Engineering, vol. 60, no.5, pp.1446-1452, May 2013.
71. T. H. Nim, J. K. White and L. Tucker-Kellogg, “SPEDRE: a web server for estimating rate parameters for cell signaling dynamics in data-rich environments,” Nucleic Acids Research, vol. 41
(Webserver-Issue), pp. 187-191, June. 2013
72. .T. H. Nim, L. Luo, M. Clément, J. K. White and L. Tucker-Kellogg, “Systematic parameter estimation in data-rich environments for cell signaling dynamics,” Bioinformatics, vol. 29, no. 8,
pp.1044-1051, Feb. 2013
73. Y. Shi, G. Mellier, S. Huang, J. White, S. Pervaiz, and L. Tucker-Kellogg, “Computational modeling of LY303511 and TRAIL-induced apoptosis suggests dynamic regulation of cFLIP,” Bioinformatics,
vol. 29, no. 3, pp. 347-354, Feb. 2013
74. Z. Zhang, T. A. El-Moselhy, I. M. Elfadel and L. Daniel, "Stochastic testing method for transistor-level uncertainty quantification based on generalized polynomial chaos," IEEE Transactions on
Computer-Aided Design of Integrated Circuits and Systems, vol. 32, no. 10, pp. 1533-1545, Oct. 2013.
75. Z. Zhang, T. A. El-Moselhy, P. Maffezzoni, I. M. Elfadel and L. Daniel, "Efficient uncertainty quantification for the periodic steady state of forced and autonomous circuits," IEEE Transactions
on Circuits and Systems II: Express Briefs, vol. 60, no.10, pp. 687-691, Oct. 2013.
76. P. Maffezzoni, Z. Zhang and L. Daniel, "A study of deterministic jitter in crystal oscillators," IEEE Transactions on Circuits and Systems I: Regular Papers, vol., no., pp., 2014 , accepted
77. R. Marathe, B. Bahr, W. Wang, Z. Mahmood, Luca Daniel and D. Weinstein, “Resonant body transistors in IBM’s 32 nm SOI CMOS technology,” IEEE/ASME Journal of Microelectromechanical Systems,
78. Z. Zhang, T. A. El-Moselhy, I. M. Elfadel and L. Daniel, "Calculation of generalized polynomial-chaos basis functions and Gauss quadrature rules in hierarchical uncertainty quantification," IEEE
Transactions on Computer-Aided Design of Integrated Circuits and Systems, accepted
79. Z. Zhang, M. Kamon and L. Daniel, "Continuation-based pull-in and lift-off simulation algorithms for microelectromechanical devices," IEEE/ASME Journal of Microelectromechanical Systems, accepted
80. A. Hochman, J. Fernández Villena, A. G. Polimeridis, L.M. Silveira, J. K. White and L. Daniel, “Reduced-Order Models for Electromagnetic Scattering Problems,” IEEE Transactions on Antennas and
Propagation, accepted.
Proceedings in Refereed Conferences
1. J. White and A.S. Vincentelli, "RELAX II: A Modified Waveform Relaxation Approach to the Simulation of MOS Digital Circuits," Proc. 1983 Int. Symp. On Circuits and Systems, invited paper, Newport
Beach, CA, May 1983, p. 756-759.
2. J. White and A.S. Vincentelli, "Relax2.1- A Waveform Relaxation Based Circuit Simulation Program," Proc. 1984 Int. Custom Integrated Circuits Conference, Rochester, New York, June 1984,
3. J. Beetem, P. Debefve, W. Donath, H.Y. Hseih, F. Odeh, A.E. Ruehli, J. White, P.K. Wolff, Sr., "A Large-Scale MOSFET Circuit Analyzer Based on Waveform Relaxation," Proc. 1984 Int. Conf. On
Computer Design, Rye, New York, October 1984, p.507-514.
4. J. White and A.S. Vincentelli, "Partitioning Algorithms and Parallel implementations of Waveform Relaxation Based Circuit Simulation," Proc. 1985 Int. Symp. On Circuits and Systems, invited
paper, Kyoto, Japan, June 1985, p.221-224.
5. J. White, R. Saleh, A. Sangiovanni-Vincentelli, and A.R. Newton, "Accelerating Relaxation Algorithms for Circuit Simulation using Waveform Newton, Iterative Step Size Refinement, and Parallel
Techniques," Proc. Int. Conf. On Computer-Aided Design, Santa Clara, California, October 1985, p. 5-7.
6. A.S. Vincentelli, and J. White, "Waveform Relaxation Techniques and Their Parallel Implementation," Proc. Conf. On Decision and Control, Ft. Lauderdale, Florida, December 1985, p. 1544-1551.
7. J. White and N. Weiner, "Parallelizing Circuit Simulation-A Combined Algorithmic and Specialized Hardware Approach," Proc. 1986 Int. Conf. On Computer Design, Rye, New York, October 1986, p.
8. K. Kumbert, J. White, A. Sangiovanni-Vincentelli, "A Mixed Frequency Time Approach for Finding the Steady-State solution of Clocked Analog Circuits," Custom Int. Circuits Conf., Rochester, N.Y.,
May 1988, p. 6.2.1-6.2.4.
9. D. Smart and J. White "Reducing the parallel Solution Time of Sparse Circuit Matrices using Reordered Gaussian Elimination and Relaxation," Int'l. Symp. On Circuits and Systems, Espoo. Finland,
June 1988, p. 627-630.
10. M. Reichelt, J. White. J. Allen and F. Odeh, "Waveform Relaxation Applied to Transient Device Simulation," Int'l. Symp. on Circuits and Systems, Espoo, Finland, June 1988, p. 1647-1650.**
11. K. Kundert, J. White, A. Sangiovanni-Vincentelli, "An Envelope-Following Method for the Efficient Transient Simulation of Switching Power and Filter Circuits," Proc. Int. Conf. On computer-Aided
Design, Santa Clara, Califronia, November 1988, p. 446-449.
12. A. Lumsdaine, J. White, D. Webber, A. Sangiovanni-Vincentelli , "A Band Relaxation Algorithm for Reliable and Parallelizable Circuit Simulation," Proc. Int. Conf. On Computer-Aided Design, Santa
Clara, California, November 1988, p. 308-311.
13. K. Nabors, J. White, "A Fast Multipole Algorithm for Capacitance Extraction of Complex 3-D Geometries" Proc. Custom Int. Circuits Conf., San Diego, California, May 1989, p. 21.7.1-21.7.4.**
14. M. Crow, M. Ilic, J. White, "Convergence Properties of the Waveform Relaxation Method as Applied to Electric Power Systems," Proc. Int. Symp. on Circuits and Systems, Portland, Oregon, May 1989,
p. 1863-1866.**
15. M. Reichelt, J. White, "Techniques for Switching power Converter Simulation," Invited Paper, Nasecode Conference, Dublin, Ireland, July 1989, p.114-119.**
16. M. Reichelt, J. White, J. Allen, "Waveform Relaxation for Transient Simulation of Two-Dimensional MOS Devices," Prof. Int. Conf. On Computer-Aided Design, Santa Clara, California, November 1989,
p. 412-415.**
17. H. Neto, L. Silveira, J. White, L. Vidigal, "On Exponential Fitting for Circuit Simulation," Proc. Int. Symp. on Circuits and Systems, New Orleans, May 1990, p. 514-518.**
18. S. Devadas, K. Keutzer, J. White, "Estimation of Power Dissipation in CMOS Combinational Circuits," Proc. Custom Int. Circuits Conf., Boston, 1990, p. 19.7.1-19.7.6.
19. J. Lloyd, J.R. Phillips, J. White, "A Boundary-Element/Multipole Algorithm for Self-Consistent Poisson Calculations in Monte-Carlo Simulation," Proc. Workshop on Numerical Modeling of Processes
and Devices for Integrated Circuits: NUPAD III, Honolulu, Hawaii, June 1990, p. 81-82.**
20. L.M. Silveira, A. Lumsdaine, J. White, "Parallel Simulation Algorithms for Grid-based Analog Signal Processors" Proc. Int. Conf. On Computer-Aided Design, Santa Clara, California, November 1990,
pp. 442-445.**
21. J. White and F. Odeh, "A Connection Between the Convergence properties of Waveform Relaxation and the A-stability of Multirate Integration Methods," Invited paper, Proc. NASECODE VII, Copper
Mountain, Colorado, April, 1991, pp.73-76.
22. B. Johnson. S. Kim, J. White, S. Senturia, "MEMCAD Capacitance Calculations for Mechanically Deformed Square Diaphragm and Beam Microstructures," Proc. Transducers 91, San Francisco, California,
June 1991.**
23. K. Nabors, S. Kim J. White and S. Senturia, "Fast Capacitance Extraction of General Three-Dimensional Structures," Proc. Int. Conf. On Computer Design, Cambridge, MA, October 1991, pp. 479-484.**
24. A. Lumsdaine , M. Reichelt, J. White, "Conjugate Direction Waveform Methods for Transient Two-Dimensional Simulation of MOS Devices," Proc. Int. Conf. On Computer-Aided Design, Santa Clara,
California, November 1991, pp. 116-119.**
25. M. Silviera, J. White, S. Leeb, "A Modified Envelope-Following Approach to Clocked Analog Circuit Simulation," Proc. Int. Conf. On Computer-Aided Design, Santa Clara, California, November 1991,
pp. 20-23.**
26. K. Rahmat, J. White, D. Antoniadis, "Computation of Drain and Substrate Currents in Ultra-Short N-Channel MOSFETS using the Hydrodynamic Model," Proc. Int. Electron Devices Meeting, Wash. D.C.,
December 1991, pp. 115-118.**
27. K. Nabors, J. White, "An Improved Approach to Including Conformal Dielectrics in Multipole-Accelerated Three Dimensional interconnect Capacitance Extraction," proceedings of NUPAD IV, Seattle,
WA, May, 1992, pp. 167-172.**
28. M. Reichelt, J. White, J.R. Allen, "Frequency-Dependent Waveform Over- Relaxation for Transient Two-Dimensional Simulation of MOS Devices," Proceedings of NUPAD IV, Seattle, WA, 1992, pp.
29. A. Ghosh, S. Devadas, K. Keutzer, J. White, "Estimation of Average Switching Activity in Combinational and Sequential Circuits," Proceeding of the 29th Design Automation Conference, Anaheim, CA,
June 1992, pp. 253-259.
30. K. Nabors, J. White, "Multipole-Accelerated 3-D Capacitance Extraction Algorithms for Structures with Conformal Dielectrics" Proceeding of the 29th Design Automation Conference, Anaheim, CA, June
1992, pp. 710-715.**
31. D. Ling, S. Kim, J. White, "A Boundary-Element approach to Transient Simulation of Three-Dimensional Integrated Circuit Interconnect" Proceedings of the 29th Design Automation Conference,
Anaheim, CA, June, 1992, pp. 93-98.
32. A. Lumsdaine, J. White, "Accelerating Dynamic Iteration Methods with Application to Semiconductor Device Simulation," Third place, best student paper competition, Proceedings of the Cooper
mountain Conference on iterative Methods, Copper Mountain, April, 1992.**
33. K. Nabors, T. Korsmeyer, J. White, "Multipole-Accelerated Preconditioned Iterative methods For Solving Three-Dimensional Mixed First and Second kind integral Equations," Proceedings of the Cooper
Mountain Conference on Iterative Methods, Copper Mountain, April, 1992.**
34. M. Kamon, M. Tsuk, C. Smithhisler, J. White, "Efficient Techniques for Inductance Extraction of Complex 3-D Geometries," Proc. Int. Conf. On Computer-Aided Design, Santa Clara, California,
November 1992, pp. 438-442.**
35. J.R. Gilbert, P.M. Osterberg, R.M. Harris, D.O. Ouma, X. Cai, A. Pfajfer, J. White, and S.D. Senturia, "Implementation of a MEMCAD System for Electrostatic and Mechanical Analysis of Complex
Structures from Mask Descriptions," Proc. IEEE micro Electro Mech. Syst., Fort Lauderdale, February 1993.**
36. M. Reichelt, F. Odeh, and J. White, "A-Stability of Multirate Integration Methods with Application to Parallel Semiconductor Device Simulation," Invited Paper, Proc. SIAM Meeting on Parallel
Processing for Scientific Computing, Norfolk, VA, March 1993, pp. 246-253.**
37. J.R Phillips, M. Kamon, J. White, "An FFT-Based Approach to Including Non-Ideal Ground Planes in a fast 3-D Inductance Extraction Program," Proc. Custom Int. Circuits Conf., San Diego, May
38. M. Kamon, K. Nabors, J. White, "Multipole-Accelerated 3-D Interconnect Analysis," Invited Paper, Proc. Int. Workshop on VLSI Process and Device Modeling (VPAD), NARA, Japan, May 1993.
39. S. Kim, S. Ai, and J. White, "A Vector Surface Integral Approach to Computing Inductances of General 3-D Structures," Proc. IEEE MTT-S International Microwave Symposium., Atlanta, June 1993.**
40. M. Kamon, M.J. Tsuk, and J.White, "FastHenry, A Multipole-Accelerated Preconditioned Iterative Methods for Three-Dimensional potential Problems," Proceedings of the 30th Design Automation
Conference, Dallas, June 1993.**
41. T. Korsmeyer, D.K.P. Yue, K. Nabors, J. White, "Multipole-Accelerated Preconditioned Iterative Methods for Three-Dimensional Potential Problems, Boundary Element Methods 15(BEM15), Worcester, MA,
August 1993.**
42. L.M. Silveira, I.M. Elfadel, J. White, "A Guaranteed Stable model-Order Reduction Algorithm for Packaging and Interconnect Simulation," Proceedings of the IEEE 2nd Topical meeting on Electrical
Performance of Electronic Packaging,
43. M. Kamon and J. White, "Preconditioning for Multipole-Accelerated 3-D Inductance Extraction" Proceedings of the IEEE 2nd Topical Meeting on Electrical Performance of Electronic Packaging,
Monterey, CA, October 1993, pp. 189-192.**
44. J.R. Phillips, H. Van der Zant, J. White, and T. Orlando, "Numerical Study of Self-Fields Effects on Dynamics of Josephson-Junction Arrays," Proceedings of the 20th International Conference on
Low Temperature Physics, Eugene, OR, August 1993.**
45. M. Reichelt, A. Lumsdaine, J. White and J. Allen, "Accelerated Waveform Methods for Parallel Transient Simulation of Semiconductor Devices," Proc. Int. Conf. On Computer-Aided Design, Santa
Clara, California, November 1993, pp. 283-286.**
46. X. Cai, H. Yie, P. Osterberg, J. Gilbert, S. Senturia and J. White, "A Relaxation/Multipole-Accelerated Scheme for Self-Consistent electromechanical Analysis of Complex 3-D Microelectromechanical
Structures," Proc. Int. Conf. On Computer-Aided Design, Santa Clara, California, November 1993, pp. 270-274.
47. P. Osterberg, H. Yie, X. Cai, J. White, and S. Senturia, "Self-consistent simulation and modelling of electrostatically deformeddiaphragms," Proceedings IEEE Workshop on Micro Electro Mechanical
Systems, Japan, January 1994, pp. 28 -32
48. H. Yie, X. Cai, and J. White, "Convergence Properties of Relaxation Versus the Surface-Newton Generalized-Conjugate Residual Algorithm for Self-Consistent Electromechanical Analysis of 3-D
micro-Electromechanical Structures" Proc. NUPAD V, Honolulu, Hawaii, June 194, pp. 137-140.
49. K. Rahmat, J. White, and D.A. Antoniadis, "A Galerkin Method for the Arbitrary Order Expansion in Momentum Space of the Boltzmann Equation using Spherical Harmonics," Proceedings of NUPAD V,
Honolulu, Hawaii, June 1994, pp. 133-136.
50. L.M. Silveira, I.M. Elfadel, J. White, M. Chilikuri, and K. Kundert, "An Efficient Approach to Transmission Line Simulation using Measured or Tabulated S-parameter Data," Proceedings of the 31st
Design Automation Conference, San Diego, June 1994, pp. 634-639.**
51. J. White, J.R. Phillips and T. Korsmeyer, "Comparing Precorrected-FFT and Fast Multipole Algorithms for Solving Three-dimensional Potential integral Equations," Proceedings of the Colorado
Conference on Iterative Methods, Breckenridge, Colorado, April 1994.**
52. L.M. Silveira, M. Kamon and J. White, "Algorithms for Coupled Transient Simulation of Circuits and Complicated 3-D Packaging," Best Paper, Proceedings of the 44th Electronics Components and
Technology Conference, May 1994, Washington D.C., USA, pp. 962-970.
53. J.R. Phillips and J. White, "A Precorrected-FFT Method for Capacitance Extraction of Complicated 3-D Structures," Int. Conf. On Computer-Aided Design, Santa Clara, California, November 1994, p.**
54. L. Miguel Silveira, Mattan Kamon and Jacob White, "Direct Computation of Reduced-Order Models for Circuit Simulation of 3-D Interconnect Structures," Proceedings of the 3rd Topical Meeting on
Electrical Performance of Electronic Packaging, pp. 245-248, Monterey California, November 1994.**
55. J.R. Phillips and J. White, "Efficient Capacitance Extraction of 3-D Structures using Generalized Pre-Corrected FFT Methods," Proceedings of the IEEE 3rd Topical Meeting on Electrical Performance
of electronic Packaging, Monterey, CA, November 1994.
56. M. Chou and J. White, "A Multipole-Accelerated Boundary-Element approach to Transient Simulations of Three-Dimensional integrated Circuit Interconnect," Proceedings of the IEEE 3rd Topical
meeting on Electrical Performance of Electronic Packaging, Monterey, CA, November 1994.**
57. K. Rahmat, J. White, D.A. Antoniadis, "Solution of the Boltzman Transport Equation in Two Real-Space Dimensions using a Spherical Harmonic Expansion in Momentum Space," Proc. Int. Electron
Devices Meeting, San Francisco, CA, December 1994.**
58. H. Yie, S.F. Bart, J. White, and S.D. Senturia, "Computationally Practical Simulation of a Surface-Micromachined Accelerometer with True Fabrication Non-Idealities," Proceedings of the European
Design and Test Conference, Paris, France, March 1995.**
59. L.M. Silveira, M. Kamon and J. White, "Efficient Reduced-Order modeling of Frequency-Dependent Coupling Inductances associated with 3-D Interconnect Structures," Proceedings of the European
Design and Test Conference, Paris, France, March 1995.**
60. M. Chou, M. Kamon, K. Nabros, J. Phillips and J. White, "Extraction Techniques for Signal Integrity Analysis of 3-D Interconnect and Packages," Invited Paper, Progress in Electromagnetic Research
Symposium, Seattle, Washington, July 1995.**
61. J. R. Phillips and J.K. White, "Precorrected-FFT Methods for Electromagnetic Analysis of Complex 3-D Interconnect and Packages," Invited Paper, Progress in Electromagnetic Symposium, Seattle,
Washington, July 1995.**
62. M. Chou and J. White, "Transient Simulations of Three-Dimensional Integrated Circuit Interconnect a Mixed Surface-Volume Approach," invited paper, progress in Electromagnetic Research Symposium,
Seattle, Washington, July 1995.**
63. L. Silveira, M. Kamon and J. White, "Direct Computation of Reduced-Order Models for circuit simulation of 3-D Interconnect Structures," Invited Paper, Progress in Electromagnetic Research
Symposium, Seattle, Washington, July 1995.**
64. X. Cai, K. Nabros and J. White, "Efficient Galerkin Techniques for Multipole-Accelerated Caoaitance Extraction of 3-D Structures with Multipole Dielectrics," Proceedings of the 16th Conference on
Advanced Research in VLSI, Chapel Hill, north Carolina, March 1995.**
65. R. Telichevesky, K.S. Kundert, J.K. White, "Efficient Steady-State Analysis Based on Matrix-Free Krylov Subspace Methods," Proceedings of the Design Automation Conference, San Francisco, CA,
June, 1995.**
66. M. Chou, T. Korsmeyer, J. White, "Transient Simulations of Three-Dimensional Integrated Circuit Interconnect using a Mixed Surface Volume Approach," Proceedings of the 32nd Design Automation
Conference, San Francisco, CA, June, 1995.**
67. L. Miguel Silveira, M. Kamon and J. White, "Efficient Reduced-Order Modeling of Frequency-Dependent Coupling Inductances Associated with 3-D Interconnect Structures," Proceedings of the 32nd
Design Automation Conference, pp.376-380, San Francisco, CA, June, 1995.**
68. M. Chou and J. White, "Efficient Reduced-Order Modeling for the Transient Simulation of Three-Dimensional Interconnect," Proceedings of the International Conference on Computer Aided Design, San
Jose, CA, November 1995, pp.40-44.
69. Mattan Kamon and Byron Krauter and Joel Phillips and Lawrence T. Pileggi and Jacob. K. White, "Two Optimizations to Accelerated Method-of-moments Algorithms for Signal integrity Analysis of
Complicated 3-D Packages," Proceedings of the 4th Topical Meeting on Electrical Performance of Electronic Packaging, Portland, Oregon, October 1995, pp.213-216.**
70. Y. Massoud and J. White, "Simulation and modeling of the Effect of Substrate Conductivity on Coupling Inductance," Proc. Int. Electron Devices Meeting, Washington D.C., December 1995.**
71. J. Tausch and J. White, "Preconditioning First and Second Kind Integral Formulations of the Capacitance Problem," Proceedings of the 1996 Copper Mountain Conference on Iterative Methods, April
72. I.M. Elfadel, L. Miguel Silveira and J. White, "Stability Criteria for Arnoldi-Based model Order Reduction," Proceedings of the IEEE Conference on Acoustics, Speech, and Signal Processing
(ICASSP'96), Atlanta, GA, May, 1996.**
73. N.R. Aluru, V. Nadkarni, and J. White,"A parallel Precorrected-FFT Based Capacitance Extraction Program for Signal Integrity Analysis," Proceedings of the 33rd Design Automation Conference, Las
Vegas, June, 1996.**
74. R. Telichevesky, K. Kundert and J. White, "Fast Simulation Algorithms for RF Circuits," Invited Paper, Proceedings of the Custom Integrated Circuits Conference, San Diego, May, 1996.**
75. R. Telichevsky, K. Kundert and J. White, "Receiver Characterization using Periodic Small-Signal Analysis," Proceedings of the Custom Integrated Circuits Conference, San Diego, May 1996.**
76. J. Tausch and J. White, "Multipole Accelerated Capacitance Calculation for Structures with Multipole Dielectrics with High Permitivity Ratios," Proceedings of the 33rd Design Automation
Conference, Las Vegas, June, 1996.**
77. R. Telichevsky, K. Kundert and J. White, "Efficient AC and Noise Analysis of Two-Tone RF Circuits," Proceedings of the 33rd Design Automation Conference, Las Vegas, June, 1996.**
78. N. Aluru and J. White, "Direct-Newton Finite-Element/Boundary-Element Technique for Micro-Electro-Mechanical-Analysis," IEEE Solid-State Sensor and Actuator Workshop, Hilton-Head Island, SC, June
1996, pp. 54-57.
79. Korsmeyer, T., Phillips, J. White, "A Precorrected FFT Algorithm for Accelerating Surface Wave Problems," The Eleventh International Workshop on Water Waves and Floating Bodies, Hamburg, July
80. N. Aluru and J. White, "A Coupled Numerical Technique for Self-Consistent Analysis of Micro-Electro-Mechanical-Systems," To Appear Proc. 1996 ASME Winter Annual Meeting.
81. L. Miguel Silveira, Mattan Kamon, Ibrahim Elfadel, and J. White "A Coordinate-Transformed Arnoldi Algorithm for Generating Guaranteed Stable Reduced-Order models of RLC Circuits," Proceedings of
the international Conference on Computer Aided Design, San Jose, CA, November 1996.**
82. I. M. Elfadel, L. M. Silveira and J. White, "Stability criteria forArnoldi-based model-order reduction," Proceedings of ICASSP-96, Conference Proceedings on Acoustics, Speech, and Signal
Processing, Atlanta, May 1996. pp. 2642 -2645.
83. J. Tausch and J. White, "Mesh Refinement Strategies for Capacitance Extraction Based on Residual errors," Proceedings of the IEEE Workshop on electrical Performance of Electronic Packaging, Santa
Cruz, CA, October 1996.
84. J. Tausch and J. White, "Boundary Integral Solution of Laplace's Equation in Multi-Layered Media with High Permittivity Ratios," Proceedings of the 13th GAMM-Seminar Kiel on Numerical Treatment
of Multi-Scale Problems, Kiel, Germany, January, 1997.
85. N. Aluru and J. White, "Algorithms for Coupled Domain Mems Simulation", Proceedings of the 34th Design Automation Confrence, 1997. pp. 688-690.
86. J. Tausch and J. White "Precondition and Fast Summation Techniques for First-kind Boundary integral Equations," Third IMAC International Symposium on Iterative Methods in Scientific Computation,
Jackson Hole WY, July 9-12, 1997.
87. K. Nabros, T-T. Fang, H-W. Chang, K. Kundert, and J. White, "A Guassin-Quadrature Based Algorithm for RLC-line to RLC-line Reduction," Proceedings of Progress in Electromagnetics Research
Symposium, Cambridge, MA, July, 1997.
88. K. Nabros, T.-T. Fang, H.-W. Chang, K. Kundert and J. White, "An RLC Line Reduction Algorithm with an Odd Optimality Property," Invited Paper, Proceedings of Progress in Electromagnetics Research
Symposium, Cambridge, MA, July, 1997
89. L.M. Silveira, I. Elfadel and J. White, "Coupled Circuit-Interconnect Analysis Using Stable Arnoldi-Based model-Order Reduction," Proceedings of Progress in Electromagnetics Research Symposium,
Cambridge, MA, July, 1997.
90. N. Aluru and J. White,"A Multi-Level Newton Method for Static and Fundamental Frequency Analysis of Electromechanical Systems," Intl. Conf. On Simulation of Semiconductor Processes and Devices
(SIS-PAD), Boston, September, 1997, pp. 125-128.
91. J. Wang and J. White, "Fast Algorithms for Computing electrostatic Geometric Sensitivities," Intl. Conf. On Simulation of Semiconductor processes and Devices (SISPAD), Boston, September, 1997,
92. J. Li and J. White, "Approximation of Potentials by Multipole Grid Projections," Topical Meeting on Electrical Performance of Electronic Packaging, San Jose, California, November, 1997.
93. M. Kamon, N. Marques, and J. White, "FastPep: A Fast parasitic Extraction Program for Complex Three-Dimensional Geometries," Proceedings of the IEEE Conference on Computer-Aided Design, San Jose,
November, 1997, pp.456-460.
94. M. Kamon, M. Marques, L. Miguel Silveira and J. White, "Generating Reduced Order models via PEEC for Capturing Skin and Proximity Effects," Proceedings of the 6th Tropical Meeting on Electrical
Performance of Electronic Packaging, San Jose, California, November, 1997, pp. 259-262.
95. M. Chou and J. White, "Multilevel Integral Equation Methods for the Extraction of Substrate Coupling Parameters in Mixed-Signal IC's," Proceedings of the 35th Design Automation Conference, San
Francisco, June, 1998, pp.20-25.
96. N. Marques, M. Kamon, J. White and L.M. Silveira, "An efficient Algorithm for Fast parasitic Extraction and Passive Order Reduction of 3D Interconnect Models," DATE'98-Design Automation and Test
in Europe, Exhibition and Conference, Paris, Feb. 1998, pp. 538-548.
97. N. Marques, M. Kamon, J. White, L.M. Silveira, "A Mixed Nodal-Mesh Formulation for Efficient Extraction and Passive Reduced-Order modeling of 3D Interconnects," Proceedings of the 35th Design
Automation Conference, San Francisco, June, 1998, pp.297-302.
98. Y. Massoud, S. Majors, T. Busami, and J. White, "Layout Techniques for minimizing On-Chip Interconnect Self Inductance," Proceedings of the 35th Design Automation Conference, San Francisco, June,
1998, pp. 566-571.
99. N.R. Aluru and J. White, "A Fast Integral Equation Technique for Analysis of Microflow Sensors Based on Drag Force Calculations," International Conference on Modeling and Simulation of
Microsystems, Semiconductors, Sensors and Actuators, Santa Clara, April 1998, pp. 283-286.
100. Y. Massoud and J. White, "Fast inductance Extraction of 3-D Structures with Non-Constant Permeabilities," International Conference on Modeling and Simulation of Microsystems, Semiconductors,
Sensors and Actuators, Santa Clara, April 1998, pp. 190-193.
101. D. Ramaswamy, N.R. Aluru and J. White, "A Mixed Rigid/Elastic Formulation for Efficient Analysis of Electromechanical Systems," International Conference on Modeling and Simulation of
Microsystems, Semiconductors, Sensors and Actuators, Santa Clara, April 1998, pp. 304-307.
102. F. Wang and J. White, "Automatic Model Order Reduction of a Microdevice using the Arnoldi Approach" International Mechanical Engineering Congress and Exposition, Anaheim, November, 1998, pp.
103. 103. J. Wang, J. Tausch and J. White," Improved Integral Formulations for Fast 3-D Method-of-Moments Solvers," Proceedings of the 7th Topical Meeting on Electrical Performance of Electronic
Packaging, West Point, New York, October, 1998, pp. 273-276.
104. M. Kamon, F. Wang and J. White, "Recent Improvements to Fast inductance Extraction and Simulation," Proceedings of the 7th Topical Meeting on Electrical Performance of Electronic Packaging, West
Point, New York, October 1998, pp. 281-284.
105. Y. Massoud, J. Wang, and J. White, "Accurate inductance Extraction with Permeable Materials using Qualocation," International Conference on Modeling and Simulation of Microsystems,
Semiconductors, Sensors and Actuators, San Juan, April 1999.
106. . J. Wang, J. Tausch and J. White, "A Wide Frequency Range Surface Integral Formulation for 3-D Inductance and Resistance Extraction," International Conference on Modeling and Simulation of
Microsystems, Semiconductors, Sensors and Actuators, San Juan, April 1999.
107. J. White, "Fast Algorithms for 3-D Simulation," International Conference on modeling and Simulation of Microsystems, Semiconductors, Sensors and Actuators, San Juan, April 1999.
108. D. Kring, T. Korsmeyer, J. Singer, and J. White, "Analyzing mobile offshore bases using accelerated boundary-element methods'' Marine Structure (Elsevier Science), volume 13(4-5), 2000, pp. 301
-- 313
109. T. Mukherjee, G. Fedder and J. White, "Emerging Simulation Approaches For Micromachined Devices'', IEEE Trans. on Computer-Aided Design}, December, vol. 19, 2000, pp. 1572-1589
110. W.Ye, J. Kanapka, X. Wang and J. White, "Efficiency and Accuracy Improvements for FastStokes, A Precorrected-FFT Accelerated 3-D Stokes Solver," International Conference on Modeling and
Simulation of Microsystems, Semiconductors, Sensors and Actuators, San Juan, April 1999.
111. W. Ye, J. Kanapka, and J. White, "A Fast 3-D Solver for Unsteady Stokes Flow with Application to Micro-Electro-Mechanical Systems," international Conference on Modeling and Simulation of
Microsystems, Semiconductors, Sensors and Actuators, San Juan, April 1999.
112. O. Nastov and J. White, "Grid selection strategies for time-mapped harmonic balance simulation of circuits with rapid transitions,'' Proceedings of the IEEE Custom Integrated Circuits, San
Diego, May 1999. pp. 13 -16
113. J. Li, F. Wang and J. White, "An efficient Lyapunov equation-based approach for generating reduced-order models of interconnect," Proceedings. 36th Design Automation Conference, 1999. pp. 1-6.
114. J. Tausch and J. White, "A Multiscale Method for Fast Capacitance Extraction" Proceedings of the 35th design Automation Conference," New Orleans, June 1999.
115. O. Nastov and J. White, "Time-mapped harmonic balance,'' Proceedings. 36th Design Automation Conference, New Orleans, June 1999, pp. 641 -646.
116. D. Korsmeyer, F. T., Singer, J., Danmeier D. and White, J. K., "Accelerated Nonlinear Wave Simulations for Large Structures", 7th Int'l Conference on Numerical Ship Hydrodynamics, Nantes,
France, 1999.
117. M. Kamon, N. Marques, Y. Massoud, L. Silveira and J. White, "Interconnect analysis: from 3D structures to circuit models,'' Proceedings. 36th Design Automation Conference, New Orleans, 1999. Pp.
910 -914
118. D. Feng, J. Phillips, K. Nabors, K. Kundert and J. White, "Efficient computation of quasi-periodic circuit operating conditions via a mixed frequency/time approach," Proceedings. 36th Design
Automation Conference, New Orleans, 1999. pp. 635 -640
119. L. M. Silveira, N. Marques, M. Kamon and J. White, "Improving the efficiency of parasitic extraction and simulation of 3D interconnect models'',Proceedings of ICECS '99. The 6th IEEE
International Conference on Electronics, Circuits and Systems, Pafos, Cyprus, Sept. 1999,Volume 3, pp. 1729 -1732
120. D. Ramaswamy, N. Aluru and J. White, "Fast Coupled-Domain, Mixed-Regime electromechanical Simulation" Proc. Int'l Conference on Solid-State Sensors and Actuators (Transducers '99), Sendai,
Japan, June 1999 pp. 314-317.
121. J. Wang, J. Tausch and J. White, "A Wide Frequency Range Surface Formulation fro 3-D RLC Extraction," Proceedings of the IEEE Conference on Computer-Aided Design, San Jose, November 1999.
122. J. Li and J. White, "Efficient Model Reduction of Interconnect Via Approximate System Grammians," Proceedings of the IEEE Conference on Computer-Aided Design, San Jose, November 1999.
123. H. Levy, D. MacMillen, and J. White, "A rank-one Update Method for Efficient Processingof Interconnect Parasitics in Timing Analysis,'' Proceedings of the Design Automation Conference, Los
Angeles, June, 2000, pp 75-78
124. J. Kanapka, J. Phillips and J. White, "Fast methods for extraction and sparsification of substrate coupling," Proceedings of the 37th Design Automation Conference, Los Angeles, June, 2000, pp
125. Y. Chen and J. White, "A Quadratic Method for Nonlinear Model Order Reduction," International Conference on Modeling and Simulation of Microsystems, Semiconductors, Sensors and Actuators, San
Diego, March 2000.
126. X. Wang, J.N. Newman and J. White, "Robust Algorithms for Boundary Element Integrals on Curved Surfaces," International Conference on Modeling and Simulation of Microsystems, Semiconductors,
Sensors and Actuators, San Diego, March 2000.
127. W. Ye, X. Wang and J. White, "A Fast Stokes solver for Generalized Flow Problems" International Conference on Modeling and Simulation of Microsystems, Semiconductors, Sensors and Actuators, San
Diego, March 2000.
128. W. Ye, X. Wang, W. Hemmert, D. Freeman and J. White, "Viscous Drag on a Lateral Micro-Resonator: Fast 3-D Fluid Simulation and Measured Data" Proc. Solid-State Sensors and Actuators Workshop,
Hilton Head Island, June 2000, pp. 124-127.
129. L. Daniel, A. Sangiovanni-Vincentelli, J. White, "Interconnect Electromagnetic Modeling using Conduction Modes as Global Basis Functions," Topical Meeting on Electrical Performance of Electronic
Packages, Scottsdale, AZ, October 2000.
130. D. Ramaswamy and J. White, "Automatic Generation of Small-Signal Dynamic Macromodels from 3-D Simulation," International Conference on Modeling and Simulation of Microsystems, Semiconductors,
Sensors and
Actuators, Hilton Head, North Carolina,March 2001
131. X. Wang, P. Mucha and J. White, "Fast Fluid Analysis for Multibody Micromachined Devices," International Conference on Modeling and Simulation of Microsystems, Semiconductors, Sensors and
Actuators, Hilton Head, North Carolina, March 2001
132. X. Wang and J. White "Analyzing Fluid Compression Effects in Complicated Micromachined Devices," Proceedings of Transducers 01, June, 2001
133. L. Daniel A. Sangiovanni-Vincentelli, and J. White, "Using conduction modes basis functions for efficient electromagneticanalysis of on-chip and off-chip interconnect,'' Proceedings of the
Design Automation Conference, 2001, pp. 563 -566
134. Y. Massoud, J. Kawa, D. MacMillen, and J. White, "Modeling and analysis of differential signaling for minimizing inductive crosstalk,'' Proceedings of the Design Automation Conference, 2001. pp.
804 -809
135. J. Kanapka and J. White, "Highly Accurate Fast Methods for Extraction and Sparsification of Substrate Coupling Based On Low-Rank Approximation," Proc. of IEEE Conference on Computer-Aided
Design, San Jose, November 2001.
136. L. Daniel, A. Sangiovanni-Vincentelli, and J. White, "Techniques for Including Dielectrics when Extracting Low-Order Models of High Speed Interconnect," Proc. of IEEE Conference on
Computer-Aided Design, San Jose, November 2001.
137. M. Rewienski, J. White, "A Trajectory Piecewise-Linear Approach to Model Order Reduction and Fast Simulation of Nonlinear Circuits and Micromachined Devices'', in proceedings of the
International Conference on Computer-Aided Design, pp. 252-257, San Jose, Nov. 2001.
138. Z. Zhu, J. Huang, and J. White, "Improving the Robustness of a Surface Integral Formulation for Wideband Impendance Extraction of 3D Structures'' Proc. of IEEE Conference on Computer-Aided
Design, San Jose, November 2001.
139. X. Wang, M. Judy and J. White, "Validating Fast Simulation of Air Damping in Micromachined Devices'', Proceedings of MEMS '02, January, 2002
140. S. De, X. Wang and J. White, "Efficiency Improvements in Fast Stokes Solvers,'' International Conference on Modeling and Simulation of Microsystems, San Juan, April, 2002
141. L. Daniel, C. S. Ong, S. C. Low, K. H. Lee, J. White "Geometrically Parameterized Interconnect Performance Models for Interconnect Synthesis," International Symposium on Physical Design,
San Diego, April 2002.
142. M. Rewienski and J. White, "Improving Trajectory Piecewise-Linear Approach to Nonlinear Model Order Reduction for Micromachined Devices Using an Aggregated Projection Basis," International
Conference on Modeling and Simulation of Microsystems, San Juan, April, 2002
143. J. Bardhan, J. H. Lee, S. Kuo, M. Altman, B. Tidor, and J. White, "Fast Methods for Biomolecule Charge Optimization," International Conference on Modeling and Simulation of Microsystems, San
Juan, April, 2002
144. Y. Massoud and J. White, "Improving the Generality of the Fictitious Magnetic Charge Approach to Computing Inductances in the Presence of Permeable Materials," Proceedings of the Design
Automation Conference, November, June 2002.
145. J. Phillips, L. Daniel, L. M. Silveira, "Guaranteed Passive Balancing Transformations for Model Order Reduction", IEEE/ACM 39th Design Automation Conference, New Orleans, Jun 2002
146. L. Daniel, J. Phillips, "Model Order Reduction for Strictly Passive and Causal Distributed Systems", IEEE/ACM 39th Design Automation Conference, New Orleans, Jun 2002.
147. Y. Massoud and J. White, "FastMag: A 3-D Magnetostatic Inductance Extraction Program for Structures with Permeable Materials," Proc. of IEEE Conference on Computer-Aided Design, San Jose,
November 2002.
148. S. Kuo, M. Altman, J. Bardhan, B. Tidor and J. White, "Fast Methods for Simulation of Biomolecule Electrostatics," Proc. of IEEE Conference on Computer-Aided Design, San Jose, November 2002.
149. L. Daniel, A. Sangiovanni-Vincentelli, J. White, "Proximity Templates for Modeling of Skin and Proximity Effects on Packages and High Frequency Interconnect," Proc. of IEEE Conference on
Computer-Aided Design, San Jose, November 2002.
150. M. Rewienski and J. White, “A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices,” IEEE Transactions on
Computer-Aided Design of Integrated Circuits and Systems , Vol. 22, No. 2, pp. 155--170, Feb. 2003.
151. Zhenhai Zhu, Song, B., White J. "Algorithms in fastimp: a fast and wideband impedance extraction program for complicated 3-D geometries," Design Automation Conference, 2003. Proceedings, June
2-6, 2003.
Page(s): 712 -717
152. D. Vasilyev, M. Rewienski, J. White "A TBR-based trajectory piecewise-linear algorithm for generating accurate low-order models for nonlinear analog circuits and MEMS," Design Automation
Conference, 2003. Proceedings , June 2-6, 2003 Page(s): 490 -495.
153. L. Daniel and J. White, “Automatic generation of geometrically parameterized reduced order models for integrated spiral RF-inductors,” Behavioral Modeling and Simulation, 2003. BMAS 2003.
Proceedings of the 2003 International Workshop on, 7-8 Oct. 2003 Pages:18 – 2.
154. B. Song, Z. Zhu, and J. White, “Algorithms in FastImp: A Fast and Wideband Impedance Extraction Program For Complicated 3-D Geometries,” Proceedings of the Design Automation Conference, Anaheim,
CA, 2003, Pages:712 – 717.
155. B. Song, Z. Zhu, J. D. Rockway and J. White, “A New Surface Integral Formulation For Wideband Impedance Extraction of 3-D Structures,” Proc. of IEEE Conference on Computer-Aided Design, San
Jose, November 2003.
156. A. Nardi, H. Zeng, J. Garrett, L. Daniel, A. Sangiovanni-Vincentelli, "A Methodology for the Computation of an Upper Bound on Noise Current Spectrum of CMOS Switching Activity", IEEE/ACM
International Conference on Computer Aided Design, p 778-85, San Jose, CA, Nov 2003.
157. X. Hu, L. Daniel and J. White, “Partitioned conduction modes in surface integral equation-based impedance extraction,” Electrical Performance of Electronic Packaging , 2003 , 27-29 Oct. 2003 pp.
355 – 358.
158. A. Vithayathil, X. Hu, and J. White, “Substrate resistance extraction using a multi-domain surface integral formulation,” Proceeding of the International Conference on Simulation of
Semiconductor Processes and Devices(SISPAD), 2003. pp. 323 – 326.
159. D. J. Willis, J. K. White, and J. Peraire, “A pFFT accelerated linear strength BEM potential solver,” In Proc. of Modeling and Simulation of Microsystems, March, 2004.
160. J.P. Bardhan, J.H. Lee, M.D. Altman, S. Leyffer, S. Benson, B. Tidor and J.K. White, “Biomolecule Electrostatic Optimization with an Implicit Hessian,” Proc. of Modeling and Simulation of
Microsystems, March, 2004.
161. C. P. Coelho, J. K. White, and L. M. Silveira, “Dealing with stiffness in time-domain stokes flow simulation,” In Proc. of Modeling and Simulation of Microsystems , March, 2004.
162. D. Vasilyev, M. Rewienski, and J. K. White, “Perturbation analysis of TBR model reduction in application to trajectory-piecewise linear algorithm for MEMS structures,” In Proc. of Modeling and
Simulation of Microsystems , March, 2004
163. L. Daniel and J. White, “Numerical techniques for extracting geometrically parameterized reduced order interconnect models from full-wave electromagnetic analysis,” In Proceedings of the IEEE
AP-S International Symposium and USNC / URSI National Radio Science Meeting , 2004.
164. J. White, “CAD challenges in bioMEMS design,” In Proceedings of the Design Automation Conference , 2004, pp. 629-632.
165. Z. Zhu, A. Demir, and J. White, “A stochastic integral equation method for modeling the rough surface effect on interconnect capacitance,” In Proceedings of the IEEE Conference on Computer-Aided
Design , 2004.
166. D. Willis, J. Peraire and J. White, ``A Combined pFFT-Multipole Tree Code, Unsteady Panel Method with Vortex Particle Wakes,'' 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV,
January, 2005
167. J. Bardhan, M. D. Altman, S. M. Lippow, B. Tidor, and J. K. White, “A curved panel integration technique for molecular surfaces,” In Proceedings of Modeling and Simulation of Microsystems ,
168. C. Coelho, S. Desai, D. Freeman, and J. White, “A robust approach for estimating diffusion constants from concentration data in microchannel mixers,” In Proceedings of Modeling and Simulation of
Microsystems , 2005.
169. J. H. Lee, D. Vasilyev, A. Vithayathil, L. Daniel, and J. White, “Accelerated optical topography inspection using parameterized model order reduction,” In Proceedings of the IEEE International
Microwave Symposium , 2005.
170. X. Hu, J. White, and L. Daniel “Analysis of conductor impedance over substrate using novel integration techniques,” Proceedings of the Design Automation Conference , 2005.
171. T. Klemas, L. Daniel, and J. White, “Segregation by primary phase factors: a full-wave algorithm for model order reduction,” In Proceedings of the Design Automation Conference , 2005.
172. Sou, K, Megretski, A, Daniel, L, "A Quasi-Convex Optimization Approach to Parameterized Model Order Reduction", IEEE/ACM Design Automation Conference, Anaheim, CA, (2005)
173. T. Klemas, L. Daniel, and J. White, “A fast full-wave algorithm to generate low order electromagnetic scattering models,'' In International Symposium on Antennas and Propagation and USNC/URSI
National Radio Science Meeting , 2005
174. M. Altman, J. Bardhan, J. White, B. Tidor, "An Accurate Surface Formulation for Biomolecule Electrostatics in Non-Ionic Solutions", 27th Annual International Conference of the Engineering in
Medicine and Biology Society, September 2005. Page(s):7591 - 7595
175. Z. Zhu, A. Demir, and J. White, "FastSies: A Fast Stochastic Integral Equation Solver for modeling the Rough Surface Effect", Proceedings of the IEEE Conference on Computer-Aided Design, San
Jose, (2005)
176. B. Bond and L. Daniel, "Parameterized Model Order Reduction of Nonlinear Dynamical Systems", Proceedings of the IEEE Conference on Computer-Aided Design, San Jose, (2005)
177. D. Vasilyev and J. White, "A more reliable reduction algorithm for behavioral model extraction", Proceedings of the IEEE Conference on Computer-Aided Design, San Jose, (2005)
178. J. White, ``Developing Design Tools for Biological and Biomedical Applications of Micro- and Nano-technology,'' ACM International Conference on Hardware/Software Codesign and System Synthesis,
New York, September 2005
179. S. Kuo and J. White, "A Nystrˆm-Like Approach to Integral Equations with Singular Kernels,'' Proceedings of the International Conference on Modeling and Simulation of Microsystems (MSM), Boston,
May, 2006.
180. S. Kuo and J. White, "A Spectrally Accurate Integral Equation Solver for Molecular Surface Electrostatics,'' Proceedings of the IEEE Conference on Computer-Aided Design, San Jose, November 2006.
181. S. Johnson, Y. Avniel, S. Boyd, and J. White, "Design Tools for Emerging Technologies," Invited Paper, International Conference on Simulation of Semiconductor Processes and Devices (SISPAD),
Monterey, CA, September 2006.
182. X. Hu, T. Moselhy, L. Daniel, and J. White, "Novel Development of Optimization-based, Frequency-parameterizing Basis functions for the Efficient Extraction of Interconnect System Impedance'',
Design Automation and Test in Europe, Nice, April 2007.
183. X. Hu, T. Moselhy, J. White and L. Daniel, "Optimization-based Wideband Basis Functions for Efficient Interconnect Extraction", IEEE Conference on Design Automation and Test in Europe (DATE),
April 2007.
184. T. Moselhy , X. Hu, L. Daniel, "pFFT in FastMaxwell: A Fast Impedance Extraction Solver for 3D Conductor Structures over Substrate", IEEE Conference on Design Automation and Test in Europe
(DATE), April 2007, (Best Paper Award Nomination).
185. T. Moselhy, L. Daniel, "Stochastic High Order Basis Functions for Volume Integral Equation with Surface Roughness", IEEE Conference on Electrical Performance of Electronic Packaging (EPEP), Oct.
2007, (Best Student Paper Award Nomination).
186. K. C. Sou, A. Megretski, L. Daniel, "Bounding L2 Gain System Error Due to Approximations of the Nonlinear Vector Field", Proceedings of the IEEE Conference on Computer-Aided Design, San Jose,
November 2007.
187. B. Bond and L. Daniel, "Stabilizing Schemes for Piecewise-Linear Reduced Order Models via Projection and Weighting Functions", Proceedings of the IEEE Conference on Computer-Aided Design, San
Jose, November 2007, (Best Paper Award Nomination).
188. T. Moselhy and L. Daniel, "Stochastic Integral Equation Solver for Efficient Variation Aware Interconnect Extraction", IEEE/ACM Design Automation Conference, Anaheim, CA, June 2008.
189. L. Zhang, J. H. Lee, A. Farjadpour, J. White and Steven Johnson, “A novel boundary element method with surface conductive absorbers for 3-D analysis of nanophotonics,” in Proc. IEEE Microwave
Symposium, pp. 523 – 526, June 2008
190. T. Moselhy, A. Elfadel and D. Widiger, “Efficient algorithm to compute capacitance sensitivities with respect to a large set of parameters,” ACM/IEEE Design Automation Conference, pp. 906-911,
June 2008.
191. K. C. Sou, A.Megretski and L. Daniel, “Convex relaxation approach to the identification of the Wiener-Hammerstein model,” IEEE Conference on Decision and Control, pp.1375-1382, Cancun, Dec. 2008
192. T. A. El-Moselhy, I. M. Elfadel and L. Daniel, “A capacitance solver for incremental variation-aware extraction,” IEEE/ACM International Conference on Computer-Aided Design, pp. 662-669, Nov.
193. B. N. Bond and L. Daniel, “Guaranteed stable projection-based model reduction for indefinite and unstable linear systems,” IEEE/ACM International Conference on Computer-Aided Design, pp.
728-735, Nov. 2008 (IEEE/ACM William J. McCalla ICCAD Best Paper Award)
194. J. White, “Design tools for emerging technologies,” ACM Great Lakes Symposium on VLSI, pp. 99-100, May 2009
195. T. A. El-Moselhy, I. M. Elfadel and B. Dewey, “An efficient resistance sensitivity extraction algorithm for conductors of arbitrary shapes,” ACM/IEEE Design Automation Conference, pp. 770-775,
June 2009
196. Y.-C. Hsiao, T. El-Moselhy and L. Daniel, "Efficient capacitance solver for 3D interconnect based on template-instantiated basis functions," IEEE Conference on Electrical Performance of
Electronic Packaging and Systems, pp.179-182, 19-21 Oct. 2009
197. M. J. Tsuk, D. Dvorscak, C. S. Ong and J. White, “An electrical-level superposed-edge approach to statistical serial link simulation,” IEEE/ACM International Conference on Computer Aided Design,
pp.717-724, San Jose, CA, Nov. 2009.
198. T. A. El-Moselhy, I. M. Elfadel and Luca Daniel, “A hierarchical floating random walk algorithm for fabric-aware 3D capacitance extraction,” IEEE/ACM International Conference on Computer Aided
Design, pp. 752-758, San Jose, CA, Nov. 2009.
199. Z. Mahmood, Br. N. Bond, T. Moselhy, A. Megretski and L. Daniel, “Passive reduced order modeling of multiport interconnects via semidefinite programming,” IEEE/ACM Design Automation and Test in
Europe, pp. 622-625, March 2010.
200. T. A. El-Moselhy and L. Daniel, “Variation-aware interconnect extraction using statistical moment preserving model order reduction’, IEEE/ACM Design Automation and Test in Europe, pp. 453-458,
March 2010. (Best Paper Nomination)
201. T. A. El-Moselhy and L. Daniel, “Stochastic dominant singular vectors method for variation-aware extraction,” IEEE/ACM Design Automation Conference, pp. 667-672, June 2010. (Best Paper Award
202. B. N. Bond and L. Daniel, “Automated compact dynamical modeling: an enabling tool for analog designers,” IEEE/ACM Design Automation Conference, pp. 415-420, June 2010. (Invited Paper)
203. Z. Mahmood and L. Daniel, “Circuit synthesizable guaranteed passive modeling for multiport structures,” IEEE Behavior Modeling and Simulation Conference, pp. 19-24, San Jose, CA, Sept. 2010.
204. Z. Zhang, Q. Wang, N. Wong and L. Daniel, “A moment-matching scheme for the passivity-preserving model order reduction of indefinite descriptor systems with possible polynomial parts,” IEEE/ACM
Asia and South Pacific Design Automation Conference, pp. 49-54, Yokohama, Japan, Jan. 2011. (Best Paper Nomination)
205. Tarek A. El-Moselhy and Luca Daniel, “Variation-aware stochastic extraction with large parameter dimensionality: Review and comparison of state of the art intrusive and non-intrusive
techniques,” IEEE International Symposium on Quality Electronic Design, pp. 508-517, San Jose, CA. March 2011. (Invited Paper)
206. Y.-C. Hsiao and L. Daniel, “A highly scalable parallel boundary element method for capacitance extraction,” ACM/IEEE Design Automation Conference, pp. 552-557, June 2011.
207. A. Hochman, B. N. Bond and J. K. White, “A stabilized discrete empirical interpolation method for model reduction of electrical, thermal, and microelectromechanical systems,” ACM/IEEE Design
Automation Conference, pp. 540-545, June 2011.
208. J. E. Toettcher, A. Castillo, B. Tidor, and J. White, “Biochemical oscillator sensitivity analysis in the presence of conservation constraints,”ACM/IEEE Design Automation Conference, pp.
806-811, June 2011.
209. Z. Zhang, I. M. Elfadel and L. Daniel, "Model order reduction of fully parameterized systems by recursive least square optimization," IEEE/ACM International Conference on Computer-Aided Design,
pp. 523-530, San Jose, CA, Nov. 2011 (Best Paper Nomination)
210. R. Suaya, C. Xu, V. Kourkoulos, K. Banrejee, Z. Mahmood and L. Daniel, "Some results pertaining electromagnetic characterization and model building for passive systems including TSVs, for 3-D IC
applications", IEEE Conference on Electrical Design of Advanced Packaging & Systems, pp. 1-4, Hangzhou, China, Dec. 2011.
211. T. El Moselhy and L. Daniel, "Stochastic Extraction for SoC and SiP Interconnect with Variability”, IEEE Conference on Electrical Design of Advanced Packaging & Systems, pp. 1-4, Hangzhou,
China, Dec. 2011. (Invited Paper)
212. Z. Mahmood, R. Suaya and L. Daniel, “An efficient framework for passive compact dynamical modeling of multiport linear systems,” IEEE/ACM Design Automation and Test in Europe, Dresden, Germany,
pp. 1203-1208, March 2012
213. R. Marathe, W. Wang, Z. Mahamood, L. Daniel and D. Weinstein, “Resonant body transistors in standard CMOS technology,” IEEE International Ultrasonic Symposium, pp. 289 – 294, Dresden, Germany,
Oct. 2012.
214. R. Marathe, W Wang, Z Mahmood, L Daniel and D Weinstein, “Resonant body transistors in IBM's 32nm SOI CMOS technology,” IEEE International SOI Conference, pp. 1-2, Napa, CA, Oct. 2012.
215. Li Yu, Omar Mysore, Lan Wei, Luca Daniel, Dimitri A. Antoniadis, Ibrahim M. Elfadel, Duane S. Boning, “An ultra-compact virtual source FET model for deeply-scaled devices: Para,” IEEE/ACM Asia
and South Pacific Design Automation Conference, pp. 521-526, Yokohama, Japan, Jan. 2013.
216. P. F. Mitros, K. K. Affidi, G. J. Sussman, C. J. Terman, J. K. White, L. Fischer, and A. Agarwal, “Teaching electronic circuits online: Lessons from MITx's 6.002x on edX,” IEEE Symposium on
Circuits and Systems, pp. 2763 – 2766, Beijing, China, May 2013.
217. Z. Mahmood, A. Chinea, G. C. Calafiore, S. Grivet-Talocia and Luca Daniel, “Robust localization methods for passivity enforcement of linear macromodels,” IEEE Workshop on Signal and Power
Integrity, pp. 1-4, May 2013.
218. M. Kamon, S. Maity, D. Dereus, Z. Zhang, S. Cunningham, S. Kim, J. McKillop, A. Morris, G. Lorenz and L. Daniel, “New simulation and experimental methodology for analyzing pull-in and release in
MEMS switches,” IEEE International Conference on Solid-State Sensors, Actuators and Microsystems (Transducers 2013), pp. 2373 - 2376 , Barcelona, Spain, June, 2013
219. J. Fernández Villena, A. G. Polimeridis, A. Hochman, J. K. White and L. Daniel, “Magnetic resonance specific integral equation solver based on precomputed numerical Green functions,” IEEE
Conference on Electromagnetics in Advanced Application, pp. 724 – 727, Torino, Italy, Sept. 2013
220. Z. Zhang, I. M. Elfadel and L. Daniel, "Uncertainty quantification for integrated circuits: Stochastic spectral methods," IEEE/ACM International Conference on Computer-Aided Design, pp. 803-810,
San Jose, CA, Nov. 2013. (Invited Paper)
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What is constant appreciation? + Example
What is constant appreciation?
1 Answer
Appreciation is a rate of positive change. So constant appreciation means the rate of change is constant. This implies a linear function, however, the appreciation occurs at certain time intervals,
so it is more like an arithmetic sequence.
An example of constant appreciation is simple interest. This is where interest is typically paid on the principal annually. For instance, $1000 is invested in a term deposit at 2% simple interest for
5 years . What is the value of the term deposit at the end of 5 years? 2% of $1000 is $20, so $20 is the constant appreciation. At the end of 5 years, the term deposit would be worth $1100: #
Note that most banks pay out using compound interest rather than simple interest.
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Specifying Formulas in a DAG
Robin Denz
In this small vignette, we give more detailed examples on how best to use the formula argument in the node() and node_td() functions. This argument allows users to directly specify the full
structural equation that should be used to generate the respective node in a clear and easy way, that does not directly rely on the parents, betas and associated arguments. Note that the formula
argument may only be used with certain node types, as mentioned in the documentation.
A simple example
We will start with a very simple example. Suppose we want to generate some data from a simple DAG with no time-varying variables. Consider the following DAG:
dag <- empty_dag() +
node("A", type="rnorm", mean=0, sd=1) +
node("B", type="rbernoulli", p=0.5, output="numeric") +
node("C", type="rcategorical", probs=c(0.3, 0.2, 0.5),
output="factor", labels=c("low", "medium", "high"))
This DAG contains only three root nodes of different types. \(A\) is normally distributed, \(B\) is Bernoulli distributed and \(C\) is a simple categorical variable with the levels “low”, “medium”
and “high”. If we generate data from this DAG alone, it would look like this:
dat <- sim_from_dag(dag, n_sim=10)
#> A B C
#> <num> <num> <fctr>
#> 1: -0.8041685 0 low
#> 2: 1.3390885 0 medium
#> 3: 0.9455804 0 high
#> 4: -2.3437852 1 low
#> 5: -0.9045554 1 medium
#> 6: 0.8532361 1 medium
Suppose we now want to generate an additional child node called \(D\) which should be based on a linear regression model of the form:
\[D \sim -8 + A \cdot 0.4 + B \cdot -2 + N(0, 1.5).\]
We could do this using the node() function, by supplying appropriate values to the parents, betas, intercept and error arguments. The following code could be used:
dag_without_formula <- dag +
node("D", type="gaussian", parents=c("A", "B"), betas=c(0.4, -2),
intercept=-8, error=1.5)
This does work just fine, but it may be a little cumbersome to specify the DAG in this way. Since we want to use a linear regression model, we could instead use the formula argument like this:
Given the same random number generator seed, the same output will be produced from both DAGs, as shown below:
dat1 <- sim_from_dag(dag_without_formula, n_sim=100)
dat2 <- sim_from_dag(dag_with_formula, n_sim=100)
all.equal(dat1, dat2)
#> [1] TRUE
Formulas should always start with a ~ sign and have nothing else on the left hand side. All parts of the formula should be connected by + signs, never - signs. The name of the respective variable
should always be connected to the associated coefficient by a * sign. It does not matter whether the name of the term or the coefficient go first, but it has to be consistent in a formula. For
example, ~ 1 + A*2 + B*3 works, and ~ 1 + 2*A + 3*B also works, but ~ 1 + 2*A + B*2 will produce an error. The formula may also be supplied as a string and will produce the same output.
Apart from being easier to read, this also allows the user a lot more options. Through the use of formulas it is possible to specify nodes that have categorical parents. It is also possible to
include any order of interaction effects and cubic terms using formulas, as shown below.
Using a Categorical Parent Variable
Suppose that \(D\) should additionally depend on \(C\), a categorical variable. For example, suppose this is the regression model we want to generate data from:
\[D \sim -8 + A \cdot 0.4 + B \cdot -2 + Cmedium \cdot -1 + Chigh \cdot -3 + N(0, 1.5).\]
In this model, the “low” category is used as a reference category. If this is what we want to do, using the simple parents, betas, intercept approach no longer works. We have to use a formula.
Fortunately, this is really simple to do using the following code:
dag2 <- dag +
node("D", type="gaussian", error=1.5,
formula=~ -8 + A*0.4 + B*-2 + Cmedium*-1 + Chigh*-3,
parents=c("A", "B", "C"))
Essentially, all we have to do is use the name of the categorical variable immediately followed by the category name. Note that if a different reference category should be used, the user needs to
re-define the factor levels of the categorical variable accordingly first.
Note that we also defined the parents argument in this case. This is not strictly necessary to generate the data in this case, but it is recommended whenever categorical variables are used in a
formula for two reasons:
• 1.) If parents is not specified, the sim_from_dag() function will not know that \(C\) is a parent of \(D\). If sort_dag=TRUE and/or the nodes are not specified in a correctly topologically sorted
order, this may lead to errors when trying to generate the data.
• 2.) If parents is not specified, other functions that take DAG objects as input (such as the plot.DAG() function) may produce incorrect output, because they won’t know that \(C\) is a parent of \
Using Interaction Effects
Interactions of any sort may also be added to the DAG. Suppose we want to generate data from the following regression model:
\[D \sim -8 + A \cdot 0.4 + B \cdot -2 + A*B \cdot -5 + N(0, 1.5),\]
where \(A*B\) indicates the interaction between \(A\) and \(B\). This can be specified in the formula argument using the : sign:
Since both \(A\) and \(B\) are coded as numeric variables here, this works fine. If we instead want to include an interaction which includes a categorical variable, we again have to use the name with
the respective category appended to it. For example, the following DAG includes an interaction between \(A\) and \(C\):
dag4 <- dag +
node("D", type="gaussian", error=1.5,
formula=~ -8 + A*0.4 + B*-2 + Cmedium*-1 + Chigh*-3 + A:Cmedium*0.3 +
parents=c("A", "B", "C"))
Higher order interactions may be specified in exactly the same way, just using more : symbols. It may not always be obvious in which order the variables for the interaction need to be specified. If
the “wrong” order was used, the sim_from_dag() function will return a helpful error message explaining which ones should be used instead. For example, if we had used “Cmedium:A” instead of
“A:Cmedium”, this would not work because internally only the latter is recognized as a valid column. Note that because \(C\) is categorical, we also specified the parents argument here just to be
Using Cubic Terms
Sometimes we also want to include non-linear relationships between a continuous variable and the outcome in a data generation process. This can be done by including cubic terms of that variable in a
formula. Suppose the regression model that we want to use has the following form:
\[D \sim -8 + A \cdot 0.4 + A^2 \cdot 0.02 + B \cdot -2 + N(0, 1.5).\]
The following code may be used to define such as node:
dag_with_formula <- dag +
node("D", type="gaussian", formula= ~ -8 + A*0.4 + I(A^2)*0.02 + B*-2,
Users may of course use as many cubic terms as they like.
Using Functions in formula
There is also limited support for including functions in the formula as well. For example, it is allowed to call any function on the beta coefficients, which is useful to specify betas on a different
scale (for example using Odds-Ratios instead of betas). For example:
is valid syntax. Any function can be used in the place of log(), as long as it is a single function that is called on a beta-coefficient. | {"url":"https://cran.dcc.uchile.cl/web/packages/simDAG/vignettes/v_using_formulas.html","timestamp":"2024-11-07T06:52:28Z","content_type":"text/html","content_length":"28922","record_id":"<urn:uuid:84e6a1b5-cd83-4b51-954f-efc00a03687c>","cc-path":"CC-MAIN-2024-46/segments/1730477027957.23/warc/CC-MAIN-20241107052447-20241107082447-00565.warc.gz"} |
Right function
I have two questions:
1. Suppose A1=4 and B1=8 then in C3 i use this formula to suffix lakhs =sum(a1+b1)&" "&"Lakhs" (12 Lakhs). How to prefix Lakhs (Lakhs 12).
2. Let again suppose A1=Nabam Raju. How to pull outin right side(Raju) having variable length? I Hate using this =RIGHT(A1,4) as i have to kept on changing 4.
first =sum(a1+b1)&" "&"Lakhs" (12 Lakhs) can be changed to: =sum(a1+b1)&" Lakhs" (12 Lakhs)
but to answer the question:
="Lakhs "&sum(a1+b1) (Lakhs 12)
for question number 2
=Mid(A1,find(" ",A1)+1,255) (Raju)
you can actually calculate the needed length, but using a large number for the length should work as long as the length of the string doesn't exceed the large number - and it is pretty simple. the
string produced is still the correct length (in your example, 4 characters) and not 4 characters with a whole bunch of spaces.
=Mid(A1,find(" ",A1)+1,len(A1)-Find(" ",A1))
is the formula if you want to calculate the 3rd argument to be exactly 4 characters. | {"url":"http://www.eluminary.org/en/QnA/Right_function_(Excel)","timestamp":"2024-11-13T21:21:16Z","content_type":"text/html","content_length":"9789","record_id":"<urn:uuid:8f257682-7b1a-4bc6-8a09-bb6b3d76125d>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00330.warc.gz"} |
ExplodeLayout | CRAN/E
Calculate Exploded Coordinates Based on Original Node Coordinates and Node Clustering Membership
CRAN Package
Current layout algorithms such as Kamada Kawai do not take into consideration disjoint clusters in a network, often resulting in a high overlap among the clusters, resulting in a visual “hairball”
that often is uninterpretable. The ExplodeLayout algorithm takes as input (1) an edge list of a unipartite or bipartite network, (2) node layout coordinates (x, y) generated by a layout algorithm
such as Kamada Kawai, (3) node cluster membership generated from a clustering algorithm such as modularity maximization, and (4) a radius to enable the node clusters to be “exploded” to reduce their
overlap. The algorithm uses these inputs to generate new layout coordinates of the nodes which “explodes” the clusters apart, such that the edge lengths within the clusters are preserved, while the
edge lengths between clusters are recalculated. The modified network layout with nodes and edges are displayed in two dimensions. The user can experiment with different explode radii to generate a
layout which has sufficient separation of clusters, while reducing the overall layout size of the network. This package is a basic version of an earlier version called [epl] that searched for an
optimal explode radius, and offered multiple ways to separate clusters in a network (Bhavnani et al(2017) ). The example dataset is for a bipartite network, but the algorithm can work also for
unipartite networks.
• Version0.1.2
• R version≥ 2.10
• Needs compilation?No
• Last release07/01/2022
Last 30 days
Last 365 days
The following line graph shows the downloads per day. You can hover over the graph to see the exact number of downloads per day.
Data provided by cranlogs
• Depends1 package
• Imports2 packages | {"url":"https://cran-e.com/package/ExplodeLayout","timestamp":"2024-11-03T09:02:45Z","content_type":"text/html","content_length":"66211","record_id":"<urn:uuid:bb037209-2906-4c8e-a60a-5c243d256976>","cc-path":"CC-MAIN-2024-46/segments/1730477027774.6/warc/CC-MAIN-20241103083929-20241103113929-00814.warc.gz"} |
Excel Formula for Correlation Coefficient
In this guide, we will learn how to calculate the correlation coefficient between TTESS Rank and Growth Score in Excel using a specific classification column. The correlation coefficient is a
statistical measure that indicates the strength and direction of the linear relationship between two variables. By analyzing the correlation coefficient, we can determine if there is a positive or
negative correlation between TTESS Rank and Growth Score based on different classifications.
To calculate the correlation coefficient, we will use the CORREL function in Excel along with the IF function to filter the data based on the desired classification. The formula will only consider
the TTESS Rank and Growth Score values that correspond to the specified classification.
Let's take a closer look at the step-by-step explanation of the formula:
1. The IF function is used to check if the value in the classification column matches the desired classification.
2. The result of the IF function is an array of TRUE and FALSE values, where TRUE represents the cells where the corresponding value in the classification column matches the desired classification.
3. The IF function is used twice, once for the TTESS Rank and once for the Growth Score. This ensures that only the values corresponding to the desired classification are used in the correlation
4. The CORREL function is then used to calculate the correlation coefficient between the filtered TTESS Rank and Growth Score values.
Let's consider an example to better understand the formula. Suppose we have a dataset with columns A, B, and C:
A B C
A 5 10
B 3 8
A 7 12
C 6 9
A 2 6
B 9 15
A 1 4
C 4 7
If we want to calculate the correlation coefficient between TTESS Rank and Growth Score for the classification 'A', we can use the formula =CORREL(IF(A:A="A", B:B), IF(A:A="A", C:C)). In this case,
the correlation coefficient would be approximately 0.981, indicating a strong positive correlation between TTESS Rank and Growth Score for the 'A' classification.
By following this guide, you can easily calculate the correlation coefficient between TTESS Rank and Growth Score in Excel based on different classifications. This analysis can provide valuable
insights into the relationship between these variables and help make informed decisions.
An Excel formula
=CORREL(IF(A:A="Classification", B:B), IF(A:A="Classification", C:C))
Formula Explanation
This formula uses the CORREL function to calculate the correlation coefficient between the TTESS Rank (column B) and Growth Score (column C) based on a specific classification (column A).
Step-by-step explanation
1. The IF function is used to check if the value in column A is equal to the desired classification.
2. The result of the IF function is an array of TRUE and FALSE values, where TRUE represents the cells where the corresponding value in column A matches the desired classification.
3. The IF function is used twice, once for the TTESS Rank (column B) and once for the Growth Score (column C). This ensures that only the values corresponding to the desired classification are used
in the correlation calculation.
4. The CORREL function is used to calculate the correlation coefficient between the TTESS Rank and Growth Score based on the filtered values.
For example, if we have the following data in columns A, B, and C:
| A | B | C |
| | | |
| A | 5 | 10 |
| B | 3 | 8 |
| A | 7 | 12 |
| C | 6 | 9 |
| A | 2 | 6 |
| B | 9 | 15 |
| A | 1 | 4 |
| C | 4 | 7 |
The formula =CORREL(IF(A:A="A", B:B), IF(A:A="A", C:C)) would return the correlation coefficient between the TTESS Rank and Growth Score for the classification 'A'. In this case, the correlation
coefficient would be approximately 0.981, indicating a strong positive correlation between the TTESS Rank and Growth Score for the 'A' classification. | {"url":"https://codepal.ai/excel-formula-generator/query/ywj0TMDj/excel-formula-correlation-coefficient-ttess-rank-growth-score","timestamp":"2024-11-06T04:31:57Z","content_type":"text/html","content_length":"101962","record_id":"<urn:uuid:164755e0-63bd-4dba-bfb8-d1b90851b519>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00024.warc.gz"} |
How to make the Grading Ring more efficient for 330kV Transmission Line
Harms caused by corona discharge such as corona noise, wireless interference or electrostatic effect attract increasing attention from people. Results of relevant studies indicate that the corona
discharge of 330kV AC transmission line grading rings in northwest high-altitude area is serious and grading rings have become one of main parts causing electromagnetic pollution. Given
characteristics of corona discharge, it is difficult to meet the requirements of high-altitude operation.
The factors affecting corona discharge of grading rings are complicated. Parts where the field strength is high are mainly located at the curves of uneven field strength distribution. The radius of
electrode curvature at the curve is small so it is likely to have partial corona discharge; meanwhile, the discharge of grading rings are easily affected by operating conditions, including pressure,
temperature and humidity etc.
In this paper, the finite element method is used to set up a simulation model for grading ring; its surface electric field distribution is calculated and analyzed with the influence of surrounding
wires, towers and equipment into consideration; corona characteristics of grading rings of many structures are studied at UHV outdoor test filed of China Electric Power Research Institute and UHVAC
test base climate lab; the ultraviolet imager is used to measure corona parameters and get characteristic curves; the altitude correction method which meets the requirements of project is put
1. Modeling and Analysis
1.1 Modeling of strain insulator grading ring
The strain insulator of 330kV AC transmission line is used to make modeling; the model of grading ring is shown in Fig.1. The nominal height of model is 15.5m; the length of strain insulator is
3255mm; the wire is aluminum conductor steel-reinforced cable 2xLGJ-300/40 with the diameter 23.9mm; split spacing is 23.9 while the pipe diameter of grading ring is 32mm.
Fig.1. Calculation model of grading ring
According to the model shown in Fig.1, the applied voltage of single phase in the calculation is the voltage peak of maximum running voltage. It can be seen that the maximum field strength of grading
ring surface with the pipe diameter 32mm is 27.8kV/m shown in Fig.2. The value is close to the critical field strength under standard conditions. To facilitate the usage on the high-altitude area,
measures should be taken to improve electric field distribution, reduce the partial high field strength and enhance the whole dielectric strength of insulation structure. Two methods - increase in
the pipe diameter of grading ring and improvement in the radius of curvature are utilized to optimize the design.
Fig.2 Surface electric field distribution of grading ring (the diameter of pipe: 32mm)
1.2 Increase in the pipe diameter of grading ring
Do calculation according to three pipe diameters: 42mm, 45mm and 50mm. Through the simulation calculation, the maximum field strength corresponding with three different diameters is 24.1kV/cm, 23.1kV
/cm and 21.7kV/cm respectively. See the Tab.1.
Tab.1 Electric field strength of grading rings with different pipe diameters
1.3 Increase in the radius of curvature
The electric field strength of grading ring surface is proportional to surface charge density. At the curve, the radius of curvature is small and the surface charge density is great, so the strength
of electric field is high and the corona is likely to happen. Its field strength can be effectively reduced through increasing the radius. Through simulation modeling, the radius increases from 120mm
to 220mm, which is shown in Fig.3. Following the optimization, the maximum field strength is 21.6kV/cm. Please see Fig.4. The value is close to the one of grading ring with the diameter 50mm.
Fig.3. Optimized model of grading ring
Fig.4 Surface electric field distribution of grading ring (pipe diameter: 42mm)
But an increase in the pipe diameter directly affects the production cost of grading ring. Through optimizing the design of structure and increasing the radius of curvature, the surface field
strength can be reduced and requirements are met. In addition, production cost is also cut.
2. Corona Test of Grading Ring
2.1 Test conditions and object of study
The power supply of UHV outdoor test site is power frequency test transformer with 2250kV nominal voltage and 9000kV·A nominal capacity. In the UHV climate lab, the diameter of tank is 22m and the
height is 32m. The atmosphere pressure can be reduced to 50kPa, simulate different altitudes, the test power supply is power frequency test transformer with 1500kV nominal voltage and 6000kV·A
nominal capacity. The length of aluminum wire is 8m and split spacing is 400mm. One end of aluminum is connected with grading ring while the other end is connected with shielding ring with the
external diameter 1m; the test object is 4m away from the ground. The grading ring with two kinds of pipe diameters 32mm and 42mm is used to carry out the corona inception voltage tests. Meanwhile,
to study the influence of altitude on the inception voltage, the corona tests of grading rings at different simulated altitudes are done at the UHVAC test base climate lab.
2.2 Test method and observing equipment
In this paper, a ultraviolent imager is used to observe and record the whole process of corona discharge. The ultraviolent imager shown in Fig.5 is placed 13m away from grading ring. Suspend two ends
of prepared strain insulator under cross-arm by means of insulation ropes. Hang the whole object under the bushings by crane at the climate lab. When testing, boost the applied voltage gradually
until the ultraviolent imager shows that the corona generates; keep for 5 minutes and mark the voltage as the inception voltage of grading ring corona; then reduce the applied voltage until the
corona disappears; record this voltage as the extinguishing voltage; keep for 5 minutes. Repeat the procedure three times and take the average value as the inception and extinguishing voltage of
Fig.5 Ultraviolet imager
3. Test Results and Analysis
3.1 Optimization test of grading ring
The optimization test of grading ring is carried out at the outdoor test site. The corona discharge tests are conducted for the grading ring before and after optimization. Before optimization, the
pipe diameter is 32mm while the radius of curvature is 120mm. After optimization, there are two structures: ① to increase pipe diameter to 42mm and not change the radius; ② to increase pipe diameter
to 42mm and the radius of curvature to 220mm. Results of corona tests for three types are shown in Tab.2.
Tab.2 Corona test results of grading rings with different types
From the Tab.2, it can be seen that the corona inception and extinguishing voltage rise by 20.8% and 26.8% respectively after optimizing the pipe diameter; after further improvement in the radius of
curvature, the inception and extinguishing voltage goes up by 25.3% and 30.3%. Results indicate that two methods are workable.
3.2 Simulation of high-altitude test
To get the law between corona characteristics and the altitude, the corona discharge test of grading ring with the pipe diameter 42mm is conducted at the climate lab where the pressure is changed to
simulate the 19-4300m altitude. Test results are shown in Fig.6. In the Fig.6, Ui is inception voltage, kV; H: altitude, km.
Fig.6 Corona inception voltage of grading ring at different simulated altitudes
According to the above test results, the corona inception voltage reduces as the altitude rises. At 4300m the corona inception voltage is 190kV, down by 30.4% than 19m. Hence, when the grading ring
works at high altitude area, the problem - the high altitude causes the reduction of corona inception voltage and serious corona discharge must be taken into account.
4. Altitude Correction of Corona Inception Voltage for Grading Ring
At present, there are two methods about altitude correction according to national and international standards:
GB311.1-1997 K=1/(1.1-0.1H)
In the formula:
H: altitude, km
The method is applicable for the voltage correction of internal insulation and dry-type transformer insulation test between 1000m and 4000m. Take the 1000m as the start point and the correction
coefficient under 1000m is 1.
IEC 60071-2:1996 presents the correction coefficient:
In the formula:
m: correction coefficient related to voltage type and gap structure
m=1 for short power frequency test.
The available correction method is based on finite test data at low altitude. In this paper, several simulated altitudes are selected to obtain the correction method based on test data. Set the
corona inception voltage of grading ring at 19m as the standard value and the following data can be obtained.
Tab.3 Correction coefficients of different methods
According to the Tab.3 the correction coefficient:
The above three methods are used to correct the inception voltages of simulated altitudes. Compare the correction results with those of 19m altitude to obtain the correction errors shown in Tab.4.
Tab.4 Correction errors of different methods
The GB311.1 correction error is negative deviation within 3500m and the maximum deviation is -8.06%; the IEC60071-2 correction error is positive deviation, which is proportional to the altitude. The
deviation absolute value can be controlled within 2% through the correction method obtained in this paper. Please refer to the method proposed in the paper when designing the grading ring of
high-altitude area transmission line. Select the size of equipment according to the altitude to meet the requirements.
5. Conclusions
1) Use the finite element method to perform the simulation calculation of electric field and set up the simulation model to obtain surface electric field distribution. When increase the pipe diameter
of grading ring to 42mm, the maximum field strength reduces to 24.1kV/cm; further increase the radius of curvature to 220mm, the surface maximum field strength falls to 21.6kV/cm.
2) Results of corona tests indicate that the optimization of pipe diameter can improve the corona inception voltage and extinguishing voltage by 20.8% and 26.8% while the radius of curvature by 25.3
and 30.3%.
3) As the altitude rises, the corona inception voltage of grading ring reduces and the discharge becomes more serious. The deviation absolute value can be controlled within 2% through the correction
method obtained in this paper. Please refer to the method proposed in the paper when designing the grading ring of high-altitude area transmission line.
The builders worked on wooden platforms suspended by ropes from the roof of the building. | {"url":"https://www.coronarings.com/blog/how-to-make-the-grading-ring-more-efficient-for-330kv-transmission-line","timestamp":"2024-11-10T18:11:19Z","content_type":"text/html","content_length":"294010","record_id":"<urn:uuid:8ff950e0-9c55-44a4-9823-a14ee0790384>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00040.warc.gz"} |
less than
Displaying results 1 to 12 of 12.
greater than
less than
mapping diagrams
Students complete number relationships using 'is greater than' and 'is less than'.
greater than
less than
mapping diagrams
Students interpret a relationship diagram about the relative heights of four children.
equal to
greater than
less than
linear scales
reading scales
Students read pairs of measurements on linear scales and identify which are greater than, less than, or equal to.
equal to
greater than
less than
Students complete inequations by identifying the number or symbol needed to make the expression correct.
greater than
less than
mapping diagrams
Students interpret and answer questions about a relationship diagram that shows which of four children are older than each other.
equal to
greater than
less than
For this NEMP task students use cards with numbers and operations on them to create number sentences.
equal to
greater than
less than
Students select the correct symbol (greater then, equal to, less than) to complete statements about the ages of some children.
equal to
greater than
less than
Students decide whether pairs of number expressions are equal to, less than, or greater than each other.
equal to
greater than
less than
Students select the correct symbol or the correct number to make number sentences true.
equal to
greater than
less than
Students complete inequations by identifying the number or symbol needed to make the expression correct.
equal to
greater than
less than
Students select from 'less than', 'equal to', and 'greater than' to complete word equations about food amounts.
equal to
greater than
less than
Students select the correct symbol (greater than, equal to, less than) to complete statements about the number of lollies in a bag. | {"url":"https://arbs.nzcer.org.nz/category/keywords/less","timestamp":"2024-11-04T10:43:59Z","content_type":"text/html","content_length":"67371","record_id":"<urn:uuid:65d606ba-2ac7-4eeb-9b14-f4d02c7cccfc>","cc-path":"CC-MAIN-2024-46/segments/1730477027821.39/warc/CC-MAIN-20241104100555-20241104130555-00408.warc.gz"} |
EViews Help: partcor
Display the partial correlation matrix derived from the observed covariance matrix.
The elements of the partial correlation matrix are the pairwise correlations conditional on the other variables.
The partial correlation matrix is computed by scaling the anti-image covariance to unit diagonal (or equivalently, by row and column scaling the inverse of the observed matrix by the square roots of
its diagonals).
factor f1.ml group01
displays and prints the partial correlation matrix for the factor object F1. | {"url":"https://help.eviews.com/content/factorcmd-partcor.html","timestamp":"2024-11-13T21:39:52Z","content_type":"application/xhtml+xml","content_length":"9810","record_id":"<urn:uuid:401825bd-f5d6-4fdc-9c94-337033d61fe5>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00508.warc.gz"} |
Different Logical Systems Can Be Used to Model Different Fragments of Natural Language
When I was teaching logic I would sometimes get students who had some prior exposure to the subject and often it was an exposure to Aristotelian logic. I had several students who were taught the
subject in Catholic high schools, and some homeschooled students said that they had to learn categorical logic as part of their “classical” homeschooling education program.
One of the unfortunate consequences of this early exposure is that many of these students associated all of logic with the one formal system that they were taught.
As a result, some of these students had a distorted view of what logic really is and how it works.
The key idea that I want students to understand, on the issue of how logic relates to language, is that different logical systems represent different fragments of the logical structure of natural
human language.
What do I mean by a “fragment”? I mean a subset, a partial description, not the whole picture.
To see what I mean, let’s take a look at the three systems of logic that most students are introduced to in an introductory symbolic logic class, and say a few words about the kinds of logical
properties of language that each is capable of modeling. | {"url":"https://criticalthinkeracademy.com/courses/propositional-logic/lectures/751628","timestamp":"2024-11-02T01:50:26Z","content_type":"text/html","content_length":"167756","record_id":"<urn:uuid:ccfe7fbf-e61b-46b9-9006-8729ce6a55cb>","cc-path":"CC-MAIN-2024-46/segments/1730477027632.4/warc/CC-MAIN-20241102010035-20241102040035-00471.warc.gz"} |
The “Weasel” Saga — With Math (Part 2)
In Part 1, I introduced the “weasel” program, gave an overview of its role as a teaching tool, and gave some analysis of random search, the procedure that is contrasted with cumulative selection.
This time, I’ll be going into the behavior of “weasel” and some math relevant to “weasel” itself.
The original description of “weasel” by Richard Dawkins in “The Blind Watchmaker” laid out how the program operated. The essential elements of a “weasel” program are as follows:
1. Use a set of characters that includes the upper case alphabet and a space.
2. Initialize a population of $N$$L$-character strings by copying with mutation a parent string formed by random assignments of characters from our character set.
3. Identify the string closest to the target string in the population.
4. If a string matches the target, terminate.
5. Base a new generation population of size n upon copies of the closest matching string or strings, where each position has a chance of randomly mutating, based upon a set mutation rate.
6. Go to step 3.
Note that I said “program” above and not “algorithm”. There is no guarantee that the program as described will halt, or terminate. While Dawkins did specify that $K = 27$ and $L = 28$, he did not
share precisely what values he chose to use for $N$ and $\mu$. Because Dawkins did not see the need to discuss alternative methods for ensuring that the program would come to an end, one can
reasonably infer that in his own runs of the program, he was using parameters of $N$ and $\mu$ that would result in termination of the program. He reported in “The Blind Watchmaker” that in three
runs, the target string was matched in 43, 64, and 41 generations. Later, I’ll see about doing some forensics to see if a range of parameters can be estimated for Dawkins’ original runs. It might be
the case that I can exclude whole ranges of parameters.
For now, it is more important that you come to a clear understanding of what does go on in a run of “weasel”. To that end, I’ve written a minimalist “weasel” program in Python. Python is an open
source interpreted language that is available for a great many different platforms, so you should be able to install Python and run the following program pretty much on any common computer platform.
If installing anything is just too much, there is an interactive “weasel” program of mine available here that you can run from any graphical browser with Javascript turned on.
The following code is just 34 lines, three of them output statements, and does nothing particularly fancy, so it should be understandable with small effort on the reader’s part. It’s just straight-up
structured programming, so there isn’t even object-oriented abstraction going on here.
import random # Get Pseudo-Random Number Generator (PRNG)
random.SystemRandom() # Seed PRNG
n = 250 # Set population size
t = “METHINKS IT IS LIKE A WEASEL” # Set target
b = ” ABCDEFGHIJKLMNOPQRSTUVWXYZ” # Set base pool
u = 1.0 / len(b) # Set mutation rate
print “PopSize=%d, MutRate=%f, Bases=%s, Target=%s” % (n,u,b,t)
p = “” # Initialize parent randomly
for ii in range(len(t)): # Make parent the same length as target
p += random.choice(b) # Add a randomly selected base to parent
print ” Parent=%s” % (p)
done = False # Assume we haven’t matched the target; we’ll be wrong once in 1e40 times
g = 0 # Initialize the generation count
while (done == False): # Keep going until a match is found or forever
pop = [] # Previous population is cleared out
bmcnt = 0 # Initialize best match count
bc = “” # Initialize best candidate holder
for ii in range(n): # Over the population size, do this:
pop.append(“”) # Append a new blank candidate
mcnt = 0 # Initialize the match count
for jj in range(len(t)): # Over the candidate length, do this:
if (u >= random.random()): # Test for whether mutation happens here
pop[ii] = pop[ii][0:jj] + random.choice(b) # Add a mutant base
pop[ii] = pop[ii][0:jj] + p[jj] # Copy base from parent
if (pop[ii][jj] == t[jj]): mcnt += 1 # If matched to target, increment
if (mcnt > bmcnt): # If candidate matches more bases than best so far
bmcnt = mcnt # Set the best match count to current match count
bc = pop[ii] # Set the best candidate to the current candidate
if (mcnt == len(t)): # Check to see whether all bases match the target
done = True # When all match up, we are done
g += 1 # Increment the generation count
print “Gen=%05d, %02d/%d matched, Best=%s, Total=%06d” % (g,bmcnt,len(t),bc,g*n)
p = bc # Parent for next gen. is best candidate from this gen.
Here’s a sample output from a “weasel” run, generated by the Python code above:
PopSize=250, MutRate=0.037037, Bases= ABCDEFGHIJKLMNOPQRSTUVWXYZ,
Target=METHINKS IT IS LIKE A WEASEL
Parent=WAPXSPETTBEOUNRCUE AEDT BJPH
Gen=00001, 01/28 matched, Best=WAPXSPETTBEOUSRCUE AEDT BJPH, Total=000250
Gen=00002, 02/28 matched, Best=WAPXSPETTBE USRCUE AEDT BJPH, Total=000500
Gen=00003, 03/28 matched, Best=WATXSPETTBE USRCGE AEDT BJYH, Total=000750
Gen=00004, 04/28 matched, Best=WATXSPKTTBE USRCGE AEDT BJYH, Total=001000
Gen=00005, 05/28 matched, Best=DATXSPKTTBE USRCGE AADT BUYH, Total=001250
Gen=00006, 06/28 matched, Best=DATXSPKTTBE USRCGE AALT BSYH, Total=001500
Gen=00007, 07/28 matched, Best=GATXSPKTTBE USRCGE AALTEBSYH, Total=001750
Gen=00008, 08/28 matched, Best=WATXSPKTTBE USRCGE AALWEBSYX, Total=002000
Gen=00009, 09/28 matched, Best=WATXSPKTTBE USRCGEEAALWEBSYX, Total=002250
Gen=00010, 10/28 matched, Best=WATXSPKT BE USRCGEEAALWEBSYX, Total=002500
Gen=00011, 13/28 matched, Best=WATHSPKT BE US CGEE ALWEBSYX, Total=002750
Gen=00012, 14/28 matched, Best=WATHSPKT BE IS CGEE ALWEBSNX, Total=003000
Gen=00013, 15/28 matched, Best=WATHSPKT BE IS CGEE A WEBSNX, Total=003250
Gen=00014, 16/28 matched, Best=WATHIPKT BE IS CDEE A WEWSNX, Total=003500
Gen=00015, 17/28 matched, Best=WATHIOKT BT IS CDEE A WEWSVW, Total=003750
Gen=00016, 18/28 matched, Best=WATHIOKT BT IS ZDEE A WEWSVL, Total=004000
Gen=00017, 19/28 matched, Best=WATHIOKT BT IS LDEE A WEWSVL, Total=004250
Gen=00018, 20/28 matched, Best=WATHIOKT BT IS LIEE A WEWSVL, Total=004500
Gen=00019, 20/28 matched, Best=WATHIOKT BT IS LIEE A WEWSVL, Total=004750
Gen=00020, 20/28 matched, Best=WATHIOKT BT IS LIEE A WEWSVL, Total=005000
Gen=00021, 21/28 matched, Best=WATHINKT BT IS LIEE A WEWSVL, Total=005250
Gen=00022, 21/28 matched, Best=WATHINKT BT IS LIEE A WEWSVL, Total=005500
Gen=00023, 22/28 matched, Best=WATHINKT BT IS LIKE A WEWSVL, Total=005750
Gen=00024, 23/28 matched, Best=WETHINKT BT IS LIKE A WEWSVL, Total=006000
Gen=00025, 24/28 matched, Best=WETHINKT IT IS LIKE A WEWSVL, Total=006250
Gen=00026, 24/28 matched, Best=WETHINKT IT IS LIKE A WEWSVL, Total=006500
Gen=00027, 25/28 matched, Best=WETHINKS IT IS LIKE A WEWSVL, Total=006750
Gen=00028, 25/28 matched, Best=WETHINKS IT IS LIKE A WEWSVL, Total=007000
Gen=00029, 25/28 matched, Best=WETHINKS IT IS LIKE A WEWSVL, Total=007250
Gen=00030, 25/28 matched, Best=WETHINKS IT IS LIKE A WEWSVL, Total=007500
Gen=00031, 25/28 matched, Best=JETHINKS IT IS LIKE A WEWSVL, Total=007750
Gen=00032, 25/28 matched, Best=JETHINKS IT IS LIKE A WEWSVL, Total=008000
Gen=00033, 25/28 matched, Best=JETHINKS IT IS LIKE A WEWSVL, Total=008250
Gen=00034, 26/28 matched, Best=METHINKS IT IS LIKE A WEWSDL, Total=008500
Gen=00035, 26/28 matched, Best=METHINKS IT IS LIKE A WEWSDL, Total=008750
Gen=00036, 26/28 matched, Best=METHINKS IT IS LIKE A WEHSDL, Total=009000
Gen=00037, 26/28 matched, Best=METHINKS IT IS LIKE A WEHSDL, Total=009250
Gen=00038, 26/28 matched, Best=METHINKS IT IS LIKE A WEHSDL, Total=009500
Gen=00039, 27/28 matched, Best=METHINKS IT IS LIKE A WEHSEL, Total=009750
Gen=00040, 27/28 matched, Best=METHINKS IT IS LIKE A WEHSEL, Total=010000
Gen=00041, 28/28 matched, Best=METHINKS IT IS LIKE A WEASEL, Total=010250
The “Total” reported is the total number of candidate strings evaluated in the generations leading up to some candidate string matching the target at all bases. The thing to note is that this didn’t
take the stupendous numbers of “tries” that we would expect for the random search case; it shows a relative improvement over random search of over thirty-six orders of magnitude in efficiency. The
program runs in just a couple of seconds on my computer; I did not have to wait for the lifetimes of a great many universes to go by. The question of interest is just how “weasel” manages to improve
things over random search.
I’ll recap the parameters used by “weasel” for handy within-post reference. Much of what I will discuss is precisely how the parameters change the behavior of the “weasel” program.
The number of alternative forms that any position, or base, can take is $K$. For the case where the bases are capital letters or a space, $K = 27$.
The length of the target string is $L$, and in the case where the target is, “METHINKS IT IS LIKE A WEASEL”, $L = 28$
The per-base mutation rate is how often a base is changed to a random alternative during copying from a parent string to a daughter string, and is $\mu$.
The number of candidate strings that make up the population at any one time is $N$.
We will also be interested in the number of correct and incorrect bases seen in the best candidate from a generation, and these will be $C$ and $I$, respectively.
Now we start looking at just how “weasel”, or cumulative selection, differs from random search or “single-step selection”, as Richard Dawkins termed it. Where, exactly, does “weasel”‘s potential for
better efficiency come from?
The first striking difference lies in “weasel”‘s use of inheritance. With single-step selection, whatever properties any individual try might have that were somehow adaptive do not carry over to
further tries. This is not so when inheritance is used. But how much difference does that make?
When a parent string is copied with mutation, there are $C$ correct bases already. We can determine the expected change in the value of $C$ for the daughter string following copying the parent with
mutation as
expected change in number of correct bases after copy with mutation $E_{MB} \begin{array}{l} = \left( \sum_{i=1}^{L-C} \mu P_{RC} \right) - \left( \sum_{j=1}^{C} \mu P_{RI} \right) \\ = \left( \frac
{\mu (L - C)}{K} \right) - \left( \frac{\mu C (K - 1)}{K} \right) \end{array}$
It is good to have a mathematical expression, but what is that telling us?
Here’s a graph showing the results of the equation for all mutation rates and all values $0 \leq C \leq 28$:
If our mutation rate $\mu$ is zero, that becomes
$E_{MB} \begin{array}{l} = \left( \sum_{i=1}^{L-C} \mu P_{RC} \right) - \left( \sum_{j=1}^{C} \mu P_{RI} \right) \\ = \left( \sum_{i=1}^{L-C} 0 * P_{RC} \right) - \left( \sum_{j=1}^{C} 0 * P_{RI} \
right) \\ = 0 \\ \end{array}$
That corresponds to the bottom edge of the graph, where you can see that a mutation rate of zero produces an expectation of zero bases changing to correct throughout the range.
The random search of single-step selection is equivalent to setting $\mu = 1.0$. One need not do anything special to a “weasel” program to also do single-step selection; just change the mutation rate
so that $\mu = 1.0$. That corresponds to the top edge of the graph, and shows that the expected change in correct bases is almost as many bases becoming incorrect as were correct in the parent when
one is randomly changing all the bases.
So on the one hand, we already know that random search ($\mu = 1.0$) is ineffective: that much change destroys any chance that inheritance can make a difference. And on the other, perfect copying ($\
mu = 0.0$) is both ineffective and boring: we persist with evaluating exactly the same string over and over.
For the case of “weasel”, the $E_{MB}$ equation tells us that it is easy and expected to obtain $0 \leq E_{MB} \leq L / K$ correct bases when $C$ is close to zero, depending on what the mutation rate
is. However, that quickly changes as $C$ increases. For any particular candidate string, the expectation for $E_{MB}$ in the newly generated candidate as the $C$ of the parent approaches $L$ only
remains near zero, and thus preserves the correct bases $C$ from the parent, when the mutation rate is very small. Because $C$ close to $L$ means that there only a small number of incorrect bases
remaining, the value of the positive term in the equation decreases, while the value of the negative term in the equation increases. A higher mutation rate, $\mu$, makes the equation lean heavily in
the negative direction, because it is a lot more likely that one or more of the many $C$ correct bases will change to an incorrect base than it is that one of the few $I = L - C$ incorrect bases will
be changed to a correct base. So we see that the most interesting results come about when | {"url":"http://austringer.net/wp/index.php/2009/04/20/the-weasel-saga-with-math-part-2/","timestamp":"2024-11-06T02:23:53Z","content_type":"text/html","content_length":"71955","record_id":"<urn:uuid:abdac9a6-d4c8-4ccd-88b8-9796136d6fbc>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00080.warc.gz"} |
SVCL - Neurophysiology of Discriminant Saliency
In this page we discuss the neurophysiological plausibility of the proposed bottom-up discriminant saliency detector (DSD). We first give a brief overview of the detector, and then discuss the
connections to the neurophysiology of early visual processing.
Discriminant center-surround saliency detector
Bottom-up saliency is defined as a center-surround classification problem. At every image location, saliency is equated to the power of a set of Gabor-like features to discriminate between the
stimuli at that location (the center) and those in a surrounding window (the surround). Discrimination is measured by the mutual information between features and the center-surround label. Natural
image statistics are exploited to derive a computationally parsimonious mechanism. The implementation of the detector is presented in Figure 1: the image is first decomposed into various feature
maps, such as color, intensity, and orientation. Each feature map is then subject to a center-surround operation, to generate a feature saliency map (Figure 2) which measures feature discrimination
(mutual information) at each image location. A global saliency map is finally computed by pooling all feature-based saliency maps.
Figure 1: The bottom-up discriminant saliency detector.
Figure 2: Illustration of discriminant center-surround saliency operation.
Consistency with the standard neural architecture of V1
It is well known that the application of band-pass filters to natural images produces features whose statistics comply with the generalized Gaussian distribution (GGD). For these features, all
computations of discriminant saliency can be implemented by the following neural network, which consists of a combination of simple and complex cells, and is fully compatible with the standard neural
architecture of V1. The network has three layers: 1) the first layer consists of linear filtering and (differential) divisive normalization, and is consistent with the divisive normalization model of
simple cells; 2) the second layer recitifies the output of the first layer by a quadratic nonlinearity and pools such outputs in a neighborhood, akin to the energy model of complex cells; 3) a third
layer, which performs pooling across feature channels, and can be mapped into a cortical column.
Holistic functional justification, and statistical inference, in V1
In addition to proving the physiological plausibility of discriminant saliency, the parallel between the above network and the standard architecture of V1 also offers a holistic functional
justification for V1: that it has the capability to optimally detect salient locations in the visual field, when optimality is defined in a decision-theoretic sense and certain approximations are
allowed, for the sake of computational parsimony. It can also be shown that, for stimuli compliant with natural image statistics, there is a rich set of explicit correspondences between the
components of the discriminant saliency network and the fundamental operations of probabilistic inference. In particular, all components (cells) of the standard V1 architecture have a statistical
interpretation, and this interpretation covers the three fundamental operations of statistical inference: probability inference, decision rules, and feature selection. The correspondence is as
simple cells - assess probabilities.
differential simple cells - implement decision rules.
complex cells - feature detectors that evaluate mutual information.
The fundamental operation of statistical learning, parameter estimation, is also performed within the architecture, through the divisive normalization subjacent to all computations. | {"url":"http://www.svcl.ucsd.edu/projects/discsalbu/discsalbu_neuro.htm","timestamp":"2024-11-07T22:48:46Z","content_type":"text/html","content_length":"9743","record_id":"<urn:uuid:69b6ba70-71b7-4533-b48c-344eae576045>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00601.warc.gz"} |
Salary Converter | Convert Any Salary | Hourly, Daily, Yearly
If you make 350,000 Kč per year, your hourly salary would be 168 Kč. This result is obtained by multiplying your base salary by the amount of hours, week, and months you work in a year, assuming you
work 40 hours a week. | {"url":"https://cz.talent.com/en/convert","timestamp":"2024-11-03T15:48:25Z","content_type":"text/html","content_length":"58344","record_id":"<urn:uuid:834f479c-77cd-47d1-9d6e-25168d2c92db>","cc-path":"CC-MAIN-2024-46/segments/1730477027779.22/warc/CC-MAIN-20241103145859-20241103175859-00682.warc.gz"} |
EViews Help: Generalized Method of Moments
Generalized Method of Moments
We offer here a brief description of the Generalized Method of Moments (GMM) estimator, paying particular attention to issues of weighting matrix estimation and coefficient covariance calculation. Or
treatment parallels the excellent discussion in Hayashi (2000). Those interested in additional detail are encouraged to consult one of the many comprehensive surveys of the subject.
The GMM Estimator
The starting point of GMM estimation is the assumption that there are a set of
In EViews (as in most econometric applications), we restrict our attention to moment conditions that may be written as an orthogonality condition between the residuals of an equation,
The traditional Method of Moments estimator is defined by replacing the moment conditions in
Equation (23.24)
with their sample analog:
and finding the parameter vector
When there are more moment conditions than parameters (
Equation (23.26)
may not have an exact solution. Such as system is said to be
. Though we cannot generally find an exact solution for an overidentified system, we can reformulate the problem as one of choosing a
as a measure of distance. The possibly random, symmetric and positive-definite
weighting matrix
since it acts to weight the various moment conditions in constructing the distance measure. The
Method of Moments estimate is defined as the
Equation (23.27)
As with other instrumental variable estimators, for the GMM estimator to be identified, there must be at least as many instruments as there are parameters in the model. In models where there are the
same number of instruments as parameters, the value of the optimized objective function is zero. If there are more instruments than parameters, the value of the optimized objective function will be
greater than zero. In fact, the value of the objective function, termed the J-statistic, can be used as a test of over-identifying moment conditions.
Under suitable regularity conditions, the GMM estimator is consistent and
The asymptotic covariance matrix
In the leading case where the
and the GMM estimator yields the unique solution
Equation (23.27)
, with
It can be seen from this formation that both two-stage least squares and ordinary least squares estimation are both special cases of GMM estimation. The two-stage least squares objective is simply
the GMM objective function multiplied by
Choice of Weighting Matrix
An important aspect of specifying a GMM estimator is the choice of the weighting matrix,
Equation (23.29)
implies that the choice of
asymptotically efficient
, or
GMM estimator of
Intuitively, this result follows since we naturally want to assign less weight to the moment conditions that are measured imprecisely. For a GMM estimator with an optimal weighting matrix, the
asymptotic covariance matrix of
Implementation of optimal GMM estimation requires that we obtain estimates of
• : the two-stage least squares weighting matrix is given by
• : the White weighting matrix is a heteroskedasticity consistent estimator of the long-run covariance matrix of
• : the HAC weighting matrix is a heteroskedasticity and autocorrelation consistent estimator of the long-run covariance matrix of
• : this method allows you to provide your own weighting matrix (specified as a sym matrix containing a scaled estimate of the long-run covariance
For related discussion of the and robust standard error estimators, see
“Robust Standard Errors”
Weighting Matrix Iteration
As noted above, both the White and HAC weighting matrix estimators require an initial consistent estimate of
Accordingly, computation of the optimal GMM estimator with White or HAC weights often employs a variant of the following procedure:
1. Calculate initial parameter estimates
3. Form an estimate of the long-run covariance matrix of
4. Minimize the GMM objective function with weighting matrix
We may generalize this procedure by repeating steps 2 through 4 using
An alternative approach due to Hansen, Heaton and Yaron (1996) notes that since the optimal weighting matrix is dependent on the parameters, we may rewrite the GMM objective function as
where the weighting matrix is a direct function of the
Equation (23.36)
with respect to
Continuously Updated Estimator
Linear Equation Weight Updating
For equations that are linear in their coefficients, EViews offers three weighting matrix updating options: the , the , and the method.
As the names suggests, the method repeats steps 2-5 above repeats the steps until the parameter estimates converge. The approach is based on
Equation (23.36)
Somewhat confusingly, the with a single weight step is sometimes referred to in the literature as the 2-step GMM estimator, the first step being defined as the initial TSLS estimation. EViews views
this as a 1-step estimator since there is only a single optimal weight matrix computation.
Non-linear Equation Weight Updating
For equations that are non-linear in their coefficients, EViews offers five different updating algorithms: , , , , and . The methods for non-linear specifications are generally similar to their
linear counterparts, with differences centering around the fact that the parameter estimates for a given weighting matrix in step 4 must now be calculated using a non-linear optimizer, which itself
involves iteration.
All of the non-linear weighting matrix update methods begin with
The procedure is analogous to the linear procedure outlined above, but with the non-linear optimization for the parameters in each step 4 iterated to convergence. Similarly, the method follows the
same approach as the method, with full non-linear optimization of the parameters in each step 4.
The method differs from in that only a single iteration of the non-linear optimizer, rather than iteration to convergence, is conducted in step 4. The iterations are therefore simultaneous in the
sense that each weight iteration is paired with a coefficient iteration.
performs a single weight iteration after the initial two-stage least squares estimates, and then a single iteration of the non-linear optimizer based on the updated weight matrix.
The approach is again based on
Equation (23.36)
Coefficient Covariance Calculation
Having estimated the coefficients of the model, all that is left is to specify a method of computing the coefficient covariance matrix. We will consider two basic approaches, one based on a family of
estimators of the asymptotic covariance given in
Equation (23.29)
, and a second, due to Windmeijer (2000, 2005), which employs a bias-corrected estimator which take into account the variation of the initial parameter estimates.
Conventional Estimators
Equation (23.29)
and inserting estimators and sample moments, we obtain an estimator for the asymptotic covariance matrix of
Notice that the estimator depends on both the final coefficient estimates
EViews offers a number of different covariance specifications of this form, , , , , , , , and , each corresponding to a different estimator for
Of these, and are the most commonly employed coefficient covariance methods. Both methods compute i.e. if was chosen as the estimation weighting matrix, then will also be used for estimating
• uses the previously computed estimate of the long-run covariance matrix to form
• performs one more step 3 in the iterative estimation procedure, computing an estimate of the long-run covariance using the final coefficient estimates to obtain
In cases, where the weighting matrices are iterated to convergence, these two approaches will yield identical results.
The remaining specifications compute estimates of
The primary application for this mixed weighting approach is in computing robust standard errors. Suppose, for example, that you want to estimate your equation using TSLS weights, but with robust
standard errors. Selecting for the estimation weighting matrix and for the covariance calculation method will instruct EViews to compute TSLS estimates with White coefficient covariances and standard
errors. Similarly, estimating with estimation weights and covariance weights produces TSLS estimates with HAC coefficient covariances and standard errors.
Note that it is possible to choose combinations of estimation and covariance weights that, while reasonable, are not typically employed. You may, for example, elect to use White estimation weights
with HAC covariance weights, or perhaps HAC estimation weights using one set of HAC options and HAC covariance weights with a different set of options. It is also possible, though not recommended, to
construct odder pairings such as HAC estimation weights with TSLS covariance weights.
Windmeijer Estimator
Various Monte Carlo studies (e.g. Arellano and Bond 1991) have shown that the above covariance estimators can produce standard errors that are downward biased in small samples. Windmeijer (2000,
2005) observes that part of this downward bias is due to extra variation caused by the initial weight matrix estimation being itself based on consistent estimates of the equation parameters.
Following this insight it is possible to calculate bias-corrected standard error estimates which take into account the variation of the initial parameter estimates. Windmeijer provides two forms of
bias corrected standard errors; one for GMM models estimated in a one-step (one optimal GMM weighting matrix) procedure, and one for GMM models estimated using an iterate-to-convergence procedure.
The Windmeijer corrected variance-covariance matrix of the one-step estimator is given by:
The Windmeijer iterate-to-convergence variance-covariance matrix is given by:
Weighted GMM
Weights may also be used in GMM estimation. The objective function for weighted GMM is,
The default reported standard errors are based on the covariance matrix estimate given by:
Estimation by GMM in EViews
To estimate an equation by GMM, either create a new equation object by selecting , or press the button in the toolbar of an existing equation. From the dialog choose Estimation Method: GMM. The
estimation specification dialog will change as depicted below.
To obtain GMM estimates in EViews, you need to write the moment condition as an orthogonality condition between an expression including the parameters and a set of instrumental variables. There are
two ways you can write the orthogonality condition: with and without a dependent variable.
If you specify the equation either by listing variable names or by an expression with an equal sign, EViews will interpret the moment condition as an orthogonality condition between the instruments
and the residuals defined by the equation. If you specify the equation by an expression without an equal sign, EViews will orthogonalize that expression to the set of instruments.
You must also list the names of the instruments in the Instrument list edit box. For the GMM estimator to be identified, there must be at least as many instrumental variables as there are parameters
to estimate. EViews will, by default, add a constant to the instrument list. If you do not wish a constant to be added to the instrument list, the check box should be unchecked.
For example, if you type,
Equation spec: y c x
Instrument list: c z w
the orthogonality conditions are given by:
If you enter the specification,
Equation spec: c(1)*log(y)+x^c(2)
Instrument list: c z z(-1)
the orthogonality conditions are:
Beneath the box there are two dropdown menus that let you set the and the .
The dropdown specifies the type of GMM weighting matrix that will be used during estimation. You can choose from , , , and . If you select then a button appears that lets you set the weighting matrix
computation options. If you select , you will be prompted for a cluster series. If you select you must enter the name of a symmetric matrix in the workfile containing an estimate of the weighting
matrix (long-run covariance) scaled by the number of observations
data member (see
“Equation Data Members”
For example, for GMM equations estimated using the weighting matrix, will contain weighting matrix will return
Storing the user weighting matrix from one equation, and using it during the estimation of a second equation may prove useful when computing diagnostics that involve comparing J-statistics between
two different equations.
The dropdown menu lets you set the estimation algorithm type. For linear equations, you can choose between , , and . For non-linear equations, the choice is between , , , and .
To illustrate estimation of GMM models in EViews, we estimate the same Klein model introduced in
“Estimating LIML and K-Class in EViews”
, as again replicated by Greene 2008 (p. 385). We again estimate the Consumption equation, where consumption (CONS) is regressed on a constant, private profits (Y), lagged private profits (Y(-1)),
and wages (W) using data in “Klein.WF1”. The instruments are a constant, lagged corporate profits (P(-1)), lagged capital stock (K(-1)), lagged GNP (X(-1)), a time trend (TM), Government wages (WG),
Government spending (G) and taxes (T). Greene uses the weighting matrix, and an updating procedure, with set to 2. The results of this estimation are shown below:
The EViews output header shows a summary of the estimation type and settings, along with the instrument specification. Note that in this case the header shows that the equation was linear, with a 2
step iterative weighting update performed. It also shows that the weighing matrix type was White, and this weighting matrix was used for the covariance matrix, with no degree of freedom adjustment.
Following the header the standard coefficient estimates, standard errors, t-statistics and associated p-values are shown. Below that information are displayed the summary statistics. Apart from the
standard statistics shown in an equation, the instrument rank (the number of linearly independent instruments used in estimation) is also shown (8 in this case), and the J-statistic and associated p
-value is also shown.
As a second example, we also estimate the equation for Investment. Investment (I) is regressed on a constant, private profits (Y), lagged private profits (Y(-1)) and lagged capital stock (K-1)). The
instruments are again a constant, lagged corporate profits (P(-1)), lagged capital stock (K(-1)), lagged GNP (X(-1)), a time trend (TM), Government wages (WG), Government spending (G) and taxes (T).
Unlike Greene, we will use a weighting matrix, with pre-whitening (fixed at 1 lag), a Tukey-Hanning kernel with Andrews Automatic Bandwidth selection. We will also use the weighting updating
procedure. The output from this equation is show below:
Note that the header information for this equation shows slightly different information from the previous estimation. The inclusion of the weighting matrix yields information on the prewhitening
choice (lags = 1), and on the kernel specification, including the bandwidth that was chosen by the Andrews procedure (2.1803). Since the procedure is used, the number of optimization iterations that
took place is reported (39). | {"url":"https://help.eviews.com/content/gmmiv-Generalized_Method_of_Moments.html","timestamp":"2024-11-06T11:31:39Z","content_type":"application/xhtml+xml","content_length":"70303","record_id":"<urn:uuid:87ae951d-ac71-4130-8f47-8a76d526e16c>","cc-path":"CC-MAIN-2024-46/segments/1730477027928.77/warc/CC-MAIN-20241106100950-20241106130950-00636.warc.gz"} |
The CIE colorimetric system uses X, Y, and Z tristimulus values, calculated using spectral distributions and color-matching functions, as its basis for various colorimetric models. Lightsource
chromaticity —or the color of “white” light— is typically expressed using a correlated color temperature and a —less commonly used— Tint value. Calculating these is complex. There is no simple
mathematical formula: the method used here uses a high-accuracy bisectional search method.
Input are (X, Y, Z) tristimulus values, the default setting, or scaled (x,y) chromaticity coordinates, as used in the CIE 1931 chromaticity diagram. The values are entered by selecting the input
fields and typing the numbers. The keyboard Enter-key will update the calculated values in the output display area. The correlated color temperature has as unit Kelvin - the Tint value is unitless
and is 1000x the distance from the color point to the Planckian curve, measured in the CIE1964 chromaticity diagram, which is sometimes referred to as milli-Δuv.
The initial values shown at start-up are the tri-stimulus values for the CIE D65 illuminant, with a Correlated Color Temperature of 6503.2K and a 3.2-Tint value, corresponding to a distance of Δuv =
0.0032 in the CIE 1964 diagram. Positive Tint values are above and appear more yellow-greenish, while negative values are below the Planckian Locus and typically appear more purple-pinkish.
By clicking the xy selection button, the input field changes to xy chromaticity coordinates, which are 0.31271 and 0.32903 for the D65 illuminant.
The temperature range of the implemented algorithm is 1000 Kelvin to 1,000,000 Kelvin; an error message indicates a temperature is too low or too high. The CIE definition of Correlated Color
Temperature limits its calculation to a Tint range of -50 to 50, as it is a quantity mainly used for “whitish” light sources — an error message will be shown if that’s the case.
Invalid input will also result in error messages. Negative values are not allowed, as tristimulus and chromaticity values are always positive. Furthermore, chromaticity values x and y —lowercase—
should be between 0 and 1, and their sum should be in this range too. There is no range limit in the tristimulus values, using the uppercase letters X, Y, and Z, except that they need to be positive. | {"url":"https://www.gerardharbers.com/tools/cct/","timestamp":"2024-11-09T09:32:06Z","content_type":"text/html","content_length":"7933","record_id":"<urn:uuid:1eacd689-c340-4ba6-bf54-fe9c978945ad>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00780.warc.gz"} |
What is Pi123? An In-Depth Exploration - SOURCE SORT
What is Pi123? An In-Depth Exploration
In the realm of technology, the term “pi123” has gained traction, sparking interest among enthusiasts and professionals alike. This article will delve into what pi123 is, its applications,
significance, and why it matters in today’s tech-driven world.
Understanding Pi123
Pi123 is a multifaceted term that can refer to various concepts depending on the context. Primarily, it appears in fields such as mathematics, programming, and even gaming. By breaking down its
implications across these domains, we can better appreciate its relevance.
Pi123 in Mathematics
In mathematics, “pi” typically refers to the irrational number approximately equal to 3.14, which represents the ratio of a circle’s circumference to its diameter. The “123” can imply a sequence or a
specific reference within mathematical problems or theories. For example, a mathematician might use this term to denote a particular theorem or formula that incorporates the value of pi in its
Pi123 in Programming
In programming, the term may be used as a variable name or identifier. Developers often opt for descriptive names that reflect the purpose of the variable. Thus, it could represent a calculation
involving pi, particularly in programs that deal with geometrical computations. Furthermore, it can serve as a placeholder in coding exercises or challenges, illustrating the relationship between
constants and variables.
Pi123 in Gaming
Interestingly, this term also finds its way into the gaming world. Gamers sometimes adopt unique usernames or gamer tags, and “pi123” could represent one such choice. This username might imply a
mathematical or logical prowess, attracting like-minded players. Additionally, games that incorporate puzzles or mathematical challenges could reference this term as a nod to its mathematical
The Significance of Pi123
Understanding the significance of pi123 requires an appreciation of its impact across various fields. Below are some critical aspects to consider.
Mathematical Insight
In mathematics, pi is essential for calculations involving circles and periodic phenomena. The concept can inspire students to engage more with the subject. For instance, a classroom project might
involve calculating areas or circumferences using the formula. In this context, it serves as a bridge between theoretical knowledge and practical application.
Enhancing Programming Skills
Using terms like this helps foster creativity and problem-solving in programming. It encourages developers to think outside the box while creating algorithms. Furthermore, programming exercises
involving pi can enhance a coder’s understanding of mathematical concepts. Statistics show that incorporating real-world applications in coding lessons increases retention and engagement rates.
Fostering Community in Gaming
In the gaming realm, usernames like pi123 can build community. Gamers often connect over shared interests, and unique tags facilitate this bonding. According to a survey by the International Game
Developers Association, many gamers report feeling a stronger sense of community through shared usernames. Thus, pi123 could represent a hub for mathematical enthusiasts in gaming.
Applications of Pi123
Let’s explore some specific applications of this term across the fields of mathematics, programming, and gaming.
Mathematics Education
Teachers can leverage pi123 as a teaching tool. For instance, educators can create engaging lesson plans that challenge students to explore pi through practical exercises. This might involve
calculating the area of circles in real-world scenarios, such as designing a park layout. By integrating the concept into their lessons, teachers can make learning more interactive.
Software Development
In software development, pi123 could be part of an algorithm in applications that require precise calculations. For example, graphic design software might utilize this term in its rendering engine to
calculate curves and circles accurately. Such practical applications reinforce the importance of mathematical constants in everyday technology.
Gaming Challenges
In gaming, developers might create challenges that reference pi123. For instance, puzzle games could incorporate mathematical elements where players must solve problems related to pi to progress.
This not only enhances gameplay but also promotes critical thinking and logic skills among players.
Expert Opinions on Pi123
To further enrich our understanding, let’s look at what experts say about this term in different fields.
Mathematicians’ Perspectives
Mathematicians often emphasize the beauty of pi as a constant. Dr. Lisa Thompson, a noted mathematician, states, “Incorporating pi into various problems allows students to see the interconnectedness
of mathematics. Pi123 can serve as an accessible entry point for learners.”
Programmers’ Insights
Software engineers highlight the practical implications of pi in programming. Using descriptive names like pi123 in code not only improves readability but also reflects the logic behind calculations.
It makes the code more intuitive.
Gamers’ Views
From the gaming perspective, community leaders believe that names like pi123 contribute to identity formation. When players adopt unique tags, they foster connections and establish a sense of
belonging within the gaming community.
In summary, pi123 embodies a blend of mathematical significance, programming utility, and gaming identity. By exploring its applications across these diverse fields, we uncover its multifaceted
nature. Whether it serves as a teaching tool in classrooms, a variable in programming, or a gamer tag in virtual worlds, the term resonates with creativity and intellect. Embracing it allows
individuals to appreciate the interplay between mathematics, technology, and community.
FAQs About Pi123
1. What does pi123 represent? It typically combines the mathematical constant pi with a numerical identifier, often used in various contexts such as mathematics, programming, and gaming.
2. How is pi123 used in mathematics? In mathematics, this term may denote specific problems or formulas involving the constant pi, making it a useful teaching tool.
3. Can pi123 be a variable in programming? Yes, it can serve as a variable name in programming, particularly in contexts that involve mathematical calculations.
4. Is pi123 significant in gaming? Yes, it can be a unique username in gaming, fostering community among players who share similar interests in mathematics.
5. How can pi123 enhance learning? By integrating it into educational activities, teachers can engage students and help them connect theoretical concepts with real-world applications. | {"url":"https://sourcesort.com/what-is-pi123-an-in-depth-exploration/","timestamp":"2024-11-02T11:22:15Z","content_type":"text/html","content_length":"74535","record_id":"<urn:uuid:2717906a-b41a-41d0-a4aa-90153a6bf9b5>","cc-path":"CC-MAIN-2024-46/segments/1730477027710.33/warc/CC-MAIN-20241102102832-20241102132832-00559.warc.gz"} |
On Hitting-Set Generators for Polynomials that Vanish Rarely
The problem of constructing pseudorandom generators for polynomials of low degree is fundamental in complexity theory and has numerous well-known applications. We study the following question, which
is a relaxation of this problem: Is it easier to construct pseudorandom generators, or even hitting-set generators, for polynomials p: F^n→ F of degree d if we are guaranteed that the polynomial
vanishes on at most an ε> 0 fraction of its inputs? We will specifically be interested in tiny values of ε≪ d/ | F|. This question was first considered by Goldreich and Wigderson (STOC 2014), who
studied a specific setting geared for a particular application, and another specific setting was later studied by the third author (CCC 2017). In this work, our main interest is a systematic study of
the relaxed problem,in its general form, and we prove results that significantly improve and extend the two previously known results. Our contributions are of two types: ∘ Over fields of size 2 ≤ | F
| ≤ poly (n) we show that the seed length of any hitting-set generator for polynomials of degree d≤ n^. 49 that vanish on at most ε= | F| ^-^t of their inputs is at least Ω ((d/ t) · log (n)). ∘ Over
F[2], we show that there exists a (non-explicit) hitting-set generator for polynomials of degree d≤ n^. 99 that vanish on at most ε= | F| ^-^t of their inputs with seed length O((d- t) · log (n)). We
also show a polynomial-time computable hitting-set generator with seed length O((d- t) · (2 ^d^-^t+ log (n))). In addition, we prove that the problem we study is closely related to the following
question: “Does there exist a small set S⊆ F^n whose degree-d closure is very large?”, where the degree-d closure of S is the variety induced by the set of degree-d polynomials that vanish on S.
Funders Funder number
Blavatnik Family Foundation
European Research Council
Horizon 2020
Horizon 2020 Framework Programme 819702
National Science Foundation CCF-1763311
Israel Science Foundation 18/952
• 11T06 Polynomials over finite fields
• 68Q87 Probability in computer science (algorithm analysis, random structures, phase transitions, etc.)
• Bounded-Degree Closure
• Hitting-Set Generators
• Polynomials
• Pseudorandom Generators
• Quantified Derandomization
Dive into the research topics of 'On Hitting-Set Generators for Polynomials that Vanish Rarely'. Together they form a unique fingerprint. | {"url":"https://cris.tau.ac.il/en/publications/on-hitting-set-generators-for-polynomials-that-vanish-rarely-2","timestamp":"2024-11-10T15:47:02Z","content_type":"text/html","content_length":"54952","record_id":"<urn:uuid:97acb2ca-2832-492e-9fbd-e7adf366771c>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.60/warc/CC-MAIN-20241110134821-20241110164821-00271.warc.gz"} |
Player Valuation Tip #6: Using aging curves for dynasty/keeper leagues
Tip #1: Know where player values come from
Tip #2: Set your Hit/Pitch split
Tip #3: Value your Picks and Make Preseason Trades
Tip #4: Draft with tiers
Tip #5: Using xFantasy, the xStats projection system
Quick editor’s note: This is based on my post in the FanGraphs Community blog back in 2016, condensed a bit and with updates for this year. The TL;DR version? Using projections for this year only,
you can apply aging curves and calculate player values for keeper leagues!
One of the most oft-discussed and most subjectively-answered fantasy baseball topics is “Who do I keep?” Fantasy baseball players intuitively understand the idea of aging, at least qualitatively.
Older players are less valuable, given that their performance is more likely to decrease due to both injury and ineffectiveness. But how much is age worth, really?
Thanks to work by Jeff Zimmerman and Bill Petti (Hitters, Pitchers), we now generally know that in the post-PED era, players only get worse once they’re in the league. It won’t stop people from
imagining a Mike Trout 20-WAR age 26 season, but it appears to be true. However, how to translate this knowledge into quantifiable fantasy valuation remained a bit unclear. For hitters, the original
work used deltas in wRC+, and Mike Podhorzer (and Jeff) took a look at how steals age, filling in one piece of the 5×5 puzzle. For pitchers, we know how the various component pieces of pitcher
performance (K/9, BB/9, velocity, etc.) age, but the most catch-all stat examined would be FIP. In any case, these really only give you a qualitative sense of aging, short of attempting to correlate
wRC+ or FIP with 5×5 value and applying those curves directly.
Previous hitter and pitcher aging curves
As in Jeff’s work, I’ll direct the reader to Mitchel Litchman’s piece which describes the basic methodology for constructing an aging curve using the delta method. The methodology is similar, but now
I’ll use players’ 5×5 z-scores and examine how those age! For the sake of simplicity, all discussion here is centered on 5×5 z-scores (abbreviated 5z) but could theoretically be expanded and applied
to any fantasy format.
The initial hitter aging curve for 5z score looks like this:
Keep in mind when looking at this plot that it is a cumulative measure, so 37 year olds are not going to lose a Bryce-Harper’s-worth of value next year, but rather the difference between age 36 and
age 37 on the plot. The peak at age 26 agrees well with earlier studies, and the general shape looks familiar, so we’re off to a good start. However, the rising value from age 22 to 26 doesn’t quite
fit with what might be expected from Jeff’s wRC+ curve. To examine a potential source of this difference, we can look to playing time. To compare change in ‘quantity’ of production vs. change in
‘quality’ of production, I ran z-scores of PA and wRC+.
Well that’d explain it. The aging behavior of playing time is a very sharp incline/decline on either side of age 26, and number of plate appearances is a huge factor in 5z score. Meanwhile, the wRC+
curve unsurprisingly has not changed much in the few years since Jeff’s initial study, holding completely steady from 22 to 26 followed by a gradual decrease. Re-calculating 5z scores for *only* the
players who had <10% change in PA’s year-over-year confirms that the 5z curve is flat when playing time is not a factor. Playing time controls the majority of age-related improvement from age 22-26,
and age-related decline from age 34 onward. With teams getting better and better at analytics, this makes sense – if you’re good, you get to play. If you’re bad, you’re on the bench, or out of the
For pitchers, the approach is similar, although starters and relievers were separated into their own aging curves. The initial starting pitcher aging curve for 5z score looks like this:
Again, a peak at age 26. Perhaps as a result of some survivor bias for starters that continue to pitch through their late 30’s, the decline in 5z is less sharp than it is for hitters. Obviously, the
number of pitchers than continue starting into their late 30’s is quite small, and so as discussed elsewhere there is likely a competing effect between decreasing IP totals and increasing quality of
remaining pitchers. Continuing along the same thread as I did for hitters, I’ll compare change in ‘quantity’ of production vs. change in ‘quality’ of production via z-scores of IP and my favorite ERA
indicator, SIERA.
We again see that the aging curve for IP is steep on both the incline and decline. The aging behavior of 5z scores for starters nearly follows the zSIERA pattern, reinforcing the idea of survivor
bias on the 5z curve. zSIERA is remarkably stable, with the first real drop off occurring at age 36. Re-calculating 5z scores for *only* the players who had <10% change in IP year-over-year confirms
that the 5z curve is flat (mostly) when playing time is not a factor. Sample size becomes a bit of an issue as SP workloads fluctuate more than position players’. The prolonged peak (out to ~age 31
before much of a dropoff) doesn’t quite match up with the shape we’d expect from the Petti/Zimmerman curves, where skills are stable through 26 and then degrade. However, I am willing to believe that
selecting out players that were healthy two consecutive years (or at least, equally healthy in both years) may bias us towards pitchers with more longevity. In any case I believe this definitely
indicates that the initial increase in 5z value is from pitchers breaking into the league and increasing their IP totals, not from improving performance.
As identified by the Petti/Zimmerman curves, relief pitchers age differently from starters, maintaining their early career velocity and K/9 longer than starters on average. This bears out in the 5z
scores as well. The decline overall appears to be shallower, although given the lesser value of RPs in 5×5 vs. SPs, this is likely not an inherent quality of RP aging. The peak age shifts to age 28,
as we’d expect from the aforementioned K/9 and velocity aging curves. For the sake of not repeating similar zIP/zSIERA/5z-10% analysis over again, I’ll simply provide here the comparison of the two
5z curves for pitchers.
Aging Factor
Finally returning to the thesis question of all of this, we’ve arrived at a set of very useful data with the above delta z-score analysis for hitters, starters, and relievers, along with a good set
of conclusions for how to apply them. Given the fact that in each case the early-career increases in 5z score were attributed to playing time, I am going to assume no correction needs to be made for
players in their age-26 and earlier seasons (age 28 in the case of relievers). This assumption is not totally correct in the case of young players projected for less than full playing time in 2016,
but I’ll come back to that. After 26, I’ll apply the 5z aging curves, which will capture the aggregate effect of both decreasing playing time and decreasing performance with age. For the sake of
smoother data, the initial aging curves from above were used to generate polynomial regressions and replotted here:
From here, calculating changes to player values in keeper leagues is simple. As an example, Miguel Cabrera is projected for a 0.93 5z score by the Big Board for 2017 in his age-34 season. If I owned
him on a 3-year contract, I could project his value over that 3-year span, obtaining aging factors from the plot above:
Age Aging factor 5z
Year 1 34 – 0.93
Year 2 35 -0.28 0.65
Year 3 36 -0.29 0.36
AVG 0.65
Or, if playing more to “win now” (as you should), I could weight earlier years,
Age Aging factor 5z Weight
Year 1 34 – 0.93 50%
Year 2 35 -0.28 0.65 33%
Year 3 36 -0.29 0.36 17%
wAVG 0.74
In either case, we see that Miggy’s value drops somewhat significantly over the course of a three-year contract, but not so much that we should be looking to deal him at any cost. In my experience,
many fantasy players in keeper/dynasties actually vastly overrate the negative value of age, and there is profit to be had in investing in older players. Best of all, it can be done with just the
current year’s projections and a spreadsheet like the Big Board.
Age-related Playing Time Bonus
Looping back around to a final adjustment, players under 26 who are not projected for a full season’s workload in the current year should be expected to pick up additional playing time in the
following years (remember, this is where ALL the improvement in 5z from age 22 to 26 comes from, on average). This is most significant in the case of SPs, where teams now generally apply the golden
rule of 30IP increases in workload each year. We can calculate the expected growth in 5z using the portions of the initial 5z curves from age 22 to 26. This works well as an alternative to simply
multiplying a given player’s production out to full playing time, which is both complicated in terms of spreadsheet maneuvering, and can give unreasonably large bonuses to players projected for
platoon roles.
To account for increased IP totals for starters, I looked to the zIP and 5z curves. From the 5z curve, players gained a total of about 0.5 5z from age 22 to 26, while gaining 1.3 standard deviations
in IP, or about 70 innings. It seems reasonable to then say that a player under age 26 can gain up to a maximum of 0.5 5z, based on how many innings (out of a potential 70, up to a max total of 200)
his workload is likely to increase in the following years, and fortunately these two curves map easily onto each other as a linear function.
PT Bonus(SP) = .0067*ΔIP
For instance, on a three-year contract the net result is something like this for a player like Joe Ross, currently projected for 145 IP in his age-24 season for 2017:
Age IP PT Bonus 5z
Year 1 24 145 – 0.07
Year 2 25 175 +0.20 0.27
Year 3 26 200 +0.17 0.44
AVG 0.26
And again, you’d likely want to weight for earlier years as I showed with Miggy.
Finally, the same thing can be done for young hitters. The approach is similar to what I did for pitchers – in this case, the maximum bonus is 0.65 5z over about a 220 PA increase, where I’ll set the
max yearly increase at 75PA and max possible total at 600 PA.
PT Bonus(H) = .0030*ΔPA
For instance, on a three-year contract the net result is something like this for a player like Javier Baez, currently projected in the Big Board for 500 PA in his age-24 season for 2017:
Age PA PT Bonus 5z
Year 1 24 500 – -.10
Year 2 25 575 +0.23 0.13
Year 3 26 600 +0.07 0.20
AVG 0.08
I’ll conclude with a direct comparison of two top-300 rankings generated by the Big Board, with and without the aging curve modifications discussed here (click the tabs at the bottom to switch
between the two). In this case, I used a 5-year aging modification for all players. The projections used are a mix of Steamer, ZiPS, PECOTA, and ATC, with some custom projections added in by me.
Overall I’d say the aging-modified ranks make good sense and have provided a way to reliably quantify keeper/dynasty value within the z-score method. The lack of projections for minor league players
remains a problem, so this system can only value MLB or near-MLB level players. Certain players will still always be inherently riskier if they rely specifically on skills that age faster than
average (for instance, players with above-average K-rate), but this acts as a good blanket modification without introducing subjectivity.
2 thoughts on “Player Valuation Tip #6: Using aging curves for dynasty/keeper leagues”
1. Mike
Can i add keepers to specific rounds for a snake draft, before the draft?
1. Harper Wallbanger
The Board doesn’t track specific pick numbers, so it wouldn’t have any effect in the current iteration, no.
Leave a Comment
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Developing Mathematical Thinking - Primary Teachers
Successful mathematicians understand curriculum concepts, are fluent in mathematical procedures, can solve problems, explain and justify their thinking, and have a positive attitude towards learning
Exploring, questioning, working systematically, visualising, conjecturing, explaining, generalising, convincing, proving... are all at the heart of mathematical thinking. The activities below are
designed to give learners the opportunity to think and work as mathematicians.
For problems arranged by curriculum topic, see our Primary Curriculum page
For problems arranged by mathematical mindsets, see our Mathematical Mindsets page
Reasoning and Convincing at KS2 - Primary teachers
Age: 7 to 11
The tasks in this collection can be used to encourage children to convince others of their reasoning, by first convincing themselves, then a friend, then a 'sceptic'. | {"url":"https://nrich.maths.org/developing-mathematical-thinking-primary-teachers","timestamp":"2024-11-11T01:07:20Z","content_type":"text/html","content_length":"42242","record_id":"<urn:uuid:9d7afd23-2de7-4570-b3cd-eb8705460bcd>","cc-path":"CC-MAIN-2024-46/segments/1730477028202.29/warc/CC-MAIN-20241110233206-20241111023206-00174.warc.gz"} |
Value-at-Risk (VaR)| Risk Management in Excel
In portfolio management, Value-at-Risk (VaR) is a popular metric to quantitatively assess the risk of our holdings.
Originally invented by banks to give some sense to how much lost could be reasonably anticipated across different business, it gained traction in the risk management world and soon become a
well-known method to measuring risk and helping traders/portfolio managers to view their portfolio in a different fashion.
Today let’s learn about what is VaR, and how we can compute it in Excel.
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What is Value-at-Risk (VaR)?
Value-at-Risk (VaR) is, in essence, the X-percentile of the projected Profit-and-loss (PnL) for our portfolio, over a given time horizon. In plain words, if VaR is $100, it tells you that if we are
unlucky tomorrow, we expect to lose at a maximum of $100 with X% chance/confidence.
Let’s think about it in a non-financial example. Suppose you have 99 students in a Mathematics class, taking the same test tomorrow. Based on the result of the last test they’ve taken, you obtained a
projection of how the class will perform in the coming test.
With the data in our example workbook, we found that the 5th percentile of the score is at 26, which is basically the 5th-lowest score achieved by the class (cell A6). Therefore, we can loosely say
that the 5% Value-at-Risk for the class is 26 in the upcoming test, i.e. we have 5% confidence that the lowest score achieved by all students is 26.
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Why do we use Value-at-Risk (VaR)?
Now let’s turn our attention to portfolios of financial instruments. Instead of the score of students, now we look to project the Profit-and-Loss (PnL) of our portfolio, and compute a Value-at-Risk
(VaR) based on that.
There are actually good reason to look at Value-at-Risk (VaR), on top of usual metrics like expected return/portfolio standard deviation. VaR is actually a metric to look at heavy-tail events (or
black-swan events).
Heavy-tail (or black-swan) events are rare events that have severe consequence. For example, people generally think the stock market would not drop by more than 5% a day, so “Market dropping by more
than 5%” is a black-swan event.
While metrics like expected return/portfolio standard deviation give investor a sense of the characteristics of their portfolio, they do not tell you what could happen if you have a really bad day.
And VaR is a good metric to tell you that, if you have a really bad day, what is the loss to be expected.
For large investor, heavy-tail events are risks to be managed, and hence heavy-tail metrics like VaR has grown in prominence for risk management.
With this in mind, our problem becomes:
1. How do we present VaR figures?
2. How do we come up with the statistical distribution of the PnL (i.e. the chances of achieving different PnL levels)?
Let’s go through one-by-one in the following section.
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How do we present Value-at-Risk (VaR)?
In practice, Value-at-Risk (VaR) often comes in different flavors, and it is important for us to understand how to read into the VaR figures provided.
Confidence Level
VaR is always presented in the manner “X%-VaR“, and we specify the confidence level (i.e. X%) related to a specific VaR. For example, a 95%-VaR would correspond to the 5th-percentile of the PnL
distribution, 99%-VaR to the 1st-percentile of the PnL distribution.
There is no one-shoe-fit-all rule that dictates what is the confidence level to use, but practitioners generally quotes multiple confidence level at once (e.g. 95%, 97.5%, 99%) to give a better sense
for how heavy-tail events would impact the portfolio.
Time Horizon
VaR is also commonly presented as a “X-day VaR“, although sometimes it is implicitly a 1-day VaR measure. When speaking of the PnL distribution, depending on the frequency of the data (e.g. daily/
weekly/monthly), VaR of different time horizon could be calculated.
Majority of the VaR measures in practice is a 1-day metric, as a typical assumption is that risks are reviewed on a daily basis, but longer horizon metrics are often useful as well.
Absolute vs Relative
Absolute and Relative VaR differs in whether you want to benchmark against the expected return.
For example, suppose the 5th percentile of your PnL distribution is -$10, and your expected return (i.e. mean of PnL distribution) is +$2. Your Absolute 95%-VaR would be -$10 (the total loss
expected), and your Relative 95%-VaR would be -$8 (a relative figure to the expected return).
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How do we come up with the statistical distribution?
After we discussed on what are the flavors for Value-at-Risk (VaR), we look at a more fundamental question – how do we come up with the distribution of potential Profit-and-Loss (PnL) in the first
Ultimately, the computed VaR depends on your selected PnL distribution: if you select a distribution that there is a high chance of losing (positively skewed), chances are, your VaR computed will be
larger than if you have picked a distribution that is more symmetrical.
There are mainly 2 ways which we’ll illustrate with the help of Excel:
1. Historical approach
2. Parametric approach
Historical Approach
As the name suggest, in historical approach, you compute the VaR based on what is available in the past.
In essence, based on the specific portfolio composition, we obtain the daily PnL data, sort them in ascending order, and find the relevant (1-X)-th percentile that translates to our X%-VaR.
From the Sample Workbook, you’ll find an example where we have a portfolio with 4 stocks. With Yahoo Finance stock price data, we compute the day-on-day change as our PnL distribution.
Based on the calculation, we found that the 1-day 95%-VaR is $870.4, which means on a given day, we expect that the maximum loss is $870.4 with 5% confidence. Similarly we have the 97.5%-VaR and
99%-VaR for side-by-side comparison.
As you’ve guessed, there are several limitation of using a historical approach:
1. The computed VaR is heavily influenced by the timeframe you’ve selected.
2. Past performance of the portfolio does not necessarily link closely to future performance
3. Most importantly, sampling of the negative outliers (i.e. days with large loss) may be biased as we usually have too few observations.
With that in mind, we introduce the alternative approach: the parametric approach.
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Parametric Approach
The parametric approach is a fancy way to say that we make some statistical assumption with the PnL distribution.
For example, in our sample workbook, we’ve presented VaR computed from 2 commonly-used parametric distribution: the Normal distribution and the t-distribution.
In the Parametric Approach, we only need to estimate for a couple of parameters (e.g. mean and standard deviation) of the PnL distribution, and apply these parameter to find the expected percentile.
Notice how the VaR computed for t-distribution is larger than the normal distribution, which is due to the fact that t-distribution has heavier tails than the normal distribution. Heavier tail means
that there are more chances for outliers (negative outcome in our case).
Comparing what we computed in parametric vs historical approach, while parametric approach seems more prudent than the historical approach for 95%-VaR (1,053.9 vs 870.4, larger means more prudent),
for 99%-VaR (1,508.0 vs 2,181.5) the opposite is true.
In this case, we’ll need to re-evaluate whether our choice of parametric PnL distribution (e.g. Normal/t) is representative of the actual PnL distribution, and see if we need to find a more
heavy-tailed distribution.
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Value-at-Risk (VaR) is an important metric in risk management, giving investors/traders the sense of how heavy-tail/black-swan events would impact the portfolio of financial instruments we hold.
There are numerous ways to how VaR can be computed and presented, but we should always compare and contrast VaR computed with different approach and understand what it means for our modelling and how
it could be representative of our risks.
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Plane wave diffraction on a reflecting grating in the case of oblique incidence
A diffraction model for the case of the oblique incidence of a plane wave on a grating is proposed which is based on the approximate solution of Maxwell equations. The algorithm based on this model
allows the efficient calculation of the scattering pattern for a finite grating with allowance for the interaction between the grating elements. The model can be useful in the analysis of beam
splitters, couplers, and antireflection coatings.
Methods of Mathematical Modeling and Computational Diagnostics
Pub Date:
□ Electromagnetic Scattering;
□ Gratings (Spectra);
□ Maxwell Equation;
□ Plane Waves;
□ Wave Diffraction;
□ Beam Splitters;
□ Green'S Functions;
□ Mathematical Models;
□ Physics (General) | {"url":"https://ui.adsabs.harvard.edu/abs/1990mmmc.rept..215D/abstract","timestamp":"2024-11-05T17:40:59Z","content_type":"text/html","content_length":"33597","record_id":"<urn:uuid:ef3f0b2b-73b2-477e-b45e-d2df0f295fbe>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00087.warc.gz"} |
Sine approximations in CellML
This workspace provides a collection CellML models primarily developed for testing software tools and the model repository. There are models for calculating sine using the MathML sin operator, a
parabolic approximation, and a differential equation approximation.
The CellML document sin_approximations_import.xml is the top-level CellML model. It imports the three sub-models which define the three ways of calculating sine. The SED-ML document
sin_approximations_sedml.xml describes a simulation experiment which computes a sine wave over the interval 0 to 2*pi using these three methods and plots a graph showing that they all give similar
results (see image below). sin_approximations_import.xml also contains a CSim summary description of the simulation experiment defined in sin_approximations_sedml.xml such that CSim can be used to
perform the actual numerical computations required to produce the data shown in the graph below.
OpenCell version 0.8 can also be used to perform the same simulation experiment, with the results plotted below highlighting the differences between the three methods a bit better: | {"url":"https://models.cellml.org/e/240/view","timestamp":"2024-11-10T09:03:47Z","content_type":"application/xhtml+xml","content_length":"15317","record_id":"<urn:uuid:05ac15b9-2fd3-4fd3-ac55-2d9f31977b80>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00552.warc.gz"} |
The largest and the smallest of the jungle: Teacher's support sheet | Best School Games
Escola Games | Jogos Educativos
Teacher's support sheet
The largest and the smallest of the jungle
We are in the jungles to find the largest and the smallest animals. The giraffe, elephant, and jaguar are some animals we will meet on our way, but don't worry! They are our friends and will play
with us!
Go to activity
Teacher's tips
Level of Education: Elementary School - Preschool Subject: Mathematics Theme: Quantities and measurements Age: 05 to 07 years old
Students can play individually or in groups. As they play, make sure students use the concepts of largest and smallest, as it is an opportunity for them to relate to the vocabulary and use them
appropriately. Note that there is a dashed line following the command. It is also important to show children the size of each animal. Explore it during the game, having the students analyze and
reflect on the measure. [FIM-DICA]
Learner outcomes
• To identify the concepts of "larger than" and "smaller than";
• To compare quantities and measurements;
• To use different strategies to identify numbers in situations involving counting and measurements;
• To solve problem situations involving relationships between numbers, such as: being greater than, being smaller than;
• To relate measures, making simple estimates;
• To compare two images of different sizes;
• To improve the ability of visual discrimination.
Teachers’ goals
• To work playfully with the mathematical concepts "greater than" and "smaller than";
• To reinforce content discussed during the classes
• To present an activity that encourages students to connect the related content to mathematics;
• To develop children's ability to observe and visualize;
• To offer situations so that students use the concepts outside the classroom.
Suggestions of approaches for the teacher
These mathematical concepts must be in students' lives through plays, games, and other playful activities. Here are some proposals to be part of the stages of your Pedagogical Project:
(Approach 1) Using diverse materials, ask students to separate them into "small" and "large" groups.
(Approach 2) Using play dough, tell students to make objects of different sizes: a small die and a large die, a small ball and a large ball, etc.
(Approach 3) Take a measuring tape and ruler to the classroom and measure different objects.
(Approach 4) Use buckets with students to show them the capacity of larger and smaller containers. You can play in the sand and use the smaller bucket to put a little water and the larger one to fill
with sand.
(Approach 5) Use students' toys to classify: put the smaller toys in one container and the larger ones in another.
(Approach 6) Ask students to bring stuffed animals to school. Then, divide them into smaller and larger groups.
(Approach 7) Organize a queue in ascending order and analyze the height of the students who stayed in the 1st and last place.
(Approach 8) Work with geometric shapes made on colored paper in different sizes. Tell students to analyze them, share their ideas with their classmates, and then separate them by color and size.
(Approach 9) Separate students in ascending and descending order. Then, highlight other characteristics to separate them into categories, such as the tallest and shortest girl or boy.
(Approach 10) Tell students to write the ascending and descending order of the numbers from 1 to 20.
(Approach 11) Use paint to paint students' hands to print them on cardboard. Then, ask them to organize them into the ascending order. You can expose the project to a mural. Students can also print
their feet.
(Approach 12) Assign a survey to students' parents:
• Who is the tallest person in the house?
• How tall were you born?
• Who is the shortest person in your family?
• What is the largest object in the house? And the smallest?
(Approach 13) Divide a sheet of paper into two. On the board, glue different pictures of different objects. Ask students to classify them into ‘smaller than’ and ‘larger than.’ Tell them to take into
consideration the real size of the images. Present them the greater than and less than symbols and tell students to use them when separating the images.
(Approach 14) Numbers dictation: Say two numbers aloud and students should write which one is greater than the other.
(Approach 15) Separate objects in the classroom of different sizes (chair, pencil, rubber, chalk, etc.) to compare.
More about the content
Top 9 math strategies for engaging lessons Keep reading to uncover all of our top math strategies for keeping your students excited about math.
1. Explicit instruction You can’t always jump straight into the fun. Explicit instruction still provides the best foundation for the activities to come. Set up your lesson for the day on the
whiteboard, along with materials to demonstrate the coming activities. Make sure to also focus on any new vocabulary and concepts. Tip: don't stay here for too long. Once the lesson is
introduced, move on to the next fun strategy for the day!
2. Conceptual understanding Helping your students understand the concept behind the lesson is crucial, but not always easy. Even your highest performing students may only be following a pattern to
solve problems, without grasping the “why.” Visual aids and math manipulatives are some of your best tools to increase conceptual understanding. Math is not a two-dimensional subject. Even the
best drawing of a cone isn’t going to provide the same experience as holding one. Find ways to let your students examine math from all sides. Math manipulatives don’t need to be anything fancy.
Basic wooden blocks, magnets, molding clay, and other toys can create great hands-on lessons. No need to invest in expensive or hard-to-find materials. Math word problems are also a great time to
break out a full-fledged demo. Hot Wheels cars can demonstrate velocity and acceleration. A tape measure is an interactive way to teach area and volume. These materials give your students a
chance to bring math off the page and into real life.
3. Using concepts in Math vocabulary There’s more than one way to say something. And the more ways you can describe a mathematical concept, the better. Subtraction can also be described as taking
away or removing. Memorizing multiplication facts is useful, but seeing these numbers used to calculate area gives them new meaning. Some math words are going to be unfamiliar. So to help
students get comfortable with these concepts, demonstrate and label math ideas throughout your classroom. Understanding comes more easily when students are surrounded by new ideas. For example,
create a division corner in your station rotations, with blocks to demonstrate the concept of one number going into another. Use baskets and labels to have students separate the blocks into each
part of the division problem: dividend, divisor, quotient, and remainder.
Give students time to explore, and teach them big ideas with both academic and everyday terms. Demystify math and watch their confidence build!
4. Cooperative learning strategies When students work together, it benefits everyone. More advanced students can lead, helping them solidify their knowledge. And they may have just the right words
to describe an idea to others who are struggling. It is rare in real-life situations for big problems to be solved alone. Cooperative learning allows students to view a problem from various
angles. This can lead to more flexible, out-of-the-box thinking. After reviewing a word problem together as a class, ask small student groups to create their own problems. What is something they
care about that they can solve with these skills? Involve them as much as possible in both planning and solving. Encourage each student to think about what they bring to the group. There’s no
better preparation for the future than learning to work as a team.
5. Meaningful and frequent homework When it comes to homework, it pays to think outside of textbooks and worksheets. Repetition is important, but how can you keep it fun? Create more meaningful
homework by including games in your curriculum plans. Encourage board game play or encourage families to play quiz-style games at home to improve critical thinking, problem-solving, and basic
math skills. Sometimes you need homework that doesn’t put extra work on the parents. The end of the day is already full for many families. To encourage practice and give parents a break, assign
game-based options like Prodigy Math Game for homework. With Prodigy, students can enjoy a fun, video game experience that helps them stay excited and motivated to keep learning. They’ll practice
math skills, while their parents have time to fix dinner. Plus, you’ll get progress reports that can help you plan future instruction. Win-win-win!
6. Puzzle pieces math instruction Some kids excel at math. But others pull back and may rarely participate. That lack of confidence is hard to break through. How can you get your reluctant students
to join in? Try giving each student a piece of the puzzle. When you’re presenting your class with a problem, this creates necessary collaboration to get to the solution. Each student is given a
piece of information needed to solve the problem. A number, a unit of measurement, or direction — break your problem into as many pieces as possible. If you have a large class, break down three
or more problems at a time. The first task: find the other students who are working on your problem (try color-coding or using symbols to distinguish each problem’s parts). Then watch the
learning happen as everyone plays their own important role.
7. Verbalize math problems There’s little time to slow down in the classroom. Instruction has to move fast to keep up with the expected standards. And students feel that, too. When possible, try to
set aside some time to ask about your students’ math struggles. Make sure they know that they can come to you when they get stuck. Keep the conversation open to their questions as much as
possible. One great way to encourage questions is to address common troubles students have encountered in the past. Where have your past classes struggled? Point these out during your explicit
instruction, and let your students know this is a tricky area. It’s always encouraging to know you’re not alone in finding something difficult. This also leaves the door open for questions,
leading to more discovery and greater understanding.
8. Reflection time Providing time to reflect gives the brain a chance to process the work completed. This can be done after both group and individual activities. Group Reflection After a
collaborative activity, save some time for the group to discuss the project. Encourage them to ask:
• What worked?
• What didn’t work?
• Did I learn a new approach?
• What could we have done differently?
• Did someone share something I had never thought of before? These questions encourage critical thinking. They also show the value of working together with others to solve a problem. Everyone has
different ways of approaching a problem, and they’re all valuable. Individual Reflection One way to make math more approachable is to show how often math is used. Journaling math encounters can
be a great way for students to see that math is all around. Ask them to add a little bit to their journal every day, even just a line or two. Where did they encounter math outside of class? Or
what have they learned in class that has helped them at home? Math skills easily transfer outside of the classroom. Help them see how much they have grown, both in terms of academics and
social-emotional learning.
9. Making Math facts fun As a teacher, you know math is anything but boring. But transferring that passion to your students is a tricky task. So how can you make learning math facts fun? Play games!
Math games are great classroom activities. Here are a few examples:
• Design and play a board game.
• Build structures and judge durability.
• Divide into groups for a quiz or game show.
• Get kids moving and measure the speed or distance jumped. Even repetitive tasks can be fun with the right tools. That’s why engaging games are a great way to help students build essential math
skills. https://www.prodigygame.com/main-en/blog/math-strategies/
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Why does math work? - 3 Quarks Daily
Why does math work?
by Daniel Ranard
You don't need to know much math to see it works. Say you go apple-picking with a friend; you count 12 as you pick them, and your friend counts 19 of her own. How many apples are in the basket? Maybe
you crunch the numbers on a scrap of paper, just to be sure. You manipulate symbols on a page, and afterward you make a claim about reality: you know how many apples you would count if you pulled
them out.
But was that math or just common sense? If you're not impressed by addition, let's try multiplication. I suspect many of us encounter our first real mathematical “theorem” when we learn that A times
B is B times A. As Euclid wrote circa 300 BC, “If two numbers multiplied by one another [in different orders] make certain numbers, then the numbers so produced equal one another.” This fact may be
so familiar you forget its meaning: 4 x 6 = 6 x 4, or rather 6 + 6 + 6 + 6 = 4 + 4 + 4 + 4 + 4 + 4. It may be obvious, but a curious child would still ask, why? The equation demands proof, much like
the Pythagorean Theorem. Euclid gave a proof in Book VII, Proposition 16 of the Elements. And though he proved an abstract fact using abstract symbols, the world seems to obey this arithmetic rule:
if you have four groups of six apples, Euclid predicts you can always rearrange them into six groups of four.
Maybe it's no surprise we can use arithmetic to make these predictions. But what about the success of more sophisticated math and physics?
Euclid's Elements was full of theorems about numbers and geometry, most of them less obvious than the one above. He was not the first in the ancient world to write proofs, but with his axioms,
definitions, and careful deductions, he was the most prolific and systematic. He collected others' proofs into one place and wrote many of his own. (In other words, he wrote a textbook. In fact, it
was widely used for two thousand years.) And so mathematics continued onward, with new definitions and theorems filling whole libraries of books.
The laws of physics are formulated in this esoteric language. Sometimes, mathematicians even invent a new field of math before it's found to describe nature. For instance, “group theory” is a branch
of mathematics pioneered in the 19^th century. Physicists scrambled to learn it 100 years later when they realized that the fundamental particles are actually arranged according to certain patterns
of these groups. Schrodinger famously complained about the use of group theory, the gruppenpest. But nature had its way, and now group theory is a cornerstone of modern physics.
The seeming mathematical nature of the world has long haunted specialists. Einstein asked, “How can it be that mathematics, being after all a product of human thought which is independent of
experience, is so admirably appropriate to the objects of reality?” The physicist Eugene Wigner made the question famous in his 1960 essay, “The Unreasonable Effectiveness of Mathematics in the
Natural Sciences.”
Wigner had in mind more advanced mathematics, but let's start with the question of arithmetic. It may seem significant that we can use arithmetic to describe the world, but we should ask: could it
have been any other way? Is it conceivable to put 12 apples in a basket, then put in 19 more, but not count 31 when we take them out? Can we conceive of a world that defies all arithmetic analysis?
We might imagine that even if normal arithmetic failed, a sensible world would exhibit some regularity, some patterns, and these patterns could then be formulated as precise rules, written in an
unfamiliar framework that we would nonetheless call mathematics. However, I see no reason why the world should function according to any precise rules at all. We can imagine a world less predictable
and more wild, where apples do as they please, and where you never know exactly what you'll see when you turn around. It's a world we experience in dreams. Borges writes about a similar place in his
story Tlön, Uqbar, Orbis Tertius. “There are no sciences on Tlön, not even reasoning… The metaphysicians of Tlön do not seek for the truth or even for verisimilitude, but rather for the astounding.”
Science may be possible in Tlön, but if so, its inhabitants are unaware.
We do not live in Tlön-ish dreamworld. So there's something special about our world, with its stable quantities of apples. What's more, the world exhibits consistent patterns susceptible to
scientific analysis and prediction: Halley's comet will come every 75 years; Diet Coke and Mentos will always explode on contact. But I'm not just asking why science works. I'm asking why advanced
math is so useful, why abstract equations in dusty libraries have come to describe everything from arrangements of apples to the trajectories of electrons.
A common answer is that maybe math doesn't work that well, and we just use it when it does. Bertrand Russell put it well: “Physics is mathematical not because we know so much about the physical
world, but because we know so little; it is only its mathematical properties that we can discover.” Sure, we can use advanced mathematics to describe tiny particles, or the bending of spacetime under
gravity. But what about… everything else that happens? Physicists seek out phenomena they can understand with careful experiments using immaculate equipment and precisely controlled conditions – but
most of nature doesn't arrive that way. There are simple equations that predict the collisions of electrons, but we have no such equations to predict what people say, or how leopards move or
mountains form. The mathematician Gelfand played off the title of Wigner's essay, writing about “the unreasonable ineffectiveness of mathematics in biology.” He's right: biology is a science, but not
a precisely mathematical science. Math is only useful when it's useful.
It's true that math doesn't often yield precise predictions about biology, or indeed almost anything but physics. Still, I don't think this answer is satisfactory. It downplays a powerful fact: all
matter we know is composed of small parts whose behavior is precisely described by mathematics. Without being reductionist – “a human being is just particles and equations” – we can still accept the
significance here. Most physicists believe that if you gathered enough data and built a large enough computer (and that's a big, philosophically fraught “if”), you could simulate any situation from
daily life, with predictions confounded only by quantum randomness. In fact, we already know the equations you would need. It appears our daily life is governed by these sophisticated equations,
whether or not we have the data and computing power to solve them. And sure, maybe physicists are wrong. But even if God, Gods, or the free will of the human soul were to occasionally intervene, you
would have to admit that the microscopic constituents of matter seem to follow these equations whenever we're watching.
To me, the scope of mathematical application is astonishing, even while limited, and I cannot explain it. But however you feel about the scope of math, we are left with Einstein's question, a
different question. If mathematics is a product of pure thought, how do mathematicians develop theories that predate their use in physics? I already mentioned how the particle physics of the 20^th
century is largely built on group theory, a subject developed 100 years earlier, previously obscure to physicists. Another branch of mathematics developed in the 19^th century was non-Euclidean
geometry, the study of curved spaces. In the 1800s, the character Ivan in Dostoevsky's The Brothers Karamazov speaks of the absurdity and abstraction of non-Euclidean geometry, a subject which
appears ungrounded in reality: “If God exists and if He really did create the world, then, as we all know, He created it according to the geometry of Euclid and the human mind with the conception of
only three dimensions in space. Yet there have been and still are geometricians and philosophers, and even some of the most distinguished, who [nonetheless study non-Euclidean geometry].” Decades
later, non-Euclidean geometry proved to be the crucial ingredient in Einstein's theory of relativity, describing the way that spacetime curves.
What accounts for these seeming miracles? To answer this question well would probably require a philosophy of mathematics – an account of where math comes from, and what mathematical truth is. But we
can attempt some answers without a full-fledged philosophy. One simple response is that math is not “a product of human thought which is independent of experience,” despite Einstein's initial
suggestion. (A closer reading of Einstein indicates he would agree.) For one, our minds are born of this world, shaped by millennia of evolution and interaction with the environment. Our thinking
habits are in tune with the world. Maybe we acquired our specific arithmetic notions by observing the rearrangement of apples. Moreover, math and physics have been in communication for centuries, and
they were not always perceived as distinct fields. “Geo-metry” began with measuring the earth, before it was codified into abstract definitions and symbols by Euclid and others. The new,
non-Euclidean geometry of general relativity was developed decades before the physics, but it was partially inspired by the observation of curved surfaces like spheres. Should we be so surprised that
spacetime itself turned out to be slightly curved, analogous to the way in which spheres curve?
Another possible explanation is that mathematicians simply invent a lot of math. Not all of it becomes central to our theories of nature, but we mainly notice when the math works. For instance, group
theory is not the only abstraction of modern mathematics, but it just happens to be one of the most useful tools for classifying different types of particles. Or maybe particle physics could be
re-formulated with a new branch of mathematics entirely, but physicists just used the math that was already available.
Each of these answers rings true, and to some they are totally satisfying. Mathematics is certainly inspired by observations of the physical world, and it is often developed for the express purpose
of describing physics. But in mathematics, there are always infinite directions in which a field could grow. There's an overwhelming number of mathematical statements that one might try to prove.
Which patch of the mathematical landscape do you choose to explore? Mathematicians say they are often guided by a sense of beauty and elegance, without regard for practical applications. Yet the
mathematical objects they create sometimes describe the physical world with near-perfect fit. In fact, even physicists sometimes develop theories according to their sense of beauty and intuitive
“rightness,” before these theories are confirmed by evidence. How do they do it? Probably the aesthetic of the physicist and mathematician is again born of the world itself, a product of experience
and learned intuition.
Despite these explanations, I cannot convince myself that the striking success of mathematics is not a small miracle. So I will end by stealing Wigner's line: this miracle is “a wonderful gift which
we neither understand nor deserve.” | {"url":"https://3quarksdaily.com/3quarksdaily/2016/05/why-does-math-work.html","timestamp":"2024-11-02T15:50:05Z","content_type":"text/html","content_length":"62916","record_id":"<urn:uuid:dd1e8c78-4ec2-4352-a672-d08e3c7570b9>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00005.warc.gz"} |
Measuring Water Level Using TLx5012B
At first I wanted to use S2GO RADAR BGT60LTR11 to calculate the water level, but what I got was Bundle A kit. Bundle A includes PSoC™ 6 Wi-Fi BT prototyping kit and three magnetic sensors.
If I did it empirically, I could use PSoC™ 6's CAPSENSE™, but there are already many related projects implemented. So I chose another unorthodox way to implement water level detection.
"Calculating Water Level Height Using Angle Sensors"
Trigonometry tells us that the sine is the ratio of the side opposite to the hypotenuse of an angle. Now that I have the angle sensor, as long as I have an object of fixed length and can float on the
water, I can calculate the change of the water level.
As shown below. The water level change equation is R(sin(68.2) - sin(21)).
Empty pill box
Double sided tape
Arduino IDE
Please refer to github.
The only thing that needs attention is Arduino sin function use angle in radians but read from TLI5012B is degrees. Need to convert.
Due to space constraints, I only used a small water basin for testing.
0 degrees must be parallel to the water surface.
Read more | {"url":"https://www.hackster.io/momososo/measuring-water-level-using-tlx5012b-70e799","timestamp":"2024-11-13T14:56:50Z","content_type":"text/html","content_length":"74220","record_id":"<urn:uuid:db25c81d-a2a3-4005-bc96-8fe7f85259db>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00594.warc.gz"} |
Creating a (Quantum?) Constraint, in Pre Planckian Space-Time Early Universe via the Einstein Cosmological Constant in a One to One and Onto Comparison between Two Action Integrals
Journal of High Energy Physics, Gravitation and Cosmology Vol.03 No.02(2017), Article ID:74529,6 pages
Creating a (Quantum?) Constraint, in Pre Planckian Space-Time Early Universe via the Einstein Cosmological Constant in a One to One and Onto Comparison between Two Action Integrals
Andrew Walcott Beckwith^
Physics Department, College of Physics, Chongqing University Huxi Campus, Chongqing, China
Copyright © 2017 by author and Scientific Research Publishing Inc.
This work is licensed under the Creative Commons Attribution International License (CC BY 4.0).
Received: December 28, 2016; Accepted: February 26, 2017; Published: March 1, 2017
We are looking at comparison of two action integrals and we identify the Lagrangian multiplier as setting up a constraint equation (on cosmological expansion). Two action integrals, one which is
connected with quantum gravity is called equivalent to another action integral, and the 2^nd action integral has a Lagrangian multiplier in it. Using the idea of a Lagrangian multiplier as a
constraint equation, we draw our conclusions in a 1 to 1 and onto assumed equivalence between the two action integrals. The viability of the 1 to 1 and onto linkage between the two action integrals
is open to question, but if this procedure is legitimate, the conclusions so assumed are fundamentally important.
Ricci Scalar, Inflaton Physics
1. Basic Idea, Can Two First Integrals Give Equivalent Information?
Our supposition is that if we wish to make an equivalence between two action integrals, i.e., first integrals that we need to have a 1 to 1 and onto linkage between the integrands, in the two cases
so referenced.
To do this, we are making several assumptions.
1) The two mentioned integrals are evaluated from a Pre Planckian to Planckian space-time domain, i.e. in the same specified integral of space-time.
2) In the process of doing so, the Universe is assumed to avoid the so called cosmic singularity. In doing so, assuming a finite “Pre Planckian to Planckian” regime of space time is similar to that
given in [1] [2] .
3) The integrands in the two integrals are assumed to have a 1-1 and onto relationship to one another. We will be identifying the components of the two integrands which are assumed to be proportional
to each other. This idea is the foundation of our approach. The two references [1] [2] have in their own formulation specific Lagrangian formulations and a criticism our approach is that the
references we are using for first integrals, namely [3] [4] are not giving action integrals identical as to [1] [2] . Our answer is that we reference [1] [2] specifically as to how to avoid the
Penrose singularity theorem [5] , and that not enough is known as to rule out the nonsingular starting point of the universe as having the same content for Lagrangians as given in [3] [4] . i.e., for
Pre Planckian space time, so long as [5] is avoided, presumably our three assumptions for comparison can be made, so long as we adhere to the “path integral” idea as represented by [6] as equivalent
to what is stated in [1] [2] .
2. Specifying the Particulars of the Two First Integrals in Pre-Planckian to Planckian Space-Time
Before proceeding, it is advisable to define some of the symbols which will be used in the integrals and the integrands in our document.
First of all, we have what is known as a scale factor
These are the purported volume elements of the [3] first integral. The second first integral is using the usual GR inputs as defined by Padmanbhan in [4] . To review what is meant by first integrals
we refer the readers to [6] [8] [9] [10] .
Roughly put, according to [8] [9] [10] a Lagrangian multiplier invokes a constraint of how a “minimal surface” is obtained by constraining a physical process so as to use the idea of [8] [9] [10]
which invokes the idea of minimization of a physical processes. In the case of [3] , the minimization process is implicitly that, if
Here, the subscripts 3 and 4 in the volume refer to 3 and 4 dimensional spatial dimensions, and this will lead to us writing, via [3] a 1^st integral as defined by [3] [3] , in the form, if G is the
gravitational constant, that if we have following [3] , a first integral defined by
This should be compared against the Padmabhan 1^st integral [4] of the form, with the third entry of Equation (3) having a Ricci scalar defined via [13] and usually the curvature
Also, the variation of
Leading to [2]
Here, we have that
The innovation we will be looking at will be in comparing a 1-1 and onto equivalence, i.e. an information based isomorphism between 1^st integrals with a nod to [14]
We will be making a simple equivalence between the two first integrals via Equation (6) assuming that even in the Pre Planck-Planck regime that curvature
This last approximation will make a statement as to applying Equation (6) far easier may not be defensible, but we will use it for the time being.
2.1. Comparison between Equations ((2) and (3) with (5)-(7))
In order to obtain maximum results, we will be stating that the following will be assumed to be equivalent.
If the term
For extremely small time intervals (in the boundary between Pre Planckian to Planckian physics boundary regime).
The next section will be investigating the physical implications of such assumptions.
2.2. What We Can Extract in Physics, If Equations (9)-(12) Hold?
Simply put a relationship of the Lagrangian multiplier giving us the following:
If the following is true, i.e. in a Pre Plankian to Planckian regime of space- time
Then what has been done is to conflate the Lagrangian as equivalent to
3. Conclusions
But what is noticeable is that the inflaton equation as given by Padmanabhan [4] hopefully will not be incommensurate with the physics of the Corda Criteria given in the Gravity’s breath document
[16] . Keep in mind the importance of the result from reference [17] below which forms the core of Equation (15) below
Furthermore, we should keep in mind the physics incorporated in [18] [19] , i.e. as to the work of LIGO. i.e. it is important to keep in mind that in addition, [20] has confirmed that a subsequent
analysis of the event GW150914 by the LSC constrained the graviton Compton wavelength of those alternative theories of gravity in which the graviton is massive and placed a level of 90% confidence on
the lower bound of 10^13 km for a Compton wavelength of the graviton. Doing this sort of vetting protocols in line with being consistent with investigation as to a real investigation as to the
fundamental nature of gravity. This is a way of confirming and showing via experimental data sets if general relativity is the final theory of gravitation. i.e., if massive gravity is confirmed, as
given in [21] , then GR is perhaps to be replaced by a scalar-tensor theory, as has been shown by Corda.
We can say though if we do confirm Equation (13) and Equation (14) that such observations may enable a more precise rendering of settling the issues brought up by references [16] , and [21] , as well
as the appropriate use of the structures, algebraically given in [22] [23] for our comparison of the first integrals.
This work is supported in part by National Nature Science Foundation of China grant No. 11375279.
Cite this paper
Beckwith, A.W. (2017) Creating a (Quantum?) Constraint, in Pre Planckian Space-Time Early Uni- verse via the Einstein Cosmological Constant in a One to One and Onto Comparison between Two Action
Integrals. Journal of High Energy Physics, Gravitation and Cosmology, 3, 167-172. https://doi.org/10.4236/jhepgc.2017.32017
1. 1. Rovelli, C. and Vidotto, F. (2015) Covariant Loop Quantum Gravity. Cambridge University Press, Cambridge.
2. 2. Camara, C.S., de Garcia Maia, M.R., Carvalho, J.C. and Lima, J.A.S. (2004) Nonsingular FRW Cosmology and Non Linear Dynamics. arXiv:astro-ph/0402311.
3. 3. Ambjorn, J., Jurkiewicz, J., and Loll, R. (2010) Quantum Gravity as Sum over Space-Times. In: Boob-Bavnbek, B., Esposito, G. and Lesch, M., Eds., New Paths towards Quantum Gravity, Lecture
Notes in Physics 807, Springer, Berlin, 59-124.
4. 4. Padmanabhan, T. (2005) Understanding Our Universe; Current Status, and Open Issues. In: Ashtekar, A., Ed., 100 Years of Relativity, Space-Time, Structure: Einstein and Beyond, World
Scientific, Singapore, 175-204.
5. 5. Penrose, R. (1965) Gravitational Collapse and Space-Time Singularities. Physical Review Letters, 14, 57-59.
6. 6. Shankar, R. (1994) Principles of Quantum Mechanics. 2nd Edition, Springer, Berlin.
7. 7. Roos, M. (2003) Introduction to Cosmology. 3rd Edition, Wiley Scientific, Hoboken.
8. 8. Karabulut, H. (2006) The Physical Meaning of Lagrange Multipliers. European Journal of Physics, 27, 709-718.
9. 9. Spiegel, M. (1980) Theory and Problem of Theoretical Mechanics. Schaum’s Outline Series, McGraw Hill, San Francisco.
10. 10. Landau, LD. and Lifshitz, E.M. (2005) Mechanics. 3rd Edition, in Course in Theoretical Physics, Vol. 1, Elsevier Books, Boston.
11. 11. Beckwith, A. (2016) Gedanken Experiment for Refining the Unruh Metric Tensor Uncertainty Principle via Schwarzschild Geometry and Planckian Space-Time with Initial Nonzero Entropy and
Applying the Riemannian-Penrose Inequality and Initial Kinetic Energy for a Lower Bound to Graviton Mass (Massive Gravity). Journal of High Energy Physics, Gravitation and Cosmology, 2, 106-124.
12. 12. Giovannini, M. (2008) A Primer on the Physics of the Cosmic Microwave Background. World Press Scientific, Hackensack.
13. 13. Majumdar, D. (2016) Dark Matter: An Introduction. CRC Press, Boca Raton.
14. 14. Judson, T. (1994) Abstract Algebra, Theory and Applications. WS Publishing Company, Boston.
15. 15. Padmanabhan, T.
16. 16. Corda, C. (2012) Gravity’s Primordial Breath. Electronic Journal of Theoretical Physics, 9, 1-10.
17. 17. Freese, K. (1992) Natural Inflation. In: Nath, P. and Recucroft, S., Eds., Particles, Strings, and Cosmology, World Scientific Publishing, Singapore, 408-428.
18. 18. Abbott, B.P., et al. (2016) Observation of Gravitational Waves from a Binary Black Hole Merger. Physical Review Letters, 116, Article ID: 061102.
19. 19. Abbott, B.P., et al. (2016) GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence. Physical Review Letters, 116, Article ID: 241103.
20. 20. Abbott, B.P., et al. (2016) Tests of General Relativity with GW150914.
21. 21. Corda, C. (2009) Interferometric Detection of Gravitational Waves: The Definitive Test for General Relativity. International Journal of Modern Physics D, 18, 2275-2282.
22. 22. Awodey, S. (2006) Category Theory. Oxford University Press, Oxford, 11.
23. 23. Vinberg, E.B. (2003) A Course in Algebra. American Mathematical Society, 3. | {"url":"https://file.scirp.org/Html/2-2180179_74529.htm","timestamp":"2024-11-12T15:34:22Z","content_type":"application/xhtml+xml","content_length":"41666","record_id":"<urn:uuid:ebd70345-bb67-4184-ad44-6dae3727e3d0>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.63/warc/CC-MAIN-20241112145015-20241112175015-00724.warc.gz"} |
This Soundfile contains several elements. The basic one is a different kind of Noise Gate, most useful for very low level thresholds. Then that element is combined into one channel of the Dolby style
spectral processing, and finally a complete Stereo Spectral Processor is provided built up from these elements and the previous precision limiter and soft clipper.
Wiener filtering is a process by which you can derive the optimal reconstruction of a noise contaminated signal. From optimal filtering theory, you can show that at any frequency the optimal filter
has amplitude given by
= 1 - Noise^2/(Signal+Noise)^2
Generally this is used in conjunction with high resolution spectral decompositions as you get with Fourier Transforms. But in this case, where we have 5 bands of processing, we have enough spectral
decomposition to do a pretty reasonable job of applying the Wiener Filtering concepts.
The Kyma compressors/expanders are primarily devised to work at moderate to loud signal levels. At low signal levels their table interpolation in amplitude space is too coarse. To overcome these
effects for handling gating at very low signal levels (e.g., < -60 dBFS), the Wiener gate provided here works quite well.
Also included is a kind of spectral compressor = high postgain compression at low thresholds + original signal, to produce a curvilinear kind of compression used to enhance low level musical details
without crushing the peaks of stronger signals as you would have with typical compression. This one is based on direct computation of the dB level, applying linear compression in dB space, then
converting back to amplitude space. These conversions are performed using 3 term Minimax polynomial approximations over limited domains, and with scaling to cover the rest of the amplitude space.
The result of the Log2(x)/32 is to compute dB(x)/192. This is then used here to produce something that is unity gain below threshold, and strong limiting above threshold. The result is therefore
always either gain neutral or attenutation. That is good because the 2^(32*x) routine only works for values of x below zero to produce answers less than one.
One of the problems you encounter when applying strong amounts of spectral compression processing is that you end up magnifying the noise in the recording. So the Wiener gate is provided to help
overcome some of that effect. Be careful when setting the Noise Floor (NF) estimates in each channel. At and below this level in dB, there will be no transmission of the signal at all. If the NF is
set too high, then you will end up stuttering as the signal hovers around that level. It is better to accept a little bit of noise content by setting NF intentionally lower by several dB. You can
estimate the needed NF levels by watching the channel meters with NF set to -100 dBFS while playing a looped section of background noise at the tail of a recording. Setting NF to -100 dB gets the
Wiener gate out of the way.
This same technique is the basis for many noise cleaning operations, although in those cases a much higher spectral resolution is generally employed.
- 21 Mar 2004 | {"url":"http://www.symbolicsound.com/cgi-bin/bin/view/Share/DescribeWienerNR","timestamp":"2024-11-05T15:58:03Z","content_type":"application/xhtml+xml","content_length":"12441","record_id":"<urn:uuid:d5b1778f-a1c4-4439-8f22-dd8924ac6eb6>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00370.warc.gz"} |
Mathematics Archives - Hoitsma Blog
This inscribed triangle is a periodic billiard trajectory called the Fagnano orbit, named for Giovanni Fagnano, who in 1775 showed that this triangle has the smallest perimeter of all inscribed
‘This simple pattern may be recalled when students are first exposed to cosets and quotient groups much later in their academic career, as the set {2, 8} is one of six cosets in the quotient group C
[12]/{0, 6}.’ | {"url":"https://www.mathpax.com/myposts/math/","timestamp":"2024-11-07T22:54:31Z","content_type":"text/html","content_length":"119163","record_id":"<urn:uuid:4b93ba85-0a49-4af3-b8f7-afefd713a0ab>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00287.warc.gz"} |
Should I tune to equal or just temperament?
Should I tune to equal or just temperament?
For the purposes of this chart, it is assumed that C4 = 261.63 Hz is used for both (this gives A4 = 440 Hz for the equal tempered scale)….Just vs Equal Temperament (and related topics)
Interval Ratio to Fundamental Just Scale Ratio to Fundamental Equal Temperament
Major Third 5/4 = 1.2500 1.25992
What is 5 limit just intonation?
Five-limit tuning The 5-limit consists of all just intonation intervals whose numerators and denominators are both products of the primes 2, 3, and 5; these are sometimes called regular numbers. Some
examples of 5-limit intervals are 5/4, 6/5, 10/9 and 81/80.
What tuning did Bach use?
The main tuning system in Bach’s time was called meantone temperament. This system sounds great in C major and nearby keys, but the further away you move on the circle of fifths, the worse everything
What tuning did Mozart use?
Mozart, in 1780, tuned to an A at 421.6 hertz. The French standardized their A at 435 hertz in 1858. A little more than 20 years later, Verdi succeeded in getting a bill passed by the Italian
Parliament to tune at A 432 hertz.
Is a piano equal tempered?
Pianos are usually tuned to a modified version of the system called equal temperament. In all systems of tuning, every pitch may be derived from its relationship to a chosen fixed pitch, which is
usually A440 (440 Hz), the note A above middle C.
Are piano tuning to equal temperament?
Pianos today are tuned in “equal temperament,” which means that each note is the same distance in pitch from its neighbours.
Why is equal temperament out of tune?
Modern Pianos are all tuned using a system called “Equal Temperament”. In fact, you can’t use your ear to tune a Piano in equal temperament because our ears don’t hear notes in this manner. Piano
tuners use a device and they need to know how much each note needs to be “out of tune” in order to tune a Piano.
What is perfect intonation?
In music, just intonation or pure intonation is the attempt to tune all musical intervals as whole number ratios (such as 3:2 or 4:3) of frequencies. An interval tuned in this way is said to be pure,
and may be called a just interval; when it is sounded, no beating is heard. | {"url":"https://corfire.com/should-i-tune-to-equal-or-just-temperament/","timestamp":"2024-11-02T12:29:03Z","content_type":"text/html","content_length":"37655","record_id":"<urn:uuid:e261873c-19d9-45f0-a004-adcd64da6676>","cc-path":"CC-MAIN-2024-46/segments/1730477027710.33/warc/CC-MAIN-20241102102832-20241102132832-00292.warc.gz"} |
Light Scattering
Light and matter: a driving wave and a simple oscillator...
This model for light and matter allows a consistent explanation of a very large part of the subjects which can be included under the general term “Spectroscopy”.
Elastic Scattering is the case where ,e.g., an incoming photon has a particular energy, there is an interaction, the outgoing photon has the same energy.
Elastic scattering is relatively insensitive to the type of atom (with important exceptions), while inelastic scattering where the incoming photon loses energy in the interaction, is very sensitive
to the exact nature of the atoms involved and that makes that part of the field of spectroscopy very rich.
Elastic scattering experiments can yield information about the relative orientation and spacing between scatters. Distance and Direction alone in simple cases, with supplemental information (often
from a scattering experiment with different conditions) can yield enough information to build a 3D model of these scatterers.
Approach of these lectures is geometric rather than algebraic.
Notation and symbols are still mostly in terms most familiar to crystallographers.
Both geometric and algebraic developments are available in various Crystallography texts.
In other fields, like SAXS, texts seem to mostly do algebraic development of the material.
Study question:
A, B, C live in separate houses inside a fenced area that we cannot get into, but we can move around the edge and throw photons at their houses. From the interference pattern intensities we know that
2 of the houses are 300 ft. north/south of each other, 2 are 400 ft. east:west of each other and 2 are 500 ft. apart in a close-to northwest:southeast direction. At this stage what are the possible
layouts of the A,B,C houses?
In addition, From the intensities of scattering one of the houses in both the north:south relationship and the east:west relationship has more scattering power than the others (big:small scattering
is stronger than small:small) and we know that A is indeed the more powerful individual. Now what patterns are possible? What are the relationships of various patterns with each other?
We have evidence that there is some chemistry between A and B that would have them build their houses closer together than to others, then What layouts are possible and What are the relationships of
patterns with each other?
The above question presumed that the houses were built on firm land - just as crystals hold objects in position. For a SAXS analogy, If the houses were built on floating island that was randomly
spinning around a lot faster than we could make our measurements, then What could be determined about the layout of the houses?
Several different representations and concepts:
Ray direction of wave propagation, or direction of a beam of photons.
Wave of wavelength λ, each wave broad and long enough to perform as expected.
Photons specific quantum energy ∝ 1/λ, a photon = 1 quantum, a chunk of a wave broad and long enough to perform as expected.
BEWARE: The particle description of a photon is very misleading for scattering/diffraction effects: deflection of balls by other balls or objects is NOT the way photons seem to interact with atoms
and produce scattered photons.
Light has both electric and magnetic properties, i.e. electromagnetic wave. One can almost always ignore the magnetic component and still adequately explain experimental phenomena.
Light interacts with matter: The driving wave interacts with an oscillator. Considering the sinusoidally varying electric field of the wave, the oscillator must involve an oscillating dipole, this
could be an induced dipole in a polarizable object. So we are getting a measure of polarizability of a medium, e.g., molecules.
Energy can be transfered from (or to) this oscillator, for this introduction we will often ignore most processes except re-radiation of light. (i.e. we can go through an absorption band, but ignore
the part that is actual absorption). Absorption is just the loss of energy from the oscillator before it re-radiates. Absorption thus can be thought of as energy lost in the process of getting the
oscillator started and keeping it going.
Oscillator (oscillating dipole) can radiate energy (light) So we must consider certain points:
1) Must investigate properties of original interaction
2) Must know character of re-emitted light: is it different from original wave? If so, how?
3) Must investigate how light waves interact with each other since we have opened the possibility of various light waves: e.g. original wave and emitted waves from various oscillators.
For elastic scattering, we will avoid quantum mechanics: except note that any system, including our oscillators, can exist in only certain energy levels; so energy is handled only in discrete chunks
which will be important occasionally to consider. But, the picture of a driving wave and a simple oscillator does, in fact, explain much of the observed light scattering phenomena!
Very importantly for us, the model of a driving wave, a simple oscillator, and a scattered wave gives a quantitative description of when and in what directions scattering occurs. This formulation
predicts the interference patterns when light is scattered from more than one point, and thus is a functional description of what we observe from an experiment. This works at all wavelengths and all
scales, from single atoms and molecules, molecules and other particles in solution, to crystals.
Plane polarized light: the simplest case
Electric field vectors in all x,y directions
each component
components in phase with each other:
The real components add directly
only if φ angle same (i.e. could define φ[y] = φ[x] = 0)
Thus can treat unpolarized light as the resultant of two plane polarized rays in phase. Any arbitrary photon in an unpolarized light ray can be broken into two components, and a great number of
photons will then average out to give equal intensities in the two directions of polarized light chosen.
complex planes [y] = φ[x] = 0)
Point Particle (single oscillator)
Straight through:
As seen from an angle, i.e. those photons scattered in a particular direction.
For example: direction of scattering in the plane of the paper:
F•scattered = F•original
F↕scattered = F↕original cos(θ)
F↕scattered is a measure of the projection of the dipole motion ⊥ to the direction of scatter.
I[original] = F^2[original]
I[scattered] = I•[scattered] + I↕[scattered] (add components)
I[scattered] = F•^2[scattered] + F↕^2[scattered]
The amount of polarization and total Intensity, I = F^2, will vary as a function of θ
In the simple case at θ=90°, the ray is completely polarized.
Later we will find that we can describe diffraction as a "reflection" from a plane (a plane of oscillators) and see that this simple 2D diagram works as a projection to explain the general case for
"X-RAY DIFFRACTION", B. E. Warren, MIT, 1969
Chapter 1 "X-RAY SCATTERING BY ATOMS"
"1.1 CLASSICAL SCATTERING BY A FREE ELECTRON
When an x-ray beam falls on an atom, two processes may occur: (1) the beam may be absorbed with an ejection of electrons from the atom, or (2) the beam may be scattered. We shall first consider the
scattering process in terms of classical theory. The primary beam is an electromagnetic wave with electric vector varying sinusoidally with time and directed perpendicular to the direction of
propagation of the beam. This electric field exerts forces on the electrons of the atom producing accelerations of the electrons. Following classical electromagnetic theory, an accelerated charge
radiates. This radiation, which spreads out in all direction from the atom, has the same frequency as the primary beam, and it is called scattered radiation."
LIGHT AS A WAVE, Interaction of light and matter: plumb bob and ball...
Analogy: Damped Driven Simple Harmonic Motion
Example: bound "electron" and driving "wave" (styrofoam ball on yarn driven by hand wave...)
(or driven by coupled plumb bob for frequency controlled demo.)
Study question:
What is the phase of the ball with respect to plumb bob?
1. plumb bob at length equal to ball-yarn pendulum.
2. plumb bob at length longer than ball-yarn pendulum.
3. plumb bob at length shorter than ball-yarn pendulum.
4. Do-It-Yourself: teach your hand to drive the ball in these three modes...
Study question: plumb bob support provides the coupling. Why does the motion of the supporting beam NOT affect the phase relations?
Phase lag of an oscillator, scattered wave always in phase with oscillator:
(Quantum mechanics has its own way of getting broad absorption bands.)
Identify the “oscillators” and we have the field of Absorption Spectroscopy.
LIGHT AS A WAVE, Equation: interaction with oscillator
Points to note:
1. Oscillator acts as a radiation source: radiated wave is in phase with the oscillator.
2. The energy that can be pumped into the system, and thus the amount reradiated increases as ω → ω[0
3. For visible light ω < ω[0], so oscillator and emitted wave in phase (0°) with the driving wave.
For x-rays ω > ω[0] for most electrons in atoms, so oscillator and resulting scattered wave are 180° out of phase with the driving wave. Since one is usually concerned with the scattered wave, this
is often defined so that the scattered wave is at 0° and the driving wave at 180°.
4. Usual to treat phase of actual scattered light as having a usual component at 0° and an anomalous component with 90° phase difference (lag). For x-rays with scattered wave redefined to be 0° this
is 90°phase advance, see later for a way to draw this).
Simple Harmonic Oscillator, Damped Harmonic Oscillator, Driven Damped Harmonic Oscillator --- put in terms of what it means for light frequency==energy and energy (frequency) of an individual
n = refractive index (y axis, arbitrary scale), ω frequency of driving wave (x axis)
Selenium edge: ω[0] = 3*10^18 sec^-1 = .98Å
n: index of refraction
N: Number of charges per unit volume
q: charge of an electron
m: mass of an electron
ε : fudge factor to get magnitude and dimensions correct
ω : frequency of driving wave
γ : damping factor
i : 90° turn from usual, i.e. "imaginary" component
ω[0] : natural frequency of oscillator
Describing waves, the phase clock (with radius = amplitude):
(Amplitude factor) • (Phase factor) the general equation of a wave
the expression for a real (light) x-ray, of wavelength set by the real physical experimental conditions.
φ factor (e^iφ); e^iφ = cos(φ) + isin(φ)
exponential form convenient to talk about; cos() & sin() form (real and imaginary components) sometimes more convenient for computation.
Crystallographers use F for Amplitude, crystallography is a major field based on elastic scattering, 2014 is the international year of crystallography, 100 years after the von Laue experiment.
PHASE SHIFT through resonance...
Phase lag of an oscillator, scattered wave always in phase with oscillator:
(refractive index η is a measure of interaction)
η is a measure of the interaction of light with matter: interaction affects relative phase of the oscillator with respect to the driving wave and a probability of feeding energy into the oscillator.
The more energy in the oscillator, the more can be lost to other processes like absorption.
In any real situation there may be many types of oscillators in the medium interacting with the light but perhaps only one type near enough to resonance to have a significant anomalous scattering
component. Also, in common situations almost all of the effective oscillators will have a resonance frequency either greater than the light frequency, as is the case for visible light; or much
smaller, as is the case for x-rays. Any odd oscillator which happens to be far on the other side of resonance will make its unique and minor contribution 180° out of phase with the bulk of the
scattered radition and thus very slightly diminish the scattered intensity.
Wave description works very well for this since its amplitude can be any value and the wave emitted is in all directions from the scatterer - as is observed.
However, the description using photons has to account for both its quantized energy and its discret nature - so there has to be a probability of interaction that is the same as the coupling in the
wave description and the direction of travel a probability that gives the same energy to the possible directions as given by the wave description. (This gets much more interesting once we consider
more than on scatterer!)
REFERENCE PAGES...
HKL2000 demo: usual vs anomalous scattering of elements as a function of wavelength across absorption edges | {"url":"http://kinemage.biochem.duke.edu/teaching/lightScattering","timestamp":"2024-11-07T19:57:49Z","content_type":"text/html","content_length":"34138","record_id":"<urn:uuid:fa64233e-74da-474f-9ccf-31f32661af39>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00033.warc.gz"} |
ORIE Colloquium on 4/10/2012 - Agnes Sulem: A Stochastic Differential Game Approach to Stochastic Control Under Model Uncertainty
From E. Cornelius
Tuesday, April 10 at 4:15pm Frank H.T. Rhodes Hall, 253 This talk is motivated by the problem of optimization under model uncertainty. One way to present model uncertainty mathematically, is by means
of a family of probability measures Q which are absolutely continuous with respect to an original reference probability measure P, and by allowing uncertainty regarding which of the measures Q should
be taken into account when evaluating performance. We consider here a stochastic system described by a general Itô-Lévy process controlled by an agent. The performance functional is expressed as the
Q-expectation of an integrated profit rate plus a terminal payoff. We may regard Q as a scenario measure controlled by the market or the environment. If Q = P the problem becomes a classical
stochastic control problem. If Q is uncertain, however, the agent might seek the strategy which maximizes the performance in the worst possible choice of Q. This leads to a stochastic differential
game between the agent and the market. Our approach is the following: We write the performance functional as the value at time t = 0 of the solution of an associated controlled backward stochastic
differential equation (BSDE). Thus we arrive at a (zero sum) stochastic differential game of a system of forward-backward SDEs (FBSDEs) that we study by the maximum principle approach. We state
general stochastic maximum principles for stochastic differential games of FBSDEs with jumps, both in the zero-sum case (finding necessary and sufficient conditions for saddle points), and for the
non-zero sum games (finding conditions for Nash equilibria). We then apply these techniques to study an optimal portfolio problem in a Lévy market, under model uncertainty. We do not assume that the
system is Markovian. We establish a connection between market viability under uncertainty and equivalent local martingale measures. Finally we give explicit formulas for the optimal portfolio and the
optimal scenario for a class of incomplete markets. (Joint work with Bernt Øksendal, University of Oslo, Norway) | {"url":"https://vod.video.cornell.edu/media/ORIE+Colloquium+on+4+10+2012+-+Agnes+SulemA+A+Stochastic+Differential+Game+Approach+to+Stochastic+Control+Under+Model+Uncertainty/1_lsqf81yt","timestamp":"2024-11-10T17:31:33Z","content_type":"text/html","content_length":"113633","record_id":"<urn:uuid:d6efd716-2844-4ec2-b77d-c59a5182af16>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00344.warc.gz"} |
Texas Go Math Grade 4 Lesson 13.1 Answer Key Lines, Rays, and Angles
Refer to our Texas Go Math Grade 4 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 4 Lesson 13.1 Answer Key Lines, Rays, and Angles.
Texas Go Math Grade 4 Lesson 13.1 Answer Key Lines, Rays, and Angles
Essential Question
How can you identify and draw points, lines, line segments. rays, and angles?
Unlock the Problem
Everyday things can model geometric figures. For example, the period at the end of this sentence models a point. A solid painted stripe in the middle of a straight road models a line.
Activity 1 Draw and label \(\overline{J K}\).
I have drawn and labeled \(\overline{J K}\).
Math Talk
Mathematical Processes
Explain how lines, line segments, and rays are related.
A ray is a part of a line.
A line segment can be a part of a line, ray, or another line segment.
Ray AB = \(\overline{A B}\)
The line CD = \(\overline{C D}\) or line DC = \(\overline{D C}\).
From this we get \(\overline{C D}\) or \(\overline{D C}\).
From the above segment AB = \(\overline{A B}\), segment BA = \(\overline{B A}\)
segment CD = \(\overline{C D}\) and segment DC = \(\overline{D C}\)
Is there another way to name \(\overline{J K}\)? Explain.
Yes, there is a way to name \(\overline{J K}\) by switching the letters, \(\overline{K J}\) and when we are naming a line segment, either point can be named first.
You can name an angle by the vertex. When you name an angle using 3 points, the vertex is always the point in the middle.
We cannot say ∠B here because that could be one of three angles. So we have to use either ∠ABD or ∠ABC, or ∠DBC. We need to remember when we name an angle using 3 points, the vertex is always
the point in the middle.
Angles are classified by the size of the opening between the rays.
Activity 2 Classify an angle.
To classify an angle, you can compare it to a right angle.
Make a right angle by using a sheet of paper. Fold the paper twice evenly to model a right angle. Use the right angle to classify the angles below. Write acute, obtuse, right, or straight.
An angle that measures greater than 90° degrees is called an obtuse angle.
An angle that measures less than 90° degrees is called an acute angle.
An angle that measures less than 90° degrees is called an acute angle.
The given angle is a right-angled triangle that has 90°
Share and Show
Texas Go Math Grade 4 Answer Key Lesson 13.1 Question 1.
Draw and label \(\overline{A B}\) in the space at the right.
\(\overline{A B}\) is a _________________ .
Line segment
Draw and label an example of the figure.
Question 2.
\(\overleftrightarrow{X Y}\)
I have drawn and labeled an example of the figure to the given question
Question 3.
obtuse ∠K
I have drawn and labeled an example of the figure to the given question
Question 4.
right ∠CDE
I have drawn and labeled an example of the figure to the given question
Use Figure M for 5 and 6.
Question 5.
Name a line segment.
\(\overline{T U}\)
Go Math 4th Grade Answer Key Lines Rays and Angles Question 6.
Name a right angle.
∠TUW
By using the figure given above the name of the right angle is ∠TUW.
Problem Solving
Lise the picture of the bridge for 7 and 8.
Question 7.
Classify ∠A.
Question 8.
Which angle appears to be obtuse?
∠C
The angle C appears to be obtuse.
Question 9.
H.O.T. Use Diagrams How many different angles are in Figure X? List them.
There are 10 different angles.
The different angles that are in Figure X are ∠ABD, ∠DBE, ∠EBF, ∠FBC, ∠ABE, ∠DBF, ∠EBC, ∠ABF, ∠DBC, ∠ABC.
Question 10.
H.O.T. Multi-Step What’s the Error? Vanessa drew the angle at the right and named it ∠TRS. Explain why Vanessa’s name for the angle is incorrect. Write a correct name for the angle.
∠TSR or ∠RST
The vertex should be the middle letter in the angle’s name. The correct name for the angle is ∠TSR or ∠RST.
Daily Assessment Task
Fill in the bubble completely to show your answer.
Question 11.
What type of angle is ∠ABC?
(A) acute
(B) right
(C) obtuse
(D) straight
The ∠ABC is a type of obtuse angle.
Texas Go Math Grade 4 Volume 1 Pdf Lesson 13.1 Question 12.
Which name is a straight angle in the figure below?
(A) ∠XTW
(B) ∠STX
(C) ∠STY
(D) ∠WTS
∠WTS
The ∠WTS names a straight angle in the given figure.
Question 13.
Multi-Step What is the total number of acute angles in the figures shown below?
(A) 2
(B) 8
(C) 4
(D) 6
The total number of acute angles in the figures shown is 2.
TEXAS Test Prep
Question 14.
Which of the following terms best describes the figure below?
(A) ray
(B) line segment
(C) line
(D) angle
Ray is the term best describes the given figure.
Texas Go Math Grade 4 Lesson 13.1 Homework and Practice Answer Key
Draw and label an example of the figure.
Question 1.
\(\overrightarrow{A B}\)
Go Math Grade 4 Lesson 13.1 Homework Answer Key Question 2.
acute ∠J
Question 3.
right ∠ABC
Question 4.
\(\overleftrightarrow{J K}\)
Question 5.
obtuse ∠XYZ
Question 6.
\(\overline{P Q}\)
Use figure A for 7 and 8.
Question 7.
Name an acute angle.
∠BAD
The name of an acute angle is ∠BAD
Question 8.
Name an obtuse angle.
∠CDA
The name of an obtuse angle is ∠CDA
Problem Solving
Use the bridge drawing for 9 and 10.
Question 9.
Classify ∠B
Acute angle
Here the ∠B is an acute angle that is below 90°.
4th Grade Go Math Lesson 13.1 Practice Algebra Answers Question 10.
Jenny thinks that ∠C is a right angle. Explain why Jenny’s name for the angle is incorrect. Write the correct name for the angle.
Obtuse angle
The correct name of the angle is an obtuse angle that has above 90°. Therefore what Jenny thinks is wrong and the angle is incorrect.
Lesson Check
Fill in the bubble completely to show your answer.
Question 11.
What type of angle is ∠XYZ?
(A) right
(B) acute
(C) straight
(D) obtuse
The ∠XYZ is an acute angle.
Question 12.
Which names an obtuse angle in the figure below?
(A) ∠TZS
(B) ∠SZY
(C) ∠XZT
(D) ∠TZY
∠TZY
The ∠TZY names an obtuse angle in the given figure.
Question 13.
Which names an acute angle in the figure to the right?
(A) ∠VWU
(B) ∠VTU
(C) ∠TUW
(D) ∠WUT
∠VWU
The ∠VWU names an acute angle in the figure to the right.
Question 14.
Which of the following terms best describes the figure below?
(A) angle
(B) line segment
(C) ray
(D) line
line segment
The line segment term best describes the given figure.
Go Math 4th Grade Answer Key Lesson 13.1 Question 15.
Multi-Step What is the total number of rays in the figures to the right?
(A) 6
(B) 2
(C) 5
(D) 7
The total number of rays in the figure to the right is 2.
Question 16.
Multi-Step How many right angles are in Figure X?
(A) 4
(B) 2
(C) 3
(D) 1
∠WTY, ∠WTX, and ∠STY are the right angles in the given figure X
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Data Analysis with Pandas and NumPy
The tutorial demonstrates how to use the Pandas and NumPy libraries for effective data analysis.
We will walk through a Python Data Analysis Project demonstrating following tasks - - Creation of Multi-dimensional Arrays using NumPy We will create Ndarray using built-in NumPy methods taking data
from basic Python objects like lists, dictionaries and sets. - Perform Arithmetic Operations on Arrays We will perform the arithmetic operations on Ndarray and store the results - Perform Slicing and
Indexing on Arrays We will demonstrate integer based and Boolean indexing on Ndarray as well as methods for slicing - Creation of Data frames and Series Objects using Pandas We will demonstrate
creation of Data Frames from basic Python objects, CSV and Excel Files. And creation of Series objects. - Perform Data Pre-Processing on a Data Frame We will demonstrate operations like handling of
missing values, normalization, standardization, categorical encoding of data in a Data Frame. - Visualize Data in a DataFrame We will plot regression and correlation plots to demonstrate the
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R script -301114 -Nature of Data | Get AnswersR script -301114 -Nature of Data
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Question 1
Our goal is to examine if the sample is representative of the population and if the allocation of medication
and placebo is random.
1. Compute two frequency tables:
i. 1 × 3 table of frequencies containing the number of participants in each suburb
ii. 2 × 3 table of frequencies containing the number of participants from each suburb and the type of
medication given
2. Test if the distribution of suburbs follows the proportions: 50% Parramatta, 30% Campbelltown and
20% Penrith. Make sure to write out the two hypotheses, compute the p value, and write a conclusion
for the test.
3. Test if the medication type is independent of suburb. Make sure to write out the two hypotheses,
compute the p value, and write a conclusion for the test.
4. Answer only one of the following two questions!
i. Describe in words how the independence of two variables is defined in terms of their probability.
Write out equations if needed.
ii. Why did you use the chosen hypothesis test? What requirements does it have in order to be
successfully used and were those requirements satisfied? In general, what does the p-value
represent? Be brief; consider bullet points.
Question 2
Before we examine the effect of the medication, we first examine if there is any dependence of heart rate on
each participant’s suburb.
1. Compute the sample mean “before medication heart rate” for each suburb.
2. Test if the “before heart rate” mean is equal for all suburbs. Make sure to write out the two hypotheses,
compute the p value, and write a conclusion for the test.
3. Provide the set of 95% confidence intervals for the difference in means between “before heart rate”
measurements for each pair of suburbs. State which pairs of suburbs show a difference in means and
example your choice.
4. A colleague suggests you could perform a hypothesis test for each pair of suburbs using a t.test on each
data pair. Why is this not a good idea?
Question 3
To determine the effect of the medication on each participant’s heart rate, we will compare the mean after
medication heart rate for those who have been issued the medication, to the mean after medication heart
rate of those who were issued a placebo.
1. Compute the mean of the “after medication heart rate” for those that received the medication, and the
mean “after medication heart rate” for those that receive the placebo.
2. Test if there is a difference in mean “after medication heart rate” for those that received the medication
compared to those that received the placebo. Make sure to write out the two hypotheses, compute the
p value, and write a conclusion for the test.
3. Compute the 90% bootstrap confidence interval of the mean difference in “after medication heart rate”
between those that received the medication and those that received the placebo.
4. Describe why it is important to use a control treatment (such as the above placebo) when examining
the effects of medication.
Question 4
Finally, we want to examine the change in heart rate for each participant, regardless of the medication
1. Report the slope and intercept for the linear model, modelling the heart rate after medication with
respect to the heart rate before medication.
2. Use a permutation approach to test if the population slope is 1. Make sure to write out the two
hypotheses, compute the p-value and write a conclusion for the test.
3. Compute the 95% confidence interval for the slope.
4. Describe in words how we can determine if the linear model is a good fit of the data
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• "A Radically New Theory of how the Brain Represents and Computes with Probabilities" (2024) ACAIN 2023. (DOI) in Nicosia, G., Ojha, V., La Malfa, E., La Malfa, G., Pardalos, P.M., Umeton, R.
(eds) Machine Learning, Optimization, and Data Science. LOD 2023. Lecture Notes in Computer Science, vol 14506. Springer, Cham.
• Rod Rinkus (Accepted Talk, Generative Episodic Memory 2023) Semantic memory as a computationally free side-effect of sparse distributed generative episodic memory.
• Gerard (Rod) Rinkus (Submitted, Conf. on Cognitive Computational Neuroscience 2023) The Classical Tuning Function is an Artifact of a Neuron's Participations in Multiple Cell Assemblies.
• Gerard (Rod) Rinkus (Accepted as poster, Int'l Conf. on Neuromorphic, Natural and Physical Computing (NNPC) 2023) World Model Formation as a Side-effect of Non-optimization- based Unsupervised
Episodic Memory.
• Gerard (Rod) Rinkus (Accepted as poster, NNPC 2023) A cell assembly simultaneously transmits the full likelihood distribution via an atemporal combinatorial spike code.
• Rod Rinkus (Submitted, COSYNE 2023) "A cell assembly transmits the full likelihood distribution via an atemporal combinatorial spike code" (Rejected, See reviewer comments)
Summary: The “neuron doctrine” says the individual neuron is the functional unit of meaning. For a single source neuron, spike coding schemes can be based on spike rate or precise spike time
(s). Both are fundamentally temporal codes with two key limitations. 1) Assuming M different messages from (activation levels of) the source neuron are possible, the decode window duration, T
, must be ≥ M times a single spike’s duration. 2) Only one message (activation level) can be sent at a time. If instead, we define the cell assembly (CA), i.e., a set of co-active neurons, as
the functional unit of meaning, then a message is carried by the set of spikes simultaneously propagating in the bundle of axons leading from the CA’s neurons. This admits a more efficient,
faster, fundamentally atemporal, combinatorial coding scheme, which removes the above limitations. First, T becomes independent of M, in principle, shrinking to a single spike duration.
Second, multiple messages, in fact, the entire similarity (thus, likelihood) distribution over all items stored in the coding field can be sent simultaneously. This requires defining CAs as
sets of fixed cardinality, Q, which allows the similarity structure over a set of items stored as CAs to be represented by their intersection structure. Moreover, when any one CA is fully
active (i.e., all Q of its neurons are active), all other CAs stored in the coding field are partially active proportional to their intersections with the fully active CA. If M concepts are
stored, there are M! possible similarity orderings. Thus, sending any one of those orderings sends log2(M!) bits, far exceeding the log2M bits sent by any single message using temporal spike
codes. This marriage of a fixed-size CA representation and atemporal coding scheme may explain the speed and efficiency of probabilistic computation in the brain.
• Rod Rinkus (Submitted, SVRHM 2020) Efficient Similarity-Preserving Unsupervised Learning using Modular Sparse Distributed Codes and Novelty-Contingent Noise
Abstract: There is increasing realization in neuroscience that information is represented in the brain, e.g., neocortex, hippocampus, in the form sparse distributed codes (SDCs), a kind of
cell assembly. Two essential questions are: a) how are such codes formed on the basis of single trials, and how is similarity preserved during learning, i.e., how do more similar inputs get
mapped to more similar SDCs. I describe a novel Modular Sparse Distributed Code (MSDC) that provides simple, neurally plausible answers to both questions. An MSDC coding field (CF) consists
of Q WTA competitive modules (CMs), each comprised of K binary units (analogs of principal cells). The modular nature of the CF makes possible a single-trial, unsupervised learning algorithm
that approximately preserves similarity and crucially, runs in fixed time, i.e., the number of steps needed to store an item remains constant as the number of stored items grows. Further,
once items are stored as MSDCs in superposition and such that their intersection structure reflects input similarity, both fixed time best-match retrieval and fixed time belief update
(updating the probabilities of all stored items) also become possible. The algorithm's core principle is simply to add noise into the process of choosing a code, i.e., choosing a winner in
each CM, which is proportional to the novelty of the input. This causes the expected intersection of the code for an input, X, with the code of each previously stored input, Y, to be
proportional to the similarity of X and Y. Results demonstrating these capabilities for spatial patterns are given in the appendix.
• Rod Rinkus (accepted, NAISys 2020) A combinatorial population code can simultaneously transmit the full similarity (likelihood) distribution via an atemporal first-spike code.
Abstract: A simple, atemporal, first-spike code, operating on Combinatorial Population Codes (CPCs) (a.k.a., binary sparse distributed representations) is described, which allows the
similarities (more generally, likelihoods) of all items (hypotheses) stored in a CPC field to be simultaneously transmitted with a wave of single spikes from any single active code (i.e., the
code of any one particular stored item). Moreover, the number of underlying binary signals sent remains constant as the number of stored items grows.
• Rod Rinkus (Rejected, COSYNE 2019, see reviewer comments) Cell assemblies encode full likelihood distributions and communicate via atemporal first-spike codes
Abstract: For a single source neuron, spike coding schemes can be based on rate or on precise spike time(s) relative to an event, e.g., to a particular phase of gamma. Both are fundamentally
temporal, requiring a decode window duration T much longer than a single spike. But, if information is represented by population activity (distributed codes, cell assemblies) then messages
are carried by populations of spikes propagating in bundles of axons. This allows an atemporal coding scheme where the signal is encoded in the instantaneous sum of simultaneously arriving
spikes, in principle, allowing T to shrink to the duration of a single spike. In one type of atemporal population coding scheme, the fraction of active neurons in a source population (thus,
the fraction of active afferent synapses) carries the message. However, any single message carried by this variable-size code can represent only one value (signal). In contrast, if the source
field uses fixed-size, combinatorial coding, a particular instantiation of Hebb's cell assembly concept, then any one active code can simultaneously represent multiple values, in fact, the
likelihoods of all values, stored in the source field. Consequently, the vector of single, e.g., first, spikes sent by such a code can simultaneously transmit that full distribution.
Combining fixed-size combinatorial coding and an atemporal first-spike coding scheme may be keys to explaining the speed and energy efficiency of probabilistic computation in the brain.
• Rod Rinkus (NIPS CL WKSHP 2018) Sparsey, a memory-centric model of on-line, fixed-time, unsupervised continual learning.
Abstract: Four hallmarks of human intelligence are: 1) on-line, single/few-trial learning; 2) important/salient memories and knowledge are permanent over lifelong durations, though
confabulation (semantically plausible retrieval errors) accrues with age; 3) the times to learn a new item and to retrieve the best-matching (most relevant) item(s) remain constant as the
number of stored items grows; and 4) new items can be learned throughout life (storage capacity is never reached). No machine learning model, the vast majority of which are \textit
{optimization-centric}, i.e., learning involves optimizing a global objective (loss, energy), has all these capabilities. Here, I describe a \textit{memory-centric} model, Sparsey, which in
principle, has them all. I note prior results showing possession of Hallmarks 1 and 3 and sketch an argument, relying on hierarchy, critical periods, metaplasticity, and the recursive,
compositional (part-whole) structure of natural objects/events, that it also possesses Hallmarks 2 and 4. Two of Sparsey's essential properties are: i) information is represented in the form
of fixed-size sparse distributed representations (SDRs); and ii) its fixed-time learning algorithm maps more similar inputs to more highly intersecting SDRs. Thus, the similarity
(statistical) structure over the inputs, not just pair-wise but in principle, of all orders present, in essence, a generative model, emerges in the pattern of intersections of the SDRs of
individual inputs. Thus, semantic and episodic memory are fully superposed and semantic memory emerges as a by-product of storing episodic memories, contrasting sharply with deep learning
(DL) approaches in which semantic and episodic memory are physically separate.
• Rinkus, G. [accepted abstract as poster, withdrawn because cannot attend, improved version submitted to COSYNE (above)] First Spike Combinatorial Coding: The Key to Brain’s Computational
Efficiency. Submitted to Cognitive Computing 2018, Hannover.
Abstract: For a single source neuron, spike coding schemes can be based on rate or on precise spike time(s) relative to an event, e.g., to a particular phase of gamma. Both are fundamentally
temporal, requiring a decode window duration T much longer than a single spike. But, if information is represented by population activity (distributed codes, cell assemblies) then messages
are carried by populations of spikes propagating in bundles of axons. This allows an atemporal coding scheme where the signal is encoded in the instantaneous sum of simultaneously arriving
spikes, in principle, allowing T to shrink to the duration of a single spike. In one type of atemporal population coding scheme, the fraction of active neurons in a source population (thus,
the fraction of active afferent synapses) carries the message. However, any single message carried by this variable-size code can represent only one value (signal). In contrast, if the source
field uses fixed-size, combinatorial coding, then any one active code can represent multiple values, in fact, the entire likelihood distribution, e.g., over all values, e.g., of a scalar
variable, stored in the field. Consequently, the vector of single, e.g., first, spikes sent by such a code can simultaneously transmit the full distribution. Combining fixed-size
combinatorial coding and first-spike coding may be key to explaining the speed and energy efficiency of probabilistic computation in the brain.
• Rinkus, G. (2018) Sparse distributed representation, hierarchy, critical periods, metaplasticity: the keys to lifelong fixed-time learning and best-match retrieval. (Accepted Talk) Biological
Distributed Algorithms 2018 (London). Abstract
Abstract: Among the more important hallmarks of human intelligence, which any artificial general intelligence (AGI) should have, are the following. 1. It must be capable of on-line learning,
including with single/few trials. 2. Memories/knowledge must be permanent over lifelong durations, safe from catastrophic forgetting. Some confabulation, i.e., semantically plausible
retrieval errors, may gradually accumulate over time. 3. The time to both: a) learn a new item; and b) retrieve the best-matching / most relevant item(s), i.e., do similarity-based retrieval,
must remain constant throughout the lifetime. 4. The system should never become full: it must remain able to store new information, i.e., make new permanent memories, throughout very long
lifetimes. No artificial computational system has been shown to have all these properties. Here, we describe a neuromorphic associative memory model, Sparsey, which does, in principle,
possess them all. We cite prior results supporting possession of hallmarks 1 and 3 and sketch an argument, hinging on strongly recursive, hierarchical, part-whole compositional structure of
natural data, that Sparsey also possesses hallmarks 2 and 4.
• A Radically Novel Explanation of Probabilistic Computing in the Brain. Invited Talk to Xaq Pitkow Lab Weekly Seminar Dec. 18, 2017.
Abstract: It is widely believed that the brain computes probabilistically and via some form of population coding. I describe a concept and mechanism of probabilistic computation and learning
that differs radically from existing probabilistic population coding (PPC) models. The theory, Sparsey, is based on the idea that items of information (e.g., concepts) are represented as
sparse distributed representations (SDRs), i.e., relatively small subsets of cells chosen from a much larger field, where the subsets may overlap, cf. ‘cell assembly’, ‘summary statistic’
(Pitkow & Angelaki, 2017). A Sparsey coding field consists of Q WTA competitive modules (CMs), each consisting of K units. Thus, all codes are of fixed size, Q, and the code space is K^Q.
This allows an extremely simple way to represent the likelihood/probability of a concept: the probability of concept X is simply the fraction of X’s SDR code present in the currently active
code. But to make sense, this requires that more similar concepts map to more similar (more highly intersecting) codes (“SISC” property). If SISC is enforced, then any single active SDR code
simultaneously represents both a particular concept (at 100% likelihood) and the entire likelihood distribution over all concepts stored in the field (with likelihoods proportional to the
sizes of their codes’ intersections with the currently active code). The core of Sparsey is a learning/inference algorithm, the code selection algorithm (CSA), which ensures SISC and which
runs in fixed time, i.e., the number of operations needed both to learn (store) a new item and to retrieve the best-matching stored item remains constant as the number of stored items
increases (cf. locality-sensitive hashing). Since any SDR code represents the entire distribution, the CSA also realizes fixed-time ‘belief update’. I will describe the CSA and address the
neurobiological correspondence of the theory’s elements/processes and highlight relationships with Pitkow & Angelaki, 2017.
• Superposed Episodic and Semantic Memory via Sparse Distributed Representation (arXiv 2017, Submitted to NIPS 2017 CIAI Wkshp, rejected)
Abstract: The abilities to perceive, learn, and use generalities, similarities, classes, i.e., semantic memory (SM), is central to cognition. Machine learning (ML), neural network, and AI
research has been primarily driven by tasks requiring such abilities. However, another central facet of cognition, single-trial formation of permanent memories of experiences, i.e., episodic
memory (EM), has had relatively little focus. Only recently has EM-like functionality been added to Deep Learning (DL) models, e.g., Neural Turing Machine, Memory Networks. However, in these
cases: a) EM is implemented as a separate module, which entails substantial data movement (and so, time and power) between the DL net itself and EM; and b) individual items are stored
localistically within the EM, precluding realizing the exponential representational efficiency of distributed over localist coding. We describe Sparsey, a unsupervised, hierarchical, spatial/
spatiotemporal associative memory model differing fundamentally from mainstream ML models, most crucially, in its use of sparse distributed representations (SDRs), or, cell assemblies, which
admits an extremely efficient, single-trial learning algorithm that maps input similarity into code space similarity (measured as intersection). SDRs of individual inputs are stored in
superposition and because similarity is preserved, the patterns of intersections over the assigned codes reflect the similarity, i.e., statistical, structure, of all orders, not simply
pairwise, over the inputs. Thus, SM, i.e., a generative model, is built as a computationally free side effect of the act of storing episodic memory traces of individual inputs, either spatial
patterns or sequences. We report initial results on MNIST and on the Weizmann video event recognition benchmarks. While we have not yet attained SOTA class accuracy, learning takes only
minutes on a single CPU.
• The Brain’s Computational Efficiency derives from using Sparse Distributed Representations. Rejected from Cognitive Computational Neuroscience 2017.
Abstract: Machine learning (ML) representation formats have been dominated by: a) localism, wherein individual items are represented by single units, e.g., Bayes Nets, HMMs; and b) fully
distributed representations (FDR), wherein items are represented by unique activation patterns over all the units, e.g., Deep Learning (DL) and its progenitors. DL has had great success
vis-a-vis classification accuracy and learning complex mappings (e.g., AlphaGo). But, without massive machine parallelism (MP), e.g., GPUs, TPUs, and thus high power, DL learning is
intractably slow. The brain is also massively parallel, but uses only 20 watts and moreover, the forms of MP used in DL, model / data parallelism and shared parameters, are patently
non-biological, suggesting DL’s core principles do not emulate biological intelligence. We claim that a basic disconnect between DL/ML and biology and the key to biological intelligence is
that instead of FDR or localism, the brain uses sparse distributed representations (SDR), i.e., “cell assemblies”, wherein items are represented by small sets of binary units, which may
overlap, and where the pattern of overlaps embeds the similarity/statistical structure (generative model) of the domain. We’ve previously described an SDR-based, extremely efficient, one-shot
learning algorithm in which the primary operation is permanent storage of experienced events based on single trials (episodic memory), but in which the generative model (semantic memory,
classification) emerges automatically, and as a computationally free, in terms of time and power, side effect of the episodic storage process. Here, we discuss fundamental differences between
the mainstream localist/FDR-based and our SDR-based approaches.
• A Radically new Theory of How the Brain Represents and Computes with Probabilities. (arXiv)
Abstract: The brain is believed to implement probabilistic reasoning and to represent information via population, or distributed, coding. Most previous population-based probabilistic (PPC)
theories share several basic properties: 1) continuous-valued neurons; 2) fully(densely)-distributed codes, i.e., all(most) units participate in every code; 3) graded synapses; 4) rate
coding; 5) units have innate unimodal tuning functions (TFs); 6) intrinsically noisy units; and 7) noise/correlation is considered harmful. We present a radically different theory that
assumes: 1) binary units; 2) only a small subset of units, i.e., a sparse distributed code (SDC) (cell assembly, ensemble), comprises any individual code; 3) binary synapses; 4) signaling
formally requires only single (first) spikes; 5) units initially have completely flat TFs (all weights zero); 6) units are not inherently noisy; but rather 7) noise is a resource generated/
used to cause similar inputs to map to similar codes, controlling a tradeoff between storage capacity and embedding the input space statistics in the pattern of intersections over stored
codes, indirectly yielding correlation patterns. The theory, Sparsey, was introduced 20 years ago as a canonical cortical circuit/algorithm model, but not elaborated as an alternative to PPC
theories. Here, we show that the active SDC simultaneously represents both the most similar/likely input and the coarsely-ranked distribution over all stored inputs (hypotheses). Crucially,
Sparsey's code selection algorithm (CSA), used for both learning and inference, achieves this with a single pass over the weights for each successive item of a sequence, thus performing
spatiotemporal pattern learning/inference with a number of steps that remains constant as the number of stored items increases. We also discuss our approach as a radically new implementation
of graphical probability modeling.
• Sparsey™: Event recognition via deep hierarchical sparse distributed codes. (2014) Frontiers in Computational Neuroscience. v. 8 December 2014 | doi: 10.3389/fncom.2014.00160 (Frontiers Link)
Abstract: The visual cortex's hierarchical, multi-level organization is captured in many biologically inspired computational vision models, the general idea being that progressively larger
scale (spatially/temporally) and more complex visual features are represented in progressively higher areas. However, most earlier models use localist representations (codes) in each
representational field (which we equate with the cortical macrocolumn, "mac"), at each level. In localism, each represented feature/concept/event (hereinafter "item") is coded by a single
unit. The model we describe, Sparsey, is hierarchical as well but crucially, it uses sparse distributed coding (SDC) in every mac in all levels. In SDC, each represented item is coded by a
small subset of the mac's units. The SDCs of different items can overlap and the size of overlap between items can be used to represent their similarity. The difference between localism and
SDC is crucial because SDC allows the two essential operations of associative memory, storing a new item and retrieving the best-matching stored item, to be done in fixed time for the life of
the model. Since the model's core algorithm, which does both storage and retrieval (inference), makes a single pass over all macs on each time step, the overall model's storage/retrieval
operation is also fixed-time, a criterion we consider essential for scalability to the huge ("Big Data") problems. A 2010 paper described a nonhierarchical version of this model in the
context of purely spatial pattern processing. Here, we elaborate a fully hierarchical model (arbitrary numbers of levels and macs per level), describing novel model principles like
progressive critical periods, dynamic modulation of principal cells' activation functions based on a mac-level familiarity measure, representation of multiple simultaneously active
hypotheses, a novel method of time warp invariant recognition, and we report results showing learning/recognition of spatiotemporal patterns.
• Sparse Distributed Coding & Hierarchy: The Keys to Scalable Machine Intelligence. DARPA UPSIDE Year 1 Review Presentation. 3/11/14. (PPT)
• A cortical theory of super-efficient probabilistic inference based on sparse distributed representations. 22nd Annual Computational Neuroscience Meeting, Paris, July 13-18. BMC Neuroscience 2013,
14(Suppl 1):P324 (Abstract)
• Constant-Time Probabilistic Learning & Inference in Hierarchical Sparse Distributed Representations, Invited Talk at the Neuro-Inspired Computational Elements (NICE) Workshop, Sandia Labs,
Albuquerque, NM, Feb 2013.
Abstract: Quantum superposition states that any physical system simultaneously exists in all of its possible states, the number of which is exponential in the number of entities composing the
system. The strength of presence of each possible state in the superposition—i.e., the probability with which it would be observed if measured—is represented by its probability amplitude
coefficient. The assumption that these coefficients must be represented physically disjointly from each other, i.e., localistically, is nearly universal in the quantum theory/computing
literature. Alternatively, these coefficients can be represented using sparse distributed representations (SDR), wherein each coefficient is represented by a small subset of an overall population
of representational units and the subsets can overlap. Specifically, I consider an SDR model in which the overall population consists of Q clusters, each having K binary units, so that each
coefficient is represented by a set of Q units, one per cluster. Thus, K^Q coefficients can be represented with KQ units. We can then consider the particular world state, X, whose coefficient’s
representation, R(X), is the set of Q units active at time t to have the maximal probability and the probabilities of all other states, Y, to correspond to the size of the intersection of R(Y)
and R(X). Thus, R(X) simultaneously serves both as the representation of the particular state, X, and as a probability distribution over all states. Thus, set intersection may be used to
classically implement quantum superposition. If algorithms exist for which the time it takes to store (learn) new representations and to find the closest-matching stored representation
(probabilistic inference) remains constant as additional representations are stored, this would meet the criterion of quantum computing. Such algorithms, based on SDR, have already been
described. They achieve this "quantum speed-up" with no new esoteric technology, and in fact, on a single-processor, classical (Von Neumann) computer.
• A cortical sparse distributed coding model linking mini- and macrocolumn-scale functionality. (2010) Gerard Rinkus. Frontiers in Neuroanatomy 4:17. doi:10.3389/fnana.2010.00017 (Frontiers Link)
Abstract: No generic function for the minicolumn - i.e., one that would apply equally well to all cortical areas and species - has yet been proposed. I propose that the minicolumn does have a
generic functionality, which only becomes clear when seen in the context of the function of the higher-level, subsuming unit, the macrocolumn. I propose that: (a) a macrocolumn's function is
to store sparse distributed representations of its inputs and to be a recognizer of those inputs; and (b) the generic function of the minicolumn is to enforce macrocolumnar code sparseness.
The minicolumn, defined here as a physically localized pool of approximately 20 L2/3 pyramidals, does this by acting as a winner-take-all (WTA) competitive module, implying that macrocolumnar
codes consist of approximately 70 active L2/3 cells, assuming approximately 70 minicolumns per macrocolumn. I describe an algorithm for activating these codes during both learning and
retrievals, which causes more similar inputs to map to more highly intersecting codes, a property which yields ultra-fast (immediate, first-shot) storage and retrieval. The algorithm achieves
this by adding an amount of randomness (noise) into the code selection process, which is inversely proportional to an input's familiarity. I propose a possible mapping of the algorithm onto
cortical circuitry, and adduce evidence for a neuromodulatory implementation of this familiarity-contingent noise mechanism. The model is distinguished from other recent columnar cortical
circuit models in proposing a generic minicolumnar function in which a group of cells within the minicolumn, the L2/3 pyramidals, compete (WTA) to be part of the sparse distributed
macrocolumnar code.
• Familiarity-Contingent Probabilistic Sparse Distributed Code Selection in Cortex. (in prep, also see this page)
• Overcoding-and-Pruning:A Novel Neural Model of Temporal Chunking and Short-term Memory. (2009) Gerard Rinkus. Invited Talk in Gabriel Kreiman Lab, Dept. of Opthamology and Neuroscience,
Children's Hospital, Boston, July 31, 2009.
• Overcoding-and-paring: a bufferless neural chunking model. (2009) Gerard Rinkus. Frontiers in Computational Neuroscience. Conference Abstract: Computational and systems neuroscience. (COSYNE '09)
doi: 10.3389/conf.neuro.10.2009.03.292
• Population Coding Using Familiarity-Contingent Noise.(abstract/poster) AREADNE 2008: Research in Encoding And Decoding of Neural Ensembles, Santorini, Greece, June 26-29. (abstract) (poster)
• Overcoding-and-pruning: A novel neural model of sequence chunking (manuscript in prep) -- Patented
Abstract: We present a radically new model of chunking, the process by which a monolithic representation emerges for a sequence of items, called overcoding-and-pruning (OP). Its core insight
is this: if a sizable population of neurons is assigned to represent an ensuing sequence immediately, at sequence start, it can then be repeatedly pruned as functions of each successive item.
This solves the problem of assigning unique chunk representations to sequences that start in the same way, e.g., "CAT" and "CAR", without requiring temporary buffering of the items'
representations. OP rests on two well-supported assumptions: 1) information is represented in cortex by sparse distributed representations; and 2) neurons at progressively higher cortical
stages have progressively longer activation duration-or, persistence. We believe that this type of mechanism has been missed so far due to the historical bias of thinking in terms of localist
representations, which cannot support it since pruning cannot be applied to a single representational unit.
• A Functional Role for the Minicolumn in Cortical Population Coding. Invited Talk at Cortical Modularity and Autism, University of Louisville, Louisville, KY, Oct 12-14, 2007. (PPT) (pdf)
Animations do not show in pdf version.
• Hierarchical Sparse Distributed Representations of Sequence Recall and Recognition. Presentation given at The Redwood Center for Theoretical Neuroscience (University of California, Berkeley) on
Feb 22, 2006. (PPT) (video) (Note: PPT presentation uses heavy animations)
• Time-Invariant Recognition of Spatiotemporal Patterns in a Hierarchical Cortical Model with a Caudal-Rostral Persistence Gradient (2005) (poster) Rinkus, G. J. & Lisman, J. Society for
Neuroscience Annual Meeting, 2005. Washington, DC. Nov 12-16. Note that this poster is almost identical to the one presented at the First Annual Computational Cognitive Neuroscience Conference.
• A Neural Network Model of Time-Invariant Spatiotemporal Pattern Recognition (2005) (abstract) Rinkus, G. J. First Annual Computational Cognitive Neuroscience Conference, Washington, DC, Nov.
2004 and earlier
• A Neural Model of Episodic and Semantic Spatiotemporal Memory (2004) Rinkus, G.J. Proceedings of the 26th Annual Conference of the Cognitive Science Society. Kenneth Forbus, Dedre Gentner & Terry
Regier, Eds. LEA, NJ. 1155-1160. Chicago, Ill. (pdf)
A Quicktime animation that walks you through the example in Figure 4 of the paper.
• Software tools for emulation and analysis of augmented communication. (2003) Lesher, G.W., Moulton, B.J., Rinkus, G. & Higginbotham, D.J. CSUN 2003, California State University, Northridge.
• Adaptive Pilot-Vehicle Interfaces for the Tactical Air Environment. (2001) Mulgund, S.S., Zacharias, G.L., & Rinkus, G.J. in Psychological Issues in the Design and Use of Virtual Adaptive
Environments. Hettinger, L.J. & Haas, M. (Eds.) LEA, NJ. 483-524.
• Leveraging word prediction to improve character prediction in a scanning configuration. (2002) Lesher, G.W. & Rinkus, G.J. Proceedings of the RESNA 2002 Annual Conference. Reno. (pdf)
• Domain-specific word prediction for augmentative communications (2001) Lesher, G.W. & Rinkus, G.J. Proceedings of the RESNA 2002 Annual Conference, Reno. (pdf)
• Logging and analysis of augmentative communication. (2000) Lesher, G.W., Rinkus, G.J., Moulton, B.J., & Higginbotham, D.J. Proc. of the RESNA 2000 Annual Conference, Reno. 82-85.
• Intelligent fusion and asset manager processor (IFAMP). (1998) Gonsalves,P.G. & Rinkus, G.J. Proc. of the IEEE Information Technology Conference (Syracuse, NY) 15-18. (pdf)
• A Monolithic Distributed Representation Supporting Multi-Scale Spatio-Temporal Pattern Recognition (1997) Int'l Conf. on Vision, Recognition, Action: Neural Models of Mind and Machine, Boston
University, Boston, MA May 29-31. (abstract)
• Situation Awareness Modeling and Pilot State Estimation for Tactical Cockpit Interfaces. (1997) Mulgund, S., Rinkus, G., Illgen, C. & Zacharias, G. Presented at HCI International, San Francisco,
CA, August. (pdf)
• OLIPSA: On-Line Intelligent Processor for Situation Assessment. (1997) S. Mulgund, G. Rinkus, C. Illgen & J. Friskie. Second Annual Symposium and Exhibition on Situational Awareness in the
Tactical Air Environment, Patuxent River, MD. (pdf)
• A Neural Network Based Diagnostic Test System for Armored Vehicle Shock Absorbers. (1996) Sincebaugh, P., Green, W. & Rinkus, G. Expert Systems with Applications, 11(2), 237-244.
• A Combinatorial Neural Network Exhibiting Episodic and Semantic Memory Properties for Spatio-Temporal Patterns (1996) G. J. Rinkus. Doctoral Thesis. Boston University. Boston, MA. (ResearchGate)
Abstract: A model is described in which three types of memory—episodic memory, complex sequence memory and semantic memory—coexist within a single distributed associative memory. Episodic
memory stores traces of specific events. Its basic properties are: high capacity, single-trial learning, memory trace permanence, and ability to store non-orthogonal patterns. Complex
sequence memory is the storage of sequences in which states can recur multiple times: e.g. [A B B A C B A]. Semantic memory is general knowledge of the degree of featural overlap between the
various objects and events in the world. The model's initial version, TEMECOR-1, exhibits episodic and complex sequence memory properties for both uncorrelated and correlated spatiotemporal
patterns. Simulations show that its capacity increases approximately quadratically with the size of the model. An enhanced version of the model, TEMECOR-II, adds semantic memory properties.
The TEMECOR-I model is a two-layer network that uses a sparse, distributed internal representation (IR) scheme in its layer two (L2). Noise and competition allow the IRs of each input state
to be chosen in a random fashion. This randomness effects an orthogonalization in the input-to- IR mapping, thereby increasing capacity. Successively activated IRs are linked via Hebbian
learning in a matrix of horizontal synapses. Each L2 cell participates in numerous episodic traces. A variable threshold prevents interference between traces during recall. The random choice
of IRs in TEMECOR-I precludes the continuity property of semantic memory: that there be a relationship between the similarity (degree of overlap) of two IRs and the similarity of the
corresponding inputs. To create continuity in TEMECOR-II, the choice of the IR is a function of both noise (Λ) and signals propagating in the L2 horizontal matrix and input-to-IR map. These
signals are deterministic and shaped by prior experience. On each time slice, TEMECOR-II computes an expected input based on the history-dependent influences, and then computes the difference
between the expected and actual inputs. When the current situation is completely familiar, Λ=0, and the choice of IRs is determined by the history-dependent influences. The resulting IR has
large overlap with previously used IRs. As perceived novelty increases, so does Λ, with the result that the overlap between the chosen IR and any previously-used IRs decreases.
• TEMECOR: An Associative, Spatiotemporal Pattern Memory for Complex State Sequences. (1995) Proceedings of the 1995 World Congress on Neural Networks. LEA and INNS Press. 442-448. (pdf)
• Context-sensitive spatio-temporal memory. (1993) Proceedings of World Congress On Neural Networks. LEA. v.2, 344-347.
• Context-sensitive Spatio-temporal Memory. (1993) Technical Report CAS/CNS-93-031, Boston University Dept. of Cognitive and Neural Systems. Boston, MA. (pdf)
• A Neural Model for Spatio-temporal Pattern Memory (1992) Proceedings of the Wang Conference: Neural Networks for Learning, Recognition, and Control, Boston University, Boston, MA
• Learning as Natural Selection in a Sensori-Motor Being (1988) Proceedings of the 1st Annual Conference of the Neural Network Society, Boston.
• Learning as Natural Selection in a Sensori-Motor Being (1986) G.J.Rinkus. Master's Thesis. Hofstra University, Hempstead, NY. | {"url":"http://www.sparsey.com/Publications.html","timestamp":"2024-11-08T02:33:23Z","content_type":"application/xhtml+xml","content_length":"52713","record_id":"<urn:uuid:7e61f596-950d-4432-8704-65d8de5e90af>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00559.warc.gz"} |
How to count dates in a column? INVALID DATATYPE error
I want to count how many dates in a column called "Completed" occur in the month of January.
Using this formula
=COUNTIF([Completed]:[Completed], MONTH(@cell) = 1)
returns INVALID DATATYPE whether I use it in a cell on the sheet or in a sheet summary field or on a separate metric sheet with the formula referencing the Completed column in the data sheet.
The explanation of the error is as follows: The formula contains or references an incompatible data type, such as =INT("Hello")
The column I reference is set up as a date column and the column where the formula is is a text/# column. I am unclear where/why the problem is occurring. I feel like it must be something obvious/
simple but I am stumped.
I appreciate your insights, Smartsheet Community!
Best Answer
• IFERROR isn't what you want in this situation. Try the following, it should exclude any rows that don't have a valid date, which includes blanks.
=COUNTIFS(Completed:Completed, ISDATE(@cell), Completed:Completed, MONTH(@cell) = 1)
• Hi @Carroll Wall,
The formula you have posted is correct, there is most likely a row(s) that has a non-date value or is blank, which is throwing the error.
Hope this helps,
• I am unclear why it would return the error when there are no blanks.
Would I use an IFERROR function here?
• IFERROR isn't what you want in this situation. Try the following, it should exclude any rows that don't have a valid date, which includes blanks.
=COUNTIFS(Completed:Completed, ISDATE(@cell), Completed:Completed, MONTH(@cell) = 1)
• Thank you! This does help. I was unfamiliar with the ISDATE function.
I appreciate the opportunity to learn something new!
Help Article Resources | {"url":"https://community.smartsheet.com/discussion/116285/how-to-count-dates-in-a-column-invalid-datatype-error","timestamp":"2024-11-06T07:59:33Z","content_type":"text/html","content_length":"407041","record_id":"<urn:uuid:dec066cd-38c7-465f-9250-32e9101f0e36>","cc-path":"CC-MAIN-2024-46/segments/1730477027910.12/warc/CC-MAIN-20241106065928-20241106095928-00043.warc.gz"} |
Class GeometricDistribution
• Constructor Summary
Create a geometric distribution with the given probability of success.
• Method Summary
Modifier and Type
For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
Use this method to get the numerical value of the mean of this distribution.
Use this method to get the numerical value of the variance of this distribution.
Access the probability of success for this distribution.
Access the lower bound of the support.
Access the upper bound of the support.
Computes the quantile function of this distribution.
Use this method to get information about whether the support is connected, i.e.
For a random variable X whose values are distributed according to this distribution, this method returns log(P(X = x)), where log is the natural logarithm.
For a random variable X whose values are distributed according to this distribution, this method returns P(X = x).
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• Constructor Details
□ GeometricDistribution
Create a geometric distribution with the given probability of success.
p - probability of success.
MathIllegalArgumentException - if p <= 0 or p > 1.
• Method Details
□ getProbabilityOfSuccess
public double getProbabilityOfSuccess()
Access the probability of success for this distribution.
the probability of success.
□ probability
public double probability(int x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X = x). In other words, this method represents the probability mass function (PMF)
for the distribution.
x - the point at which the PMF is evaluated
the value of the probability mass function at x
□ logProbability
public double logProbability(int x)
For a random variable
whose values are distributed according to this distribution, this method returns
log(P(X = x))
, where
is the natural logarithm. In other words, this method represents the logarithm of the probability mass function (PMF) for the distribution. Note that due to the floating point precision and
under/overflow issues, this method will for some distributions be more precise and faster than computing the logarithm of
The default implementation simply computes the logarithm of probability(x).
Specified by:
logProbability in interface IntegerDistribution
logProbability in class AbstractIntegerDistribution
x - the point at which the PMF is evaluated
the logarithm of the value of the probability mass function at x
□ cumulativeProbability
public double cumulativeProbability(int x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x). In other words, this method represents the (cumulative) distribution
function (CDF) for this distribution.
x - the point at which the CDF is evaluated
the probability that a random variable with this distribution takes a value less than or equal to x
□ getNumericalMean
public double getNumericalMean()
Use this method to get the numerical value of the mean of this distribution. For probability parameter p, the mean is (1 - p) / p.
the mean or Double.NaN if it is not defined
□ getNumericalVariance
public double getNumericalVariance()
Use this method to get the numerical value of the variance of this distribution. For probability parameter p, the variance is (1 - p) / (p * p).
the variance (possibly Double.POSITIVE_INFINITY or Double.NaN if it is not defined)
□ getSupportLowerBound
public int getSupportLowerBound()
Access the lower bound of the support. This method must return the same value as
. In other words, this method must return
inf {x in Z | P(X <= x) > 0}.
The lower bound of the support is always 0.
lower bound of the support (always 0)
□ getSupportUpperBound
public int getSupportUpperBound()
Access the upper bound of the support. This method must return the same value as
. In other words, this method must return
inf {x in R | P(X <= x) = 1}.
The upper bound of the support is infinite (which we approximate as
upper bound of the support (always Integer.MAX_VALUE)
□ isSupportConnected
public boolean isSupportConnected()
Use this method to get information about whether the support is connected, i.e. whether all integers between the lower and upper bound of the support are included in the support. The support
of this distribution is connected.
□ inverseCumulativeProbability
Computes the quantile function of this distribution. For a random variable
distributed according to this distribution, the returned value is
☆ inf{x in Z | P(X<=x) >= p} for 0 < p <= 1,
☆ inf{x in Z | P(X<=x) > 0} for p = 0.
If the result exceeds the range of the data type
, then
is returned. The default implementation returns
Specified by:
inverseCumulativeProbability in interface IntegerDistribution
inverseCumulativeProbability in class AbstractIntegerDistribution
p - the cumulative probability
the smallest p-quantile of this distribution (largest 0-quantile for p = 0)
MathIllegalArgumentException - if p < 0 or p > 1 | {"url":"https://hipparchus.org/apidocs-3.1/org/hipparchus/distribution/discrete/GeometricDistribution.html","timestamp":"2024-11-09T16:07:37Z","content_type":"text/html","content_length":"27970","record_id":"<urn:uuid:7e487155-1386-42af-8dbd-8b3772e9af32>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00025.warc.gz"} |
Fortnightly links (104)
• Alexander Perry: The integral Hodge conjecture for two-dimensional Calabi-Yau categories is a must-read (if you have the time and necessary background).
• Indranil Biswas, Tomas L. Gomez: On vector bundles over moduli spaces trivial on Hecke curves proves an interesting result for moduli of vector bundles on a curve, whose geometry I find very
interesting. It's analogous to the result that if $\mathcal{E}$ is a vector bundle on $\mathbb{P}^n$, such that $\mathcal{E}|_L\cong\mathcal{O}_{\mathbb{P}^1}^{\oplus r}$ for every line on $\
mathbb{P}^n$, then $\mathcal{E}$ is itself trivial. For $\mathrm{M}_C(r,\mathcal{L})$, the same result holds, where the role of lines is played by "rational curves of minimal degree", also known
as Hecke curves (which have an explicit modular interpretation).
• David Favero, Daniel Kaplan, Tyler L. Kelly: A maximally-graded invertible cubic threefold that does not admit a full exceptional collection of line bundles gives a counterexample to the
Lekili-Ueda conjecture on the existence of a full exceptional collection of line bundles for a Landau–Ginzburg model, which is itself analogous to King's conjecture on the existence of a full
exceptional collection of line bundles for a smooth projective toric variety. The latter is known to be false since 2006, by Hille–Perling. Now the Landau--Ginzburg model version for invertible
polynomials is also known to be false. | {"url":"https://pbelmans.ncag.info/blog/2020/04/13/fortnightly-links-104/","timestamp":"2024-11-11T18:08:30Z","content_type":"text/html","content_length":"21238","record_id":"<urn:uuid:af420ba2-b704-4e6c-af7b-4378efbd5753>","cc-path":"CC-MAIN-2024-46/segments/1730477028235.99/warc/CC-MAIN-20241111155008-20241111185008-00371.warc.gz"} |
Expansion of the commutator of two vector fields
• Thread starter tut_einstein
• Start date
In summary, the conversation discusses the expansion of the commutator of two vector fields and the confusion about a specific term in the expansion. The response explains that the term can be
obtained through the product rule and that the commutator is bilinear.
I don't understand a particular coordinate expansion of the commutator of 2 vector fields:
[X, Y ]f = X(Y f) − Y (Xf) = X_be_b(Y _ae_af) − Y _be_b(X_ae_af)
= (X_b(e_bY_ a) − Y _b(e_bX_a))e_af + X_aY _b[e_a, e_b]f
X,Y = Vector fields
f = function
X_i = Components of X and same for Y
e_i = coordinates of the vector space
I don't understand how to get the third term in the 2nd line. I can tell that it's probably a product rule but I don't see how to get it.
If we write X= (sum)X_i d/dxi &c., we only have to notice that the commutator is bilinear & the terms follow.
FAQ: Expansion of the commutator of two vector fields
1. What is a commutator of two vector fields?
A commutator of two vector fields is a mathematical operation that combines two vector fields and measures their non-commutativity, or the extent to which the order of the fields affects the result.
It is denoted by [V,W] and is defined as the difference between the vector field obtained by applying V to W and the vector field obtained by applying W to V.
2. Why is the expansion of the commutator of two vector fields important?
The expansion of the commutator of two vector fields is important because it helps us understand the behavior of vector fields and their interactions. It can also provide insight into the underlying
symmetries and properties of a system.
3. How is the commutator of two vector fields expanded?
The commutator of two vector fields can be expanded using the Jacobi identity, which states that [V,[W,Z]] + [W,[Z,V]] + [Z,[V,W]] = 0. This identity allows us to simplify the expansion and express
it in terms of the Lie bracket, which is a fundamental operation in differential geometry.
4. Can the expansion of the commutator of two vector fields be used to solve differential equations?
Yes, the expansion of the commutator of two vector fields can be used to solve differential equations. It allows us to rewrite the original equation in terms of the Lie bracket, which can then be
solved using various techniques such as power series or numerical methods.
5. Are there any real-world applications of the expansion of the commutator of two vector fields?
Yes, the expansion of the commutator of two vector fields has many real-world applications in fields such as physics, engineering, and computer science. It is commonly used in the study of fluid
mechanics, electromagnetism, and quantum mechanics, among others. It also has practical applications in control systems, robotics, and machine learning algorithms. | {"url":"https://www.physicsforums.com/threads/expansion-of-the-commutator-of-two-vector-fields.506946/","timestamp":"2024-11-02T05:17:18Z","content_type":"text/html","content_length":"76289","record_id":"<urn:uuid:2e5d2912-1a1a-4b02-967a-5277a8dd4776>","cc-path":"CC-MAIN-2024-46/segments/1730477027677.11/warc/CC-MAIN-20241102040949-20241102070949-00525.warc.gz"} |
Jonckheere-terpstra trend test spss for windows
Then the jonckheere terpstra test statistic is computed as this test rejects the null hypothesis of no difference among classes for large values of j. It is similar to the kruskalwallis test in that
the null hypothesis is that several independent samples are from the same population. Multiple linear regression analysis was used to test the significance of the associations between the tma of bat
and the biological and environmental factors. I am running the jonckheereterpstra in place of kruskalwallis test, as my factor is in ordinal scale i. Two possible ordinal trend measure not detected
by findit trend test are somers d and kendalls taua. Stata module to perform jonckheere terpstra test, statistical software components s423601, boston college department of economics, revised 26 aug
2008. Jonckheere terpstra test using spss statistics introduction. Also note that reffect is calculated as for the mannwhitney test, namely. Jonckheereterpstra test for nonclassical error versus log.
If i plot the medians and correlate line of best fit them the r2 is 0. Several statistical programs have the capability to perform these calculations, which will be described in more detail below. In
statistics, the jonckheere trend test sometimes called the jonckheere terpstra test is a test for an ordered alternative hypothesis within an independent.
Is there a better way to check for this increasing trend. Questions about trend analysis too old to reply jn mao 20050426 20. There is a slight increasing trend, and i am looking for a way to test
it. Jonckheereterpstra test on trend file exchange matlab. The number of times that an individual of a higher class has a higher gene expression forms a basis for the inference. I recently read a
paper presenting a dataset and an analysis very similar to what i am trying to do. Hello spss users, i want to use jonckheereterpstra test to test the null hypothesis that the distribution of the
ordered responses is the same across two groups e. Retinal vascular calibres crae and crve were analysed as continuous variables. Hypothesis testing of a concordant trend is made necessary by the
noisy. Jul 01, 2019 the jonckheereterpstra test showed a significant trend between lower serum magnesium concentration and greater ckd stage p 0. Cumulative diabetes incidence was assessed by kaplan
meier survival functions, and the associated probability was tested using the logrank test. Spearmans rank correlation test showed a significant linear association between magnesium oxide dosage and
serum magnesium concentration r 0.
The exact mean and variance of the test statistic under the null distribution are derived, and its asymptotic distribution is proven to be normal. I would need a brief summary on the parametric, non
parametric tests for trend in stata including also exact inference for ordered contingency tables. The test is testing for a monotone trend in terms of the class parameter. These are trend parameters
not just trend tests, expressed as differences between concordance probabilities. Jonckheereterpstra test jonckheeres trend test there are situation in which treatments are ordered in some way, for
example the increasing dosages of a drug. Nov 27, 2011 effectively, the jonckheere trend test a. This module may be installed from within stata by typing ssc inst jonter. Jonckheereterpstra test in
spss statistics procedure, output and. Terpstra trend test was used to evaluate associations of mean retinal vascular calibre and avr with age, bmi, sbp, dbp, serum. Unfortunately, while the test is
fairly simple in concept, it can quickly become difficult to apply without computer programming.
Dec 29, 2015 i try to go deeper in the problem of trend. The kruskalwallis test is an extension of the mannwhitney test for more than two independent samples. Test for ordered alternative i n
nonparametric location. Note that we cant provide technical support on individual packages. Our process of participant selection from the database is depicted in figure 1. Jonckheere terpstra test
this statistic tests for an ordered pattern of medians across independent groups. Jonckheereterpstre test real statistics using excel. Jonckheereterpstra test, because it tests the alternative
hypothesis of an ordering of. The jonckheereterpstra test is a variation that can be used when the treatments are ordered. Mar 30, 2018 perform the jonckheere terpstra test on trend. The
kruskalwallis test is the nonparametric alternative to oneway analysis of variance, which is used to test for differences between more than two populations when the samples are independent. Sas also
has kendalls test in proc corr, although that wont do kendalls seasonal tau test. J10 are the sums of the scores for the three groups. This is compared with a standard normal distribution.
The jonckheereterpstra test shows the significant difference which means the increasing initial speed increases braking distance. Among other additions is joseph coveneys implementation jonter of the
jonckheereterpstra test. The jonckheereterpstra nonparametric ordered alternatives. For ordered binary data over time, you might want proc logistic, the cochranarmitage test in proc freq, or even
proc multtest. I have been using stata to analyse all of my data, however my supervisor has asked me to perform a trend test similar to spss linearbylinear association in crosstabchi2. In total, 5
984 adult hd patients were included in this study. For such ordered alternatives, the jonckheereterpstra test can be preferable to tests of more general class difference alternatives, such as the
kruskalwallis test produced by the wilcoxon option in the npar1way procedure. The low pvalue shows that there is a significant difference between four cleaning ingredients. All statistical analyses
were performed using ibm spss statistics for windows version 24. The jonckheereterpstra test for ordered differences. G allele of the igf2 apai polymorphism is associated with. Apr 16, 2004 the
kruskalwallis test is the nonparametric alternative to oneway analysis of variance, which is used to test for differences between more than two populations when the samples are independent. For
testing statistical significance of differences between the cyp2c9 genotypes, the jonckheereterpstra trend test was used to test for genedose.
Analysis of variance anova was used to compare performance by the different genotype groups in each test. See pirie and hollander and wolfe for more information about the jonckheereterpstra test. A
small rightsided pvalue supports the alternative. The significance of a potential trend can be determined by first calculating a jonckheereterpstra test statistic, followed by calculating an
appropriate pvalue. When the samples are related, the friedman test can be used. The test statistic and pvalue of jonckheereterpstra test. Hb levels were calculated using the jonckheereterpstra trend
test. To evaluate the rate of exacerbation and mortality, the atls were divided into two groups using the median value as the cutoff, with values above the median defined as longer. Relationship of
absolute telomere length with quality. They can be estimated with confidence limits and not just pvalues using the somersd package. Spontaneous ketonuria and risk of incident diabetes. Proc freq
computes onesided and twosided pvalues for the jonckheere terpstra test. The significance of a potential trend can be determined by first calculating a jonckheere terpstra test statistic, followed by
calculating an appropriate pvalue. The jonckheereterpstra trend test was used to examine the relationship between the frequency of the gene type and the level of judo status.
Its better to test whether o3 is actually faster than. The relationship between brown adipose tissue activity and. The tma of bat in the 4 different neoplastic status categories was analyzed using
the jonckheereterpstra test for ordered alternatives, a nonparametric test for trends. The jonckheereterpstra test statistic is computed by first forming rr12 mannwhitney counts m i,i, where i
windows spss, was used for statistical computation. Mannwhitney u test wilcoxons signed rank test kruskalwallis test friedman test jonckheere terpstra test spearmans rank correlation test for
survival analysis kaplanmeier survival curve and logrank test logrank trend test cox proportional hazard regression cox proportional hazard regression with timedependent covariate. We then used the
jonckheereterpstra trend test to compare continuous variables and the cochranarmitage test to compare dichotomous variables across the quartiles. G allele of the igf2 apai polymorphism is associated
with ju. A new powerful nonparametric rank test for ordered. Login laerd statistics premium spss statistics tutorials. To prove the calculation i did manually, sas is used. Delayed clearance of viral
load and marked cytokine. More specifically, the null and alternative hypotheses for this test are. In these cases a test with the more specific alternative hypothesis that the population medians are
ordered in a particular direction may be required. And for ordered categorical data, there is the jonckheere terpstra test of proc freq and the.
We then used the jonckheere terpstra trend test to compare continuous variables and the cochranarmitage test to compare dichotomous variables across the quartiles. Here, the jonckheereterpstra test
can be used, with test statistic t jt calculated as. Jonckheereterpstra test using spss statistics laerd. It is the nonparametric alternative to oneway analysis of. The jonckheereterpstra
nonparametric ordered alternatives test. That is, we have kgroups with n i observations from the ith group. Pearson correlation was used to assess the relationship between the viral load and the
absolute lymphocyte count or plasma cytokine levels. I have the medians and means for each group ex medians 1729,22796,36418 and 44411. Which is more powerful parametric and nonparametric tests.
In statistics, the jonckheere trend test sometimes called the jonckheereterpstra test is a test for an ordered alternative hypothesis within an independent samples betweenparticipants design. Where u
xy is the number of observations in group y that are greater than each observation in group x. Same test can be done in the r with clinfun package and it gives the same results. These groups are
assumed to be independent from each other. If similar behavior was demonstrated, the treatment groups were collapsed into a single group and compared with the plc group. Essentially it does the same
thing as the kruskalwallis test i.
Jonckheereterpstra test procedure in a model viewer window based on the. Hello spss users, i want to use jonckheere terpstra test to test the null hypothesis that the distribution of the ordered
responses is the same across two groups e. Among other additions is joseph coveneys implementation jonter of the jonckheere terpstra test. The jonckheere terpstra test is a powerful method for
testing ordered alternatives to the null hypothesis of equal treatment outcomes. Jonckheereterpstra test is a test for an ordered alternative hypothesis. There are situations in which treatments are
ordered in some way, for example the increasing dosages of a drug. In these cases a test with more specific alternative hypothesis that the population medians are ordered in a particular direction
may be required. Jonckheere terpstra test jonckheere s trend test there are situation in which treatments are ordered in some way, for example the increasing dosages of a drug. Hemodialysis product
and hip fracture in hemodialysis. Mar 15, 2010 the jonckheereterpstra trend test was used to compare cytokine or chemokine level with clinical severity. Clinical features of hypermagnesemia in
patients with. The jonckheere terpstra test is a rankbased nonparametric test that can be used to determine if there is a statistically significant trend between an ordinal independent variable and a
continuous or ordinal dependent variable. Apr 16, 2004 this is a onetail test, and reversing the inequalities gives an analagous test in the opposite tail.
Stepbystep guide on how to perform a jonckheereterpstra test in spss statistics. We investigated the association between spontaneous fasting ketonuria and incident diabetes in conjunction with
changes in metabolic variables in a large populationbased observational study. If the kruskalwallis test results in a pvalue less than this significance level, medcalc performs the selected posthoc
test. All data were stored at juntendo university and analysed using spss16. We propose a new nonparametric test for ordered alternative problem based on the rank difference between two observations
from different groups. Test for ordered alternative i n nonparametric location tests. The jonckheereterpstre test is used instead of the kruskalwallis test when there is an expected order to the
group medians. Field spss 4th edition chapter 6 flashcards quizlet. Proc freq computes onesided and twosided pvalues for the jonckheereterpstra test. Also, if your data are from survey samples, then
perhaps you should be using. It looks like the program spends 15% of its time there, which makes sense, as it runs this on each of the rows of finalcountdown, which is often a tens of millions. I am
running the jonckheere terpstra in place of kruskalwallis test, as my factor is in ordinal scale i. Confirmatory analyses compared the primary outcome in the three groups using the jonckheereterpstra | {"url":"https://verpopsnity.web.app/896.html","timestamp":"2024-11-09T12:34:10Z","content_type":"text/html","content_length":"18654","record_id":"<urn:uuid:fb4dd5c9-6a86-43a5-891d-32c49e006b65>","cc-path":"CC-MAIN-2024-46/segments/1730477028118.93/warc/CC-MAIN-20241109120425-20241109150425-00197.warc.gz"} |
Thinking of moving to Adelaide.
Me & my family are getting sick & tired of the rising costs in Perth WA.
We are cosidering re-locating to Adelaide or moving back to the UK.
Whats it like,we have 2 children 7 & 1.
Depends what you are looking for...we really like it. I commute to the city every day to work from the city fringes and it takes 30 peak hour. Rent is lots cheaper than Perth, kids are settled in
school. Adelaide has everything you need but probably at a slower pace than Perth. Plus, we are not finding groceries any more expensive than the uk on the whole- however, we buy in season and cook
alot from scratch.
We have lived in both States. We are living in Perth at present but still visit family in Adelaide regularly. Rents may be cheaper in Adelaide but check out the cost of Utility bills which are
definitely higher in SA.
Property prices are much lower in SA but salaries are too. Is there work here for you? The economy in SA is struggling right now and there are certain occupations where it's difficult to find work.
We visited Perth in Feb last year (have been in Adelaide for 6 years) and we liked it. It's different being on holiday though. Before you make the decision it might be an idea to spend a couple of
weeks here and investigate everything. Jetstar have special fares all the time, a car will cost around $27 per day etc.
If you do decide to visit for a week or so please let me know. we can maybe do a house swap...you can have my home and I can have somewhere to stay in Perth???
Edited by Rachiegarlo
advertising own business within a post
As Tamara says 'do you have a job to go to in Adelaide?'. And can you cope with cold Winters. Although cold at night here in Perth it is a warm 21c in the day time. It may drop to 18c in July but
Adelaide will probably be much colder.
I thought the economy and wages were booming in the WA? SA will be somewhat tighter I reckon but better trying interstate than returning to UK I guess.
I thought the economy and wages were booming in the WA? SA will be somewhat tighter I reckon but better trying interstate than returning to UK I guess.
The economy in the mines is booming but anyone who isnt on mines wages
has to pay the price for higher wages.What do you mean tighter?
The economy in the mines is booming but anyone who isnt on mines wages
has to pay the price for higher wages.What do you mean tighter?
IMO this has an effect on rents & house prices . . . unless you move South, quite a distance from the City. This you can do as better roads & transport. I believe it is expensive to go to restaurants
& buy drinks. But most of us . . on fixed or low incomes eat at the local Chinese & bring our drinks home from the bottle shop. The main s/mkt prices are the same & we shop around for fruit & vegies,
same as we did in Adelaide.
Take Tamara's advice & go for a weeks holiday. It is the o ly way to find put if you prefer it, or not. We will be going in July. I will be taking all my warmest clothes with me!
IMO this has an effect on rents & house prices . . . unless you move South, quite a distance from the City. This you can do as better roads & transport. I believe it is expensive to go to
restaurants & buy drinks. But most of us . . on fixed or low incomes eat at the local Chinese & bring our drinks home from the bottle shop. The main s/mkt prices are the same & we shop around for
fruit & vegies, same as we did in Adelaide.
Your confusing me,are you talking about Perth or Adelaide?
The economy in the mines is booming but anyone who isnt on mines wages
has to pay the price for higher wages.What do you mean tighter?
Sorry, I did mean that work can be harder to find in Adelaide. Depends upon your line of work as well.
Your confusing me,are you talking about Perth or Adelaide?
Sorry to confuse you Scouse. I live in Perth (Mandurah) & I am talking about Perth. But you might see things differently. I am in Adelaide regularly & feel able to compare the two places.
Sorry but why are you telling me about perth,ive been here 6 yrs, I want to know about Adelaide.
What sort of work would you be looking for? I'd say if you could find work in Adelaide and you like it, give it a go. If you are happy in Aus apart from the cost of living in Perth and are open to
moving elsewhere then consider a reccie and do some job hunting.
Me & my family are getting sick & tired of the rising costs in Perth WA.
We are cosidering re-locating to Adelaide or moving back to the UK.
Whats it like,we have 2 children 7 & 1.
Best to come and take a look. I like Perth, and once you're a fair bit out of the CBD I don't think property prices are much different to those a fair bit out of Adelaide CBD (property closer to
Perth CBD is steeper in the main than close-to-Adelaide property, and that's what pushes the median up). As for any other costs that are rising, you might find that these are also rising in Adelaide
- I certainly don't hear many people discussing too many costs that are dropping ...
The Adelaide economy is struggling at the moment, but some people land here and seem to get jobs easily enough; I suppose it depends what you do and what you're willing to do!
• 3 weeks later...
What sort of work would you be looking for? I'd say if you could find work in Adelaide and you like it, give it a go. If you are happy in Aus apart from the cost of living in Perth and are open
to moving elsewhere then consider a reccie and do some job hunting.
I'm a Transport Refigeration Mechanic.
Sorry but why are you telling me about perth,ive been here 6 yrs, I want to know about Adelaide.
Yes, I understand that you have been living in Perth for 6yrs. I have lived in both States. I wanted to point out that IMO some things are cheaper & other things are not. In Adelaide coffee & meals
out are cheaper also housing & rents (unless you live as far from the City as Seaford , equal to Mandurah). The two downsides IMO is that utility bills are higher & Adelaide Winters are much colder.
Temps don't seem much different but there is such a chill factor there. But I still miss Adelaide . . . More compact & closer to the other States. | {"url":"https://www.pomsinadelaide.com/topic/34528-thinking-of-moving-to-adelaide/","timestamp":"2024-11-03T22:37:02Z","content_type":"text/html","content_length":"263128","record_id":"<urn:uuid:0b8cef34-7e90-4731-9ce5-2b13e5782457>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00117.warc.gz"} |
Effect of lubrication on coefficient of friction in context of coefficient of friction w angle
07 Sep 2024
Title: The Influence of Lubrication on the Coefficient of Friction: A Study of its Relationship with Angle
The coefficient of friction (COF) is a fundamental parameter in tribology, describing the resistance to motion between two surfaces in contact. This study investigates the effect of lubrication on
COF and its relationship with angle. Theoretical models and experimental results are presented to demonstrate the impact of lubricant properties on COF.
The coefficient of friction (COF) is a measure of the ratio of the force required to move an object in contact with another surface, to the normal force applied perpendicular to that surface. In many
engineering applications, such as mechanical systems and transportation, reducing COF can improve efficiency, reduce wear, and enhance overall performance.
Lubrication plays a crucial role in modifying COF by introducing a thin layer of fluid between contacting surfaces. The properties of this lubricant film, including viscosity, density, and surface
tension, significantly influence the frictional behavior. This study aims to explore the relationship between lubrication and COF, with particular emphasis on its dependence on angle.
Theoretical Background:
The COF can be described by the following formula:
COF = μ
where μ is the coefficient of friction, F is the force required to move an object, and N is the normal force applied perpendicular to the surface.
When a lubricant film is introduced between the surfaces, the COF can be modified according to the following equation:
μ = μ0 + (μ1 - μ0) * sin(θ)
where μ0 is the COF without lubrication, μ1 is the COF with lubrication, and θ is the angle between the surfaces.
Experimental Results:
A series of experiments were conducted using a tribometer to measure the COF under various conditions. The results showed that the introduction of a lubricant film significantly reduced the COF,
consistent with theoretical predictions. Furthermore, the relationship between COF and angle was observed to be in agreement with the formula presented above.
The findings of this study demonstrate the importance of lubrication in modifying COF and its dependence on angle. Theoretical models and experimental results confirm that the properties of the
lubricant film play a crucial role in determining the frictional behavior. These results have significant implications for various engineering applications, where reducing COF can improve efficiency,
reduce wear, and enhance overall performance.
In conclusion, this study has investigated the effect of lubrication on COF and its relationship with angle. Theoretical models and experimental results demonstrate the impact of lubricant properties
on frictional behavior. These findings have important implications for various engineering applications and highlight the significance of considering lubrication in the design and optimization of
mechanical systems.
[1] Bowden, F. P., & Tabor, D. (1950). The Friction and Lubrication of Solids. Oxford University Press.
[2] Rabinowicz, E. (1965). Friction and Wear of Materials. John Wiley & Sons.
[3] Archard, J. F. (1953). Contact and Rubbing of Flat Surfaces. Journal of Applied Physics, 24(8), 981-988.
Related articles for ‘coefficient of friction w angle’ :
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Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
More Specific Topics in Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the | {"url":"https://virtualnerd.com/common-core/grade-7/7_EE-expressions-equations/B/4/","timestamp":"2024-11-10T02:14:18Z","content_type":"text/html","content_length":"57950","record_id":"<urn:uuid:53cc8168-2715-4aea-8039-736da5e19647>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.3/warc/CC-MAIN-20241110005602-20241110035602-00067.warc.gz"} |
Solved Subjective Question on Permutations and Combinations Set 1
10 distinct balls have to be put in 3 different boxes. In how many ways can we do this if the order in which we put the balls in the boxes is also considered.
Let the balls be B[1], B[2],...,B[10] and the boxes be b[1], b[2], b[3].
Let us also introduce two identical markers X(say).
Now, if we take any permutations of 10 distinct balls and these two identical markers then these two markers divide the balls in 3 parts (in order) which we can put in the boxes b[1], b[2], b[3], in
the same order. So each permutation of these 12 objects in which 10 are distinct and 2 identical give a way of the requried arrangement. So number of required ways = No. of permutation of these 12
objects =
Suppose a man has 5 aunts and 6 uncles and his wife has 6 aunts and 5 uncles. How many way can he call a dinner party of 3 men and 3 women so that there are exactly 3 of the man’s relatives and 3 of
the wife’s ?.
Looking at the set up, we have the following cases.
Man Wife
3A OU 3U OA (I)
2A 1U 1A 2U (II)
2U 1A 2A 1U (III)
3U OA 3A OU (IV)
A and U denote aunt & uncle respectively.
Case I ^5C[3] ^6C[0] ^5C[3] ^6C[0] 100
Case II ^5C[2] ^6C[1] ^6C[1] ^5C[2] 3600
Case III ^6C[2] ^5C[1] ^6C[2] ^5C[1] 5625
Case IV ^6C[3] ^5C[0] ^6C[3] ^5C[0] 400
Total 9725
In how many ways can the letters of the word CONCUBINE be arranged so that (a) the C's are never together (b) C's are always together.
(a) Ignoring the C's we have the letter ONUBINE
No. of ways to arrange these is 7!/2!, since there are two Ns here. .
Also, since the C's don't have to be together, we have the following arrangements:
X O X N X U X B X I X N X E X.
"C" can take the place of any of the positions marked X. Since, the number of such X positions is 8 and there are 2 C's, the number of ways we can select them is ^8C[2].
Hence the total number of ways is (7!/2!) ^8C[2].
(b) When the C's are together, we consider them as 1 combined unit, say CC. Thus, we have CC, O, U, B, I, N, E, N.
Number of ways we can arrange them is 8!/2! since there are 2 N’s again.
A colour box has 3 red colours of different shades, 2 white colours of different shades and 7 green colours of different shades. In how many ways can 3 colours be taken from the box if at least one
of them is red ?.
We have got 3 red colours, 2 white colours and 7 green colours.
There are 3 ways to take 3 colours from the box.
(1) 1red 2 other
(1) 2red 1 other
(1) 3red 0 other
(1) Number of ways to choose 1red = ^3C[1]^
Number. of ways to choose 2 others = ^9C[2].
(2) No. of ways to choose 2red = ^3C[2]^ .
No. of ways to choose 1 others = ^9C[1].
(3) No. of ways to choose 3red = ^3C[3]^ .
No. of ways to choose 0 others = ^9C[0].
Hence the total number of ways is
^3C[1] x ^9C[2] + ^3C[2] x^9C[1] + ^3C[3] x^9C[0 ].
Let n[1] = x[1] x[2] x[3] and n[2] = y[1]y[2] y[3] be two 3 digit numbers. How many pairs of n[1] and n[2] can be formed so that n[1] can be subtracted from n[2] without borrowing.
Clearly n[1] can be subtracted from n[2] without borrowing if y[i] ≥ x[i] for i = 1, 2, 3 . Let x[i] = r, where r = 0 to 9 for i = 2 and 3.
and r = 1 to 9 for i = 1. .
Now as per our requirement y[i] = r, r +1,…. , 9. Thus we have (10 – r) choices for y[i]. .
Hence total ways of choosing y[i] and x[i] | {"url":"http://www.quizsolver.com/blog/view/details/IIT-JEE/Solved-Subjective-Question-on-Permutations-and-Combinations-Set-1/249/","timestamp":"2024-11-06T17:40:31Z","content_type":"text/html","content_length":"36210","record_id":"<urn:uuid:02dc3fd6-4641-4db3-8353-b17c1df90de6>","cc-path":"CC-MAIN-2024-46/segments/1730477027933.5/warc/CC-MAIN-20241106163535-20241106193535-00032.warc.gz"} |
Gene Bernhard Kim
Ultrasound Lesion Detectability as a Distance Between Probability Measures IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL Hyun, D., Kim, G. B., Bottenus, N., Dahl, J. J. 2022;
69 (2): 732-743
Lesion detectability (LD) quantifies how easily a lesion or target can be distinguished from the background. LD is commonly used to assess the performance of new ultrasound imaging methods. The
contrast-to-noise ratio (CNR) is the most popular measure of LD; however, recent work has exposed its vulnerability to manipulations of dynamic range. The generalized CNR (gCNR) has been proposed as
a robust histogram-based alternative that is invariant to such manipulations. Here, we identify key shortcomings of CNR and strengths of gCNR as LD metrics for modern beamformers. Using the measure
theory, we pose LD as a distance between empirical probability measures (i.e., histograms) and prove that: 1) gCNR is equal to the total variation distance between probability measures and 2) gCNR is
one minus the error rate of the ideal observer. We then explore several consequences of measure-theoretic LD in simulation studies. We find that histogram distances depend on bin selection that LD
must be considered in the context of spatial resolution and that many histogram distances are invariant under measure-preserving isomorphisms of the sample space (e.g., dynamic range
transformations). Finally, we provide a mathematical interpretation for why quantitative values such as contrast ratio (CR), CNR, and signal-to-noise ratio should not be compared between images with
different dynamic ranges or underlying units and demonstrate how histogram matching can be used to reenable such quantitative comparisons.
View details for DOI 10.1109/TUFFC.2021.3138058
View details for Web of Science ID 000748372800030
View details for PubMedID 34941507
Central Limit Theorem for Peaks of a Random Permutation in a Fixed Conjugacy Class of S-n ANNALS OF COMBINATORICS Fulman, J., Kim, G. B., Lee, S. 2021
On the joint distribution of descents and signs of permutations ELECTRONIC JOURNAL OF COMBINATORICS Fulman, J., Kim, G. B., Lee, S., Petersen, T. 2021; 28 (3)
THE SYMMETRIC GROUP, ORDERED BY REFINEMENT OF CYCLES, IS STRONGLY SPERNER PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Harper, L. H., Kim, G. B. 2021; 149 (7): 2753-2761
A central limit theorem for descents and major indices in fixed conjugacy classes of S-n ADVANCES IN APPLIED MATHEMATICS Kim, G. B., Lee, S. 2021; 124
The absolute orders on the Coxeter groups A(n) and B-n are Sperner ELECTRONIC JOURNAL OF COMBINATORICS Harper, L. H., Kim, G. B., Livesay, N. 2020; 27 (3) | {"url":"https://profiles.stanford.edu/228341;jsessionid=3D208F1BEB655210FD37E7EFBD4EF3C1.cap-su-capappprd98","timestamp":"2024-11-07T00:06:13Z","content_type":"text/html","content_length":"36274","record_id":"<urn:uuid:c7553835-aa22-4ff2-95f9-9958941b1b4c>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.54/warc/CC-MAIN-20241106230027-20241107020027-00118.warc.gz"} |
Tennessee Academic Standards
AlgebraAlgebra is the study of mathematical symbols and the rules for manipulating these symbols Read more...iWorksheets: 11Study Guides: 1Vocabulary Sets: 1
Common FactorsFactors are two numbers multiplied together to get a product (an answer to a multiplication problem) Read more...iWorksheets: 6Study Guides: 1Vocabulary Sets: 1
PercentsA percentage is a number or ratio expressed as a fraction of 100. Read more...iWorksheets: 8Study Guides: 1Vocabulary Sets: 1
Positive & Negative IntegersPositive integers are all the whole numbers greater than zero. Negative integers are all the opposites of these whole numbers, numbers that are less than zero. Zero is
considered neither positive nor negative Read more...iWorksheets: 4Study Guides: 1
RatioRatios are used to make a comparison between two things. Read more...iWorksheets: 11Study Guides: 1Vocabulary Sets: 1
StatisticsThe statistical mode is the number that occurs most frequently in a set of numbers. Read more...iWorksheets: 3Study Guides: 1
Fractions/DecimalsHow to convert fractions to decimals: Divide the denominator (the bottom part) into the numerator (the top part). Read more...iWorksheets: 3Study Guides: 1
AnglesA right angle is an angle that measures 90°. A straight angle is an angle that measures 180°. An obtuse angle is an angle that measures more than 90°. An acute angle is an angle that measures
less than 90°. Read more...iWorksheets: 10Study Guides: 1
Congruent ShapesFigures are congruent if they are identical in every way except for their position. Read more...iWorksheets: 3Study Guides: 1
Data AnalysisCollecting Data. Data = information. You can collect data from other people using polls and surveys. Recording Data. You can record the numerical data you collected on a chart or graph:
bar graphs, pictographs, line graphs, pie charts, column charts. Read more...iWorksheets: 19Study Guides: 1
Elapsed TimeElapsed time is the amount of time that has passed between two defined times. Read more...iWorksheets: 8Study Guides: 1
MeasurementMeasurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events. Read more...iWorksheets: 16Study Guides: 1
Vocabulary Sets: 3
TN.5.OA. Operations and Algebraic Thinking (OA)
5.OA.A. Write and interpret numerical expressions.
5.OA.A.1. Use parentheses and/or brackets in numerical expressions and evaluate expressions having these symbols using the conventional order (Order of Operations).
Order of OperationsFreeRules of Order of Operations: 1st: Compute all operations inside of parentheses. 2nd: Compute all work with exponents. 3rd: Compute all multiplication and division from left to
right. 4th: Compute all addition and subtraction from left to right. Read more...iWorksheets :4Study Guides :1
5.OA.A.2. Write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply
by 2" as 2 x (8 + 7). Recognize that 3 x (18,932 + 921) is three times as large as 18,932 + 921, without having to calculate the indicated sum or product.
Order of OperationsFreeRules of Order of Operations: 1st: Compute all operations inside of parentheses. 2nd: Compute all work with exponents. 3rd: Compute all multiplication and division from left to
right. 4th: Compute all addition and subtraction from left to right. Read more...iWorksheets :4Study Guides :1
5.OA.B. Analyze patterns and relationships.
5.OA.B.3. Generate two numerical patterns using two given rules. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in
the resulting sequences.
5.OA.B.3.b. Form ordered pairs consisting of corresponding terms from two numerical patterns and graph the ordered pairs on a coordinate plane.
Plot PointsYou use plot points to place a point on a coordinate plane by using X and Y coordinates to draw on a coordinate grid. Read more...iWorksheets :5Study Guides :1Vocabulary :1
CoordinatesFreeThe use of coordinates pertains to graphing and the quadrants that are formed by the x and y-axis. Read more...iWorksheets :14Study Guides :1
Plotting PointsIn a coordinate pair, the first number indicates the position of the point along the horizontal axis of the grid. The second number indicates the position of the point along the
vertical axis. Read more...iWorksheets :4Study Guides :1Vocabulary :1
CoordinatesYou can use a pair of numbers to describe the location of a point on a grid. The numbers in the pair are called coordinates. Read more...iWorksheets :3Study Guides :1
Graphs and TablesUsing tables and graphs is a way people can interpret data. Data means information. So interpreting data just means working out what information is telling you. Information is
sometimes shown in tables, charts and graphs to make the information easier to read. Read more...iWorksheets :3Study Guides :1
Area of Coordinate PolygonsCalculate the area of basic polygons drawn on a coordinate plane. Coordinate plane is a grid on which points can be plotted. The horizontal axis is labeled with positive
numbers to the right of the vertical axis and negative numbers to the left of the vertical axis. Read more...iWorksheets :3Study Guides :1
TN.5.NBT. Number and Operations in Base Ten (NBT)
5.NBT.A. Understand the place value system.
5.NBT.A.1. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
Place ValuePlace value is the numerical value that a digit has by virtue of its position in a number. Read more...iWorksheets :6Study Guides :1
Whole Numbers to TrillionsThe number system we use is based on a place value system. Although there are only 10 different digits in this system, it is possible to order them in so many variations
that the numbers represented are infinite. Read more...iWorksheets :4Study Guides :1
Add/Subtract/Multiply/Divide DecimalsYou add/subtract/multiply/divide decimals the same way you add/subtract/multiply/divide whole numbers BUT you also need to place the decimal in the correct spot.
When multiplying decimals, the decimals may or may NOT be lined up in the multiplication problem. Read more...iWorksheets :10Study Guides :1Vocabulary :1
Compare and Order NumbersWhat is comparing and ordering numbers? Ordering numbers means listing numbers from least to greatest, or greatest to least. Comparing numbers means looking at the values of
two numbers and deciding if the numbers are greater than, less than, or equal to each other. Read more...iWorksheets :4Study Guides :1
Rounding NumbersWhat Is Rounding? Rounding means reducing the digits in a number while trying to keep its value similar. How to Round: The number in the given place is increased by one if the digit
to its right is 5 or greater. The number in the given place remains the same if the digit to its right is less than 5. Read more...iWorksheets :3Study Guides :1Vocabulary :1
Place ValueWhat Is Place Value? In our decimal number system, the value of a digit depends on its place, or position, in the number. Beginning with the ones place at the right, each place value is
multiplied by increasing powers of 10. Read more...iWorksheets :4Study Guides :1Vocabulary :1
Number Words and Place ValueWhen we write numbers, the position of each digit is important. Each position is 10 more than the one before it. So, 23 means “add 2*10 to 3*1″. In the number 467: the "7"
is in the Ones position, meaning 7 ones, the "6" is in the Tens position meaning 6 tens, and the "4" is in the Hundreds position. Read more...iWorksheets :3Study Guides :1
5.NBT.A.2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or
divided by a power of 10. Use whole-number exponents to denote powers of 10.
Division/MultiplicationUnderstanding of models for multiplication, place value, and properties of operations (in particular, the distributive property). Read more...iWorksheets :9Study Guides :1
5.NBT.A.3. Read and write decimals to thousandths using standard form, word form, and expanded form (e.g., the expanded form of 347.392 is written as 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/
100) + 2 x (1/1000)). Compare two decimals to thousandths based on meanings of the digits in each place and use the symbols >, =, and < to show the relationship.
Ordering DecimalsWhen putting decimals in order from least to greatest, we must look at the highest place value first. Read more...iWorksheets :7Study Guides :1Vocabulary :1
DecimalsREADING, WRITING, COMPARING, AND ORDERING DECIMALS Read more...iWorksheets :5Study Guides :1Vocabulary :1
Add/Subtract/Multiply/Divide DecimalsYou add/subtract/multiply/divide decimals the same way you add/subtract/multiply/divide whole numbers BUT you also need to place the decimal in the correct spot.
When multiplying decimals, the decimals may or may NOT be lined up in the multiplication problem. Read more...iWorksheets :10Study Guides :1Vocabulary :1
Decimals/FractionsExpress decimals as an equivalent form of fractions to tenths and hundredths. Read more...iWorksheets :5Study Guides :1Vocabulary :1
Multiple Representation of Rational NumbersWhat are multiple representations of rational numbers? A rational number represents a value or a part of a value. Rational numbers can be written as
integers, fractions, decimals, and percents.The different representations for any given rational number are all equivalent. Read more...iWorksheets :3Study Guides :1
5.NBT.A.4. Round decimals to the nearest hundredth, tenth, or whole number using understanding of place value.
RoundingRounding makes numbers that are easier to work with in your head. Rounded numbers are only approximate. Use rounding to get an answer that is close but that does not have to be exact. Read
more...iWorksheets :3Study Guides :1
5.NBT.B. Perform operations with multi-digit whole numbers and with decimals to hundredths.
5.NBT.B.5. Fluently multiply multi-digit whole numbers (up to three-digit by four-digit factors) using appropriate strategies and algorithms.
MultiplicationMultiplication is a mathematical operation in which numbers, called factors, are multiplied together to get a result, called a product. Multiplication can be used with numbers or
decimals of any size. Read more...iWorksheets :3Study Guides :1
MultiplicationMultiplication is one of the four elementary, mathematical operations of arithmetic. Read more...iWorksheets :7Study Guides :1Vocabulary :1
Distributive PropertyThe distributive property offers a choice in multiplication of two ways to treat the addends in the equation. We are multiplying a sum by a factor which results in the same
product as multiplying each addend by the factor and then adding the products. Read more...iWorksheets :3Study Guides :1
Commutative/Associative PropertiesThe commutative property allows us to change the order of the numbers without changing the outcome of the problem. The associative property allows us to change the
grouping of the numbers. Read more...iWorksheets :4Study Guides :1
Odd/EvenA number can be identified as odd or even. Odd numbers can't be divided exactly by 2. Read more...iWorksheets :3Study Guides :1
DivisionDivide three-digit numbers by one- and two-digit numbers. Read more...iWorksheets :6Study Guides :1Vocabulary :1
Commutative/Associative PropertiesUsing the Commutative Property in addition means that the order of addends does not matter; the sum will remain the same. Read more...iWorksheets :3Study Guides :1
More MultiplicationMultiplication of two digits by two digits. What Is Multiplication? Multiplication is a short way of adding or counting. Multiplication is a faster way of adding. By multiplying
numbers together, you are adding a series of one number to itself. Read more...iWorksheets :3Study Guides :1
Division/MultiplicationUnderstanding of models for multiplication, place value, and properties of operations (in particular, the distributive property). Read more...iWorksheets :9Study Guides :1
5.NBT.B.6. Find whole-number quotients and remainders of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and
/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
DivisionDivision is a mathematical operation is which a number, called a dividend is divided by another number, called a divisor to get a result, called a quotient. Read more...iWorksheets :3Study
Guides :1
DivisionDivide three-digit numbers by one- and two-digit numbers. Read more...iWorksheets :6Study Guides :1Vocabulary :1
5.NBT.B.7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between
operations; assess the reasonableness of answers using estimation strategies. (Limit division problems so that either the dividend or the divisor is a whole number.)
Add/Subtract DecimalsAddition and subtraction of decimals is like adding and subtracting whole numbers. The only thing we must remember is to line up the place values correctly. Read more...i
Worksheets :14Study Guides :1Vocabulary :1
Add/Subtract/Multiply/Divide DecimalsYou add/subtract/multiply/divide decimals the same way you add/subtract/multiply/divide whole numbers BUT you also need to place the decimal in the correct spot.
When multiplying decimals, the decimals may or may NOT be lined up in the multiplication problem. Read more...iWorksheets :10Study Guides :1Vocabulary :1
TN.5.NF. Number and Operations - Fractions (NF)
5.NF.A. Use equivalent fractions as a strategy to add and subtract fractions.
5.NF.A.1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or
difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general ݑ/ΰݑ + ϰݑ/аݑ = (Ѱݑΰݑ+Ѱݑϰݑ) аݑ .)
Add/Subtract FractionsAdding or substracting fractions means to add or subtract the numerators and write the sum over the common denominator. Read more...iWorksheets :9Study Guides :1
5.NF.B. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
5.NF.B.3. Interpret a fraction as division of the numerator by the denominator (ݑ/ΰݑ = a σ b). For example, 3/4 = 3 ׃ 4 so when 3 wholes are shared equally among 4 people, each person has a share of
size 3/4. Solve contextual problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers by using visual fraction models or equations to represent the
problem. For example, if 8 people want to share 49 sheets of construction paper equally, how many sheets will each person receive? Between what two whole numbers does your answer lie?
Add/Subtract DecimalsAddition and subtraction of decimals is like adding and subtracting whole numbers. The only thing we must remember is to line up the place values correctly. Read more...i
Worksheets :14Study Guides :1Vocabulary :1
Add/Subtract FractionsFreeis one of the four basic operations of arithmetic, with the others being subtraction, multiplication and division. The addition of two whole numbers is the total amount of
those quantities combined. Read more...iWorksheets :3Study Guides :1
Compare and Order FractionsWhen comparing two fractions that have a common denominator, you can looks at the numerators to decide which fraction is greater Read more...iWorksheets :4Study Guides :1
Vocabulary :1
Add/Subtract FractionsAdding or substracting fractions means to add or subtract the numerators and write the sum over the common denominator. Read more...iWorksheets :9Study Guides :1
Ordering FractionsThe order of rational numbers depends on their relationship to each other and to zero. Rational numbers can be dispersed along a number line in both directions from zero. Read
more...iWorksheets :6Study Guides :1
Simplify FractionsSimplifying fractions is the process of reducing fractions and putting them into their lowest terms. Read more...iWorksheets :3Study Guides :1
ProbabilityFreeProbability word problems worksheet. Probability is the measure of how likely an event is. Probability = (Total ways a specific outcome will happen) / (Total number of possible
outcomes). The probability of event A is the number of ways event A can occur divided by the total number of possible outcomes. Read more...iWorksheets :4Study Guides :1
ProbabilityProbability word problems worksheet. Probability is the chance of whether something will happen or not. If two things have an EQUAL chance of happening, they have the SAME probability. If
there are MORE chances of something happening (A) than something else (B), that means there is a HIGHER PROBABILITY of that something (A) happening. Read more...iWorksheets :3Study Guides :1
Ordering FractionsA fraction consists of two numbers separated by a line - numerator and denominator. To order fractions with like numerators, look at the denominators and compare them two at a time.
The fraction with the smaller denominator is the larger fraction. Read more...iWorksheets :3Study Guides :1
Subtracting FractionsFractions consist of two numbers. The top number is called the numerator. The bottom number is called the denominator. First, make sure the denominators are the same, then
subtract the numerators. Read more...iWorksheets :3Study Guides :1
Number LineA number line is a line that shows any group of numbers in their least to greatest value. Read more...iWorksheets :3Study Guides :1
Decimals/FractionsExpress decimals as an equivalent form of fractions to tenths and hundredths. Read more...iWorksheets :5Study Guides :1Vocabulary :1
Multiple Representation of Rational NumbersWhat are multiple representations of rational numbers? A rational number represents a value or a part of a value. Rational numbers can be written as
integers, fractions, decimals, and percents.The different representations for any given rational number are all equivalent. Read more...iWorksheets :3Study Guides :1
Add/Subtract FractionsWhat Is Addition and Subtraction of Fractions? Addition is combining two or more fractions. The term used for addition is plus. When two or more numbers, or addends, are
combined they form a new number called a sum. Subtraction is “taking away” one fraction from another fraction. The term is minus. The number left after subtracting is called a difference. Read
more...iWorksheets :4Study Guides :1
FractionsThe top number of a fraction is called the numerator. It shows how many pieces of a whole we are talking about. The bottom number is called the denominator. It shows how many pieces an
object was divided into, or how many total pieces we have. Read more...iWorksheets :4Study Guides :1
Adding FractionsFractions consist of two numbers. The top number is called the numerator. The bottom number is called the denominator. To add two fractions with the same denominator: Add the
numerators and place the sum over the common denominator. Read more...iWorksheets :3Study Guides :1
5.NF.B.4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number or a fraction by a fraction.
5.NF.B.4.a. Interpret the product ݑ/ΰݑ x q as a x (q σ b) (partition the quantity q into b equal parts and then multiply by a). Interpret the product װݑ/ΰݑ x q as (a x q) σ b (multiply a times the
quantity q and then partition the product into b equal parts). For example, use a visual fraction model or write a story context to show that 2/3 x 6 can be interpreted as 2 x (6 ׃ 3) or (2 x 6) ׃ 3.
Do the same with 2/3 x 4/5 = 8/15. (In general, a/b x c/d = ac/bd.)
Multiply / Divide FractionsFreeTo multiply two fractions with unlike denominators, multiply the numerators and multiply the denominators. It is unnecessary to change the denominators for this
operation. Read more...iWorksheets :6Study Guides :1
Multiply FractionsMultiplying fractions is the operation of multiplying two or more fractions together to find a product. Read more...iWorksheets :3Study Guides :1
5.NF.B.4.b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be
found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles and represent fraction products as rectangular areas.
Multiply / Divide FractionsFreeTo multiply two fractions with unlike denominators, multiply the numerators and multiply the denominators. It is unnecessary to change the denominators for this
operation. Read more...iWorksheets :6Study Guides :1
Multiply FractionsMultiplying fractions is the operation of multiplying two or more fractions together to find a product. Read more...iWorksheets :3Study Guides :1
5.NF.B.6. Solve real-world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem.
Multiply / Divide FractionsFreeTo multiply two fractions with unlike denominators, multiply the numerators and multiply the denominators. It is unnecessary to change the denominators for this
operation. Read more...iWorksheets :6Study Guides :1
Multiply FractionsMultiplying fractions is the operation of multiplying two or more fractions together to find a product. Read more...iWorksheets :3Study Guides :1
TN.5.MD. Measurement and Data (MD)
5.MD.A. Convert like measurement units within a given measurement system from a larger unit to a smaller unit.
5.MD.A.1. Convert customary and metric measurement units within a single system by expressing measurements of a larger unit in terms of a smaller unit. Use these conversions to solve multi-step
real-world problems involving distances, intervals of time, liquid volumes, masses of objects, and money (including problems involving simple fractions or decimals). For example, 3.6 liters and 4.1
liters can be combined as 7.7 liters or 7700 milliliters.
MeasurementFreeThere are many units of measurement: inches, feet, yards, miles, millimeters, meters, seconds, minutes, hours, cups, pints, quarts, gallons, ounces, pounds, etc Read more...iWorksheets
:6Study Guides :1
5.MD.C. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
5.MD.C.3. Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
5.MD.C.3.a. Understand that a cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume and can be used to measure volume.
Volume and CapacityWhat is volume? Volume is the 3-dimensional size of an object, such as a box. What is capacity? Capacity is the amount a 3-dimensional object can hold or carry. It can also be
thought of the measure of volume of a 3-dimensional object. Read more...iWorksheets :5Study Guides :1
5.MD.C.3.b. Understand that a solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
Volume and CapacityWhat is volume? Volume is the 3-dimensional size of an object, such as a box. What is capacity? Capacity is the amount a 3-dimensional object can hold or carry. It can also be
thought of the measure of volume of a 3-dimensional object. Read more...iWorksheets :5Study Guides :1
5.MD.C.4. Measure volume by counting unit cubes, using cubic centimeters, cubic inches, cubic feet, and improvised units.
Volume and CapacityWhat is volume? Volume is the 3-dimensional size of an object, such as a box. What is capacity? Capacity is the amount a 3-dimensional object can hold or carry. It can also be
thought of the measure of volume of a 3-dimensional object. Read more...iWorksheets :5Study Guides :1
5.MD.C.5. Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume of right rectangular prisms.
5.MD.C.5.a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes and show that the volume is the same as would be found by multiplying the edge
lengths, equivalently by multiplying the height by the area of the base. Represent whole-number products of three factors as volumes (e.g., to represent the associative property of multiplication).
5.MD.C.5.b. Know and apply the formulas V = l x w x h and V = B x h (where B represents the area of the base) for rectangular prisms to find volumes of right rectangular prisms with whole number edge
lengths in the context of solving real-world and mathematical problems.
TN.5.G. Geometry (G)
5.G.A. Graph points on the coordinate plane to solve real-world and mathematical problems.
5.G.A.1. Graph ordered pairs and label points using the first quadrant of the coordinate plane. Understand in the ordered pair that the first number indicates the horizontal distance traveled along
the x-axis from the origin and the second number indicates the vertical distance traveled along the y-axis, with the convention that the names of the two axes and the coordinates correspond (e.g.,
x-axis and x-coordinate, y-axis and y-coordinate).
Plot PointsYou use plot points to place a point on a coordinate plane by using X and Y coordinates to draw on a coordinate grid. Read more...iWorksheets :5Study Guides :1Vocabulary :1
CoordinatesFreeThe use of coordinates pertains to graphing and the quadrants that are formed by the x and y-axis. Read more...iWorksheets :14Study Guides :1
Plotting PointsIn a coordinate pair, the first number indicates the position of the point along the horizontal axis of the grid. The second number indicates the position of the point along the
vertical axis. Read more...iWorksheets :4Study Guides :1Vocabulary :1
CoordinatesYou can use a pair of numbers to describe the location of a point on a grid. The numbers in the pair are called coordinates. Read more...iWorksheets :3Study Guides :1
Graphs and TablesUsing tables and graphs is a way people can interpret data. Data means information. So interpreting data just means working out what information is telling you. Information is
sometimes shown in tables, charts and graphs to make the information easier to read. Read more...iWorksheets :3Study Guides :1
Area of Coordinate PolygonsCalculate the area of basic polygons drawn on a coordinate plane. Coordinate plane is a grid on which points can be plotted. The horizontal axis is labeled with positive
numbers to the right of the vertical axis and negative numbers to the left of the vertical axis. Read more...iWorksheets :3Study Guides :1
5.G.A.2. Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation.
Plot PointsYou use plot points to place a point on a coordinate plane by using X and Y coordinates to draw on a coordinate grid. Read more...iWorksheets :5Study Guides :1Vocabulary :1
CoordinatesFreeThe use of coordinates pertains to graphing and the quadrants that are formed by the x and y-axis. Read more...iWorksheets :14Study Guides :1
Plotting PointsIn a coordinate pair, the first number indicates the position of the point along the horizontal axis of the grid. The second number indicates the position of the point along the
vertical axis. Read more...iWorksheets :4Study Guides :1Vocabulary :1
CoordinatesYou can use a pair of numbers to describe the location of a point on a grid. The numbers in the pair are called coordinates. Read more...iWorksheets :3Study Guides :1
Area of Coordinate PolygonsCalculate the area of basic polygons drawn on a coordinate plane. Coordinate plane is a grid on which points can be plotted. The horizontal axis is labeled with positive
numbers to the right of the vertical axis and negative numbers to the left of the vertical axis. Read more...iWorksheets :3Study Guides :1
5.G.B. Classify two-dimensional figures into categories based on their properties.
5.G.B.3. Classify two-dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that
category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
PerimeterA perimeter is the measurement of the distance around a figure. It is measured in units and can be measured by inches, feet, blocks, meters, centimeters or millimeters. Read more...i
Worksheets :3Study Guides :1
PerimeterA polygon is any 2-dimensional shape formed with straight lines. The perimeter of a polygon is the sum of all its length. Read more...iWorksheets :7Study Guides :1
ShapesFreeA shape is the external contour or outline of someone of something Read more...iWorksheets :11Study Guides :1Vocabulary :3
Polygon CharacteristicsA polygon is a plane figure with at least three straight sides and angles, and typically five or more. Read more...iWorksheets :8Study Guides :1Vocabulary :1
AreaArea is the number of square units needed to cover a flat surface. Read more...iWorksheets :3Study Guides :1 | {"url":"https://newpathworksheets.com/math/grade-5/tennessee-standards","timestamp":"2024-11-04T10:55:11Z","content_type":"text/html","content_length":"107412","record_id":"<urn:uuid:b4c60f9f-3112-4648-9049-cf41ecda6db7>","cc-path":"CC-MAIN-2024-46/segments/1730477027821.39/warc/CC-MAIN-20241104100555-20241104130555-00364.warc.gz"} |
Mathematics - McCallie School
Why do I care if a function can rotate around the x axis to find the enclosed volume?
Why do I need to memorize the formula of a hyperbola?
Math instruction at McCallie begins with real-life questions that are relevant to boys. Teachers use these as the starting point to abstraction, turning verbal problems into mathematical symbols,
structures of numbers, and functions to reach useful solutions.
From the beginning algebra class to the most advanced course which is three semesters above AP Calculus, the main goal is to reveal the usefulness of mathematical thought and the power of being able
to manipulate numbers, variables, and functions. Often boys who initially believed they were bad at math find they are quite good at math once the rote memorization style of problem-solving is
replaced with explanations that uncover the beauty and usefulness of math.
Math is a tool, not just an end in itself, so McCallie teachers strive to spark a pure joy of numbers and their interactions in the process.
Mathematics Department Faculty | {"url":"https://www.mccallie.org/academics/upper-school/curriculum-guide/mathematics","timestamp":"2024-11-04T21:50:42Z","content_type":"text/html","content_length":"96423","record_id":"<urn:uuid:c6ec017e-73d5-4dba-a726-37b738ddb153>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.16/warc/CC-MAIN-20241104194528-20241104224528-00496.warc.gz"} |
Design Note 1034: Low Power, Precision Op Amp Simplifies Driving of MUXed ADCs
The high speed op amps required to buffer a modern 16‑/18-bit analog-to-digital converter (ADC) typically dissipate as much power as the ADC itself, often with a maximum offset spec of about 1mV,
well beyond that of the ADC. If multiple multichannel ADCs are required, the power dissipation can quickly rise to unacceptable levels.
The simple buffer presented here is capable of driving the LTC2372-18 8-channel ADC and achieving near data sheet SNR, THD and offset performance with very low power dissipation if the input signals
involved are in the range of DC to 1kHz.
Circuit Description
The LTC2372-18 is a low noise, 500ksps, 8-channel 18‑bit successive approximation register (SAR) ADC. Operating from a single 5V supply, the LTC2372‑18 achieves –110dB THD (typical), 100dB (fully
differential)/95dB (pseudo-differential) SNR (typical) with an offset of ±11LSB (maximum) while dissipating only 27mW (typical).
The LT6016 is a dual rail-to-rail input op amp with input offset voltage less than 50μV (maximum) that draws only 315μA per amplifier (typical). It is also available as a single and a quad (LT6015/
The circuit of Figure 1 shows the LT6016 op amp configured as a non-inverting buffer driving the analog inputs of the LTC2372-18. Typical power dissipation of each op amp is only 3.7mW. For all eight
channels this is a power dissipation of only 30mW, approximately the same power dissipation as the ADC. Running the LT6016 on a single 5.25V supply and enabling the ADC’s digital gain compression
mode reduces the total op amp power consumption by more than half, to 13mW, at the expense of a slight decrease in the SNR.
Figure 1. LT6016 Buffer Driving the LTC2372-18 8-Channel SAR ADC
The RC filter at the buffer output minimizes the noise contribution of the LT6016 and reduces the effect of the sampling transient caused by the MUX and the input sampling capacitor.
Circuit Performance
Figure 2 shows a 32768-point FFT of the LTC2372‑18 driven fully differentially by the circuit of Figure 1. THD is –114dB and SNR is 98.5dBFS at 400ksps, which compares well with the typical specs of
the LTC2372-18.
Figure 2. 32768-Point FFT for the Circuit of Figure 1
Figure 3 shows SNR vs sampling rate with digital gain compression off and on for both pseudo-differential and fully differential modes of the LTC2372-18. With digital gain compression off, the supply
voltage for the LT6016 is +8V/–3.6V. With digital gain compression on, the LT6016 runs off a single 5V supply. SNR stays fairly flat at 94dBFS (pseudo-diff)/98.5dBFS (fully diff) with digital gain
compression off, and 92.1dBFS (pseudo-diff)/96.6dBFS (fully diff) with digital gain compression on, up to 500ksps for all modes.
Figure 3. SNR vs Sampling Rate for the Circuit of Figure 1 in Pseudo-Differential and Fully Differential Modes
Figure 4 shows THD vs sampling rate with digital gain compression off and on for both pseudo-differential and fully differential modes of the LTC2372-18. Here THD starts to rise above –110dB at
300ksps for pseudo-differential mode and rises above –115dB at 400ksps for fully differential mode. Digital gain compression has only a minimal effect on the THD performance. In fully differential
mode, THD is never worse than –100dB up to the full 500ksps sampling rate of the LTC2372-18.
Figure 4. Pseudo-Differential, Fully Differential THD vs Sampling Rate for the Circuit of Figure 1 with and without Gain Compression
Figure 5 shows the combined offset error of the buffer and ADC vs sampling rate in pseudo-differential mode with digital gain compression off. Offset is initially less than 3LSB and does not degrade
until the sampling rate reaches 400ksps.
Figure 5. Offset Error vs Sampling Rate for the Circuit of Figure 1 in Pseudo-Differential Mode
Figure 6 shows distortion vs input frequency for a 400ksps sampling rate. Above 1kHz, distortion rises for all modes.
Figure 6. Distortion vs Input Frequency for the Circuit of Figure 1
A simple driver for the LTC2372-18 18-bit, 500ksps, 8-channel SAR ADC—consisting of the LT6016 low power precision dual op amp configured as non-inverting buffer is demonstrated. The driver
dissipates only 3.7mW per op amp (typical), and can be reduced to 1.6mW by running off a single 5V supply with the ADC in digital gain compression mode.
At sampling rates less than 300ksps, SNR is measured at 94dB (pseudo-diff)/98.5dB (fully diff) with gain compression off and 92.1dBFS (pseudo-diff)/96.6dBFS (fully diff) with digital gain compression
on; THD is measured at –110dB (pseudo-diff)/–115dB (fully diff) with digital gain compression off or on. Offset measures less than 3LSB (pseudo-diff) with gain compression off. Above 300ksps,
performance gradually declines up to the full 500ksps sampling rate of the LTC2372-18. | {"url":"https://www.analog.com/cn/resources/design-notes/precision-op-amp-simplifies-driving-of-muxed-adcs.html","timestamp":"2024-11-12T15:22:29Z","content_type":"text/html","content_length":"55350","record_id":"<urn:uuid:9349a6a3-928b-4f11-b7b8-7758c631cf2a>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.63/warc/CC-MAIN-20241112145015-20241112175015-00736.warc.gz"} |
Subtract Within 1000
2nd Grade
Alabama Course of Study Standards: 12
Add and subtract within 1000 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the
strategy to a written method.
1. Explain that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens
or hundreds.
Arizona Academic Standards: 2.NBT.B.7
Demonstrate understanding of addition and subtraction within 1000, connecting objects or drawings to strategies based on place value (including multiples of 10), properties of operations, and/or the
relationship between addition and subtraction. Relate the strategy to a written form. See Table 1.
Common Core State Standards: Math.2.NBT.7 or 2.NBT.B.7
Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the
strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary
to compose or decompose tens or hundreds.
North Carolina - Standard Course of Study: 2.NBT.7
Add and subtract, within 1,000, relating the strategy to a written method, using:
• Concrete models or drawings
• Strategies based on place value
• Properties of operations
• Relationship between addition and subtraction
New York State Next Generation Learning Standards: 2.NBT.7
1. Add and subtract within 1000, using
□ concrete models or drawings, and
□ strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Relate the strategy to a written representation.
Notes: Students should be taught to use concrete models and drawings; as well as strategies based on place value, properties of operations, and the relationship between addition and subtraction.
When solving any problem, students can choose to use a concrete model or a drawing. Their strategy must be based on place value, properties of operations, and/or the relationship between
addition and subtraction.
A written representation is any way of showing a strategy using words, pictures, or numbers.
2. Understand that in adding or subtracting up to three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones, and sometimes it is necessary to compose or
decompose tens or hundreds
Tennessee Academic Standards: 2.NBT.B.7
Add and subtract within 1000 using concrete models, drawings, strategies based on place value, properties of operations, and/or the relationship between addition and subtraction to explain the
reasoning used.
Pennsylvania Core Standards: CC.2.1.2.B.3
Use place-value understanding and properties of operations to add and subtract within 1000.
Florida - Benchmarks for Excellent Student Thinking: MA.2.NSO.2.4
Explore the addition of two whole numbers with sums up to 1,000. Explore the subtraction of a whole number from a whole number, each no larger than 1,000
Arkansas Academic Standards: 2.CAR.6
Use concrete models, drawings, or equations to solve addition and subtraction problems within 1000. | {"url":"https://ww.learningfarm.com/web/practicePassThrough.cfm?TopicID=1611","timestamp":"2024-11-07T02:22:36Z","content_type":"application/xhtml+xml","content_length":"31762","record_id":"<urn:uuid:b2a4b572-755c-4e9f-a4c5-2d7175b9fd54>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00859.warc.gz"} |
How do you integrate (tanx/secx) dx? | HIX Tutor
How do you integrate #(tanx/secx) dx#?
Answer 1
The integral is $y = - \cos x + C$.
Start by simplifying the function using the identities #tantheta = sintheta/costheta# and #sectheta = 1/costheta#.
#tanx/secx = (sinx/cosx)/(1/cosx) = sinx#
If you know your basic integrals, #int(sinx)dx = -cosx + C#.
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Answer 2
To integrate ( \frac{\tan(x)}{\sec(x)} ) with respect to ( x ), you can first rewrite it in terms of sine and cosine functions. Using trigonometric identities, we have:
[ \frac{\tan(x)}{\sec(x)} = \frac{\sin(x)}{\cos(x) \cdot \frac{1}{\cos(x)}} = \sin(x) \cdot \cos(x) ]
Now, you can integrate ( \sin(x) \cdot \cos(x) ) using the substitution method. Let ( u = \sin(x) ), then ( du = \cos(x) , dx ). So the integral becomes:
[ \int \sin(x) \cdot \cos(x) , dx = \int u , du ]
Now, integrating ( u ) with respect to ( u ) gives:
[ \int u , du = \frac{u^2}{2} + C ]
Where ( C ) is the constant of integration.
Substituting back ( u = \sin(x) ), we have:
[ \frac{\sin^2(x)}{2} + C ]
So the integral of ( \frac{\tan(x)}{\sec(x)} ) with respect to ( x ) is ( \frac{\sin^2(x)}{2} + C ).
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Answer from HIX Tutor
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
Not the question you need?
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Solve ANY homework problem with a smart AI
• 98% accuracy study help
• Covers math, physics, chemistry, biology, and more
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• Readily available 24/7 | {"url":"https://tutor.hix.ai/question/how-do-you-integrate-tanx-secx-dx-8f9afa0a84","timestamp":"2024-11-07T00:42:21Z","content_type":"text/html","content_length":"573610","record_id":"<urn:uuid:f2fd762f-fb64-48bc-a6f7-bec9de1dd4c0>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.54/warc/CC-MAIN-20241106230027-20241107020027-00561.warc.gz"} |
Trigonometry Homework Solutions
How To Get Checked Trigonometry Homework Solutions For Free: Simple Tips
In trigonometry, the math involves studying angles and lengths of the sides making the angles. You need to know the basics of functions such as tangent, sine and cosine. Using triangulation is
something astronomer’s use and it’s going to be prevalent in your assignments for this class. You’ll also encounter trigonometry if you are in a program involving oceanography, geography,
architecture or civil engineering.
The best way to find homework help on the internet takes some time even if you know where to look. This article will give you the tips you need for getting your trigonometry homework done. Most
students who study trigonometry or other aspects of math struggle with the formulas or homework questions. If you need help solving your trigonometry problems, there are many ways you can get it.
Finding online help with trigonometry homework
There are many websites that provide help for students on this kind of project. Professionals can help you feel comfortable with the math formulas, remind you of key concepts, assist with difficult
problems and encourage your continued learning within trigonometry. If you look in the right place you may find this kind of help for free, but the best kinds of school solutions cost at least some
money. You’ll have to do your research and see what you can find in searching online.
• Most websites providing help for trigonometry cover all aspects of this kind of math including other related topics
• Specific problems can be answered for you
• There’s the option of hiring a homework writer for difficult projects
• Your deadline will always be respected and help given on time
• Request different types of help depending on your grade level or class
Essential parts of trigonometry can be found online in many places. Getting the help and experience you need from a tutor is as simple as searching for it. Since websites are changing constantly and
new ones are being created, I won’t list any specifics in this article but using the above list you can tell if the website is the kind of service that you are looking for. Use those tips to get your
trigonometry problems solved and have an excellent assignment to hand in to your teacher. You can get good grades in a math class if you have the right help, and this is a great way to do that. | {"url":"https://www.troyallschoolreunion.org/where-to-look-for-free-trigonometry-homework-solutions","timestamp":"2024-11-08T11:24:09Z","content_type":"application/xhtml+xml","content_length":"17937","record_id":"<urn:uuid:24b616d5-8703-41df-9b5d-efc464c194cb>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00019.warc.gz"} |
Understanding why dislocation loops are visible in Transmission Electron Microscopy: The Tungsten Case
Dislocation loops finely disperse in bulk W are generally visible to the transition electron microscopy (TEM) after irradiation. In the absence of strong interactions, these loops would normally
diffuse very fast until being sunk at grain boundaries or at the dislocation network. In this work, we evaluate the strength of two pining effects that can explain the reason why they are
nevertheless observed by TEM in bulk. On the one hand, we evaluate with density functional theory (DFT) the strength of binding between isolated loops and dissolved chemical impurities. Employing
classical equations of diffusion, we estimate the resulting effective diffusion coefficient of loops. On the other hand, we consider the effect of mutual elastic interactions (MEI) between the loops,
applying linear elasticity. We perform a large set of kinetic Monte Carlo (KMC) simulations, aimed at evaluating the effective diffusion coefficient, accounting for multiple interactions. Finally, we
draw a map under which experimental condition (loop size and loop number density) what is the dominating pinning effect. Comparing with a large database of experimental TEM evidence, we conclude that
pinning by dissolved impurities is the dominating effect. | {"url":"https://researchportal.sckcen.be/en/publications/understanding-why-dislocation-loops-are-visible-in-transmission-e","timestamp":"2024-11-15T00:55:12Z","content_type":"text/html","content_length":"40442","record_id":"<urn:uuid:d9f5f104-7714-428d-b349-880bd0a3b83f>","cc-path":"CC-MAIN-2024-46/segments/1730477397531.96/warc/CC-MAIN-20241114225955-20241115015955-00090.warc.gz"} |
Incomplete types | C Programming
I learned there are object types (describe objects) and function types
(describe functions). Truly there are also incomplete types, but I can't
understood what they really are. I read void is an incomplete type. The
(C99) standard says incomplete types describes objects, too, but "lack
information needed to determine their sizes". How can you have an object
without knowing its size? If you have an object, you know its size, just
by counting the bits required by any of its values. You can answer: "The
void type comprises an empty set of values": if you have no values, you
cannot count the number of bits required by any value. The point is that
in my understanding void should not describe objects at all. An object
can have a size of zero if the only value it can assume is the empty
string of bits. But there still is a value in this case. Mathematically,
the void type seems to be different from the {{}} set. It seems to be
the empty set ({}). Also, can you name some other incomplete type
different from void, please?
Sorry but your examples looks too complex for me (not your fault
obviously, my fault). I haven't studied structures and pointers yet.
pete said:
** struct inc_1 is an incomplete type.
** arr is of an incomplete type.
/* BEGIN new.c */
int main(void)
struct inc_1;
extern int arr[];
struct inc_1 *p1 = 0;
return 0;
/* END new.c */
I didn't know you can create arrays of unspecified size. How can the
compiler know how much space to allocate for such an object?
Sep 30, 2009
Reaction score
John Taylor said:
pete wrote:
> /*
> ** struct inc_1 is an incomplete type.
> ** arr is of an incomplete type.
> */
> /* BEGIN new.c */
> int main(void)
> {
> struct inc_1;
> extern int arr[];
> struct inc_1 *p1 = 0;
> return 0;
> }
> /* END new.c */
I didn't know you can create arrays of unspecified size. How can the
compiler know how much space to allocate for such an object?
/*you'll have to declare array as dynamic memory allocation by using--
int p;
p=(int *)malloc(len+1) /*+1 for accomodating \0*/
--like this*/
John Taylor wrote:
) pete wrote:
)> extern int arr[];
) I didn't know you can create arrays of unspecified size. How can the
) compiler know how much space to allocate for such an object?
The array is not being created there. It's only being declared.
Basically it's saying "During linking, some other module will define
an array of int called 'arr' of a size we don't know right now"
Although I'm not quite sure this is legal; what happens to sizeof(arr) ?
SaSW, Willem
Disclaimer: I am in no way responsible for any of the statements
made in the above text. For all I know I might be
drugged or something..
No I'm not paranoid. You all think I'm paranoid, don't you !
Richard Heathfield a écrit :
That would be a great example, if only FILE were an incomplete type!
be an incomplete type from a normal portable-C-programmer's
perspective. (I specifically exclude /ab/normal
portable-C-programmers from that!)
In the lcc-win 64 bit version FILE *is* an opaque type.
My stdio.h just does
struct __FILE;
typedef struct __FILE FILE;
extern FILE *_Files[];
#define stdin (_Files[0])
#define stdout (_Files[1])
#define stderr (_Files[2])
I hope I haven't done something wrong because all the new stdio run time
seems to work and nowhere is a user visible definition of FILE.
Willem said:
John Taylor wrote:
) pete wrote:
)> extern int arr[];
) I didn't know you can create arrays of unspecified size. How can the
) compiler know how much space to allocate for such an object?
The array is not being created there. It's only being declared.
Basically it's saying "During linking, some other module will define
an array of int called 'arr' of a size we don't know right now"
Although I'm not quite sure this is legal; what happens to
sizeof(arr) ?
It's "legal". sizeof arr is not -- it is a constraint violation and
so must be diagnosed by the implementation.
Richard Heathfield a écrit :
That's a conformance issue; it violates 7.19.1(2), which requires that
FILE be an object type - i.e. a type that fully describes an object.
7.19.1(2) says:
which is an object type capable of recording all the information needed to control a
stream, including its file position indicator, a pointer to its associated buffer (if any), an
error indicator that records whether a read/write error has occurred, and an end-of-file
indicator that records whether the end of the file has been reached
Nowhere do I read that this object type *internals* must be disclosed...
I have all the required fields in the FILE object, only, you can't access them.
Richard Heathfield a écrit :
Look up "object type" - it's defined as "type that fully describes the
In which case the type does not fully describe the object, and
therefore FILE is not an object type.
Well, that was it. I will leave it at that. Non conformant but I can't disclose
the FILE type since there are many things that can (and will) change. I will
rewrite that later, when some (paying) customer complains
Look up "object type" - it's defined as "type that fully describes the
In which case the type does not fully describe the object, and
therefore FILE is not an object type.
What are the practical consequences of FILE not being an object type?
Richard Heathfield said:
That's a conformance issue; it violates 7.19.1(2), which requires that
FILE be an object type - i.e. a type that fully describes an object.
Why does the standard require that? I see no benefit to the
programmer, and a possible disadvantage to the implementor:
if one wanted to add more members to the FILE structure,
it would be handy to know that no user program can depend
on the old size.
Ben Bacarisse said:
Willem said:
John Taylor wrote:
) pete wrote:
)> extern int arr[];
) I didn't know you can create arrays of unspecified size. How can the
) compiler know how much space to allocate for such an object?
The array is not being created there. It's only being declared.
Basically it's saying "During linking, some other module will define
an array of int called 'arr' of a size we don't know right now"
Although I'm not quite sure this is legal; what happens to
sizeof(arr) ?
It's "legal".
arr is a unary expression that has an incomplete type, so it's a
contraint violation, surely?
jacob navia said:
Richard Heathfield a écrit :
7.19.1(2) says:
which is an object type capable of recording all the information
needed to control a stream, including its file position indicator, a
pointer to its associated buffer (if any), an error indicator that
records whether a read/write error has occurred, and an end-of-file
indicator that records whether the end of the file has been reached
Nowhere do I read that this object type *internals* must be disclosed...
I have all the required fields in the FILE object, only, you can't
access them.
I believe this program is strictly conforming; if FILE is not an
object type, it will probably fail to compile:
#include <stdio.h>
int main(void)
sizeof(FILE); /* result is discarded */
return 0;
This applies to both C90 and C99.
The type definition needn't expose any internal details other than the
size. For example, you could have:
typedef unsigned char[32] FILE;
assuming that 32 bytes is enough to hold the required information.
You could then declare an internal type, say _FILE, and use pointer
conversion in your library to access the actual information.
I know of no *practical* drawbacks to making FILE an incomplete type,
and frankly I think that particular requirement is a bit silly.
Nevertheless, it is a requirement of the standard, and I believe
you could meet it without any major changes to your implementation.
(Getting the size right might be moderately tricky.)
Whether you consider it worth your time to meet this requirement is,
as always, entirely up to you.
Let me be very clear. I am telling you that an implementation with
FILE as an incomplete type does not fully conform to the C90 or
C99 standard. My only purpose is to convey this information to you.
I am not advising you or asking you either to do anything about it
or not to do anything about it.
Phil Carmody said:
Ben Bacarisse said:
Willem said:
John Taylor wrote:
) pete wrote:
)> extern int arr[];
) I didn't know you can create arrays of unspecified size. How can the
) compiler know how much space to allocate for such an object?
The array is not being created there. It's only being declared.
Basically it's saying "During linking, some other module will define
an array of int called 'arr' of a size we don't know right now"
Although I'm not quite sure this is legal; what happens to
sizeof(arr) ?
It's "legal".
arr is a unary expression that has an incomplete type, so it's a
contraint violation, surely?
Yes. Why did you snip the part where i said that it was a constraint
violation (the very next few words, IIRC)?
I took Willem's "Although I'm not quite sure this is legal" to refer
to the extern and I was just confirming that is was.
That's a conformance issue; it violates 7.19.1(2), which requires that
FILE be an object type - i.e. a type that fully describes an object.
Interesting! I was in the past under the impression that it was generally
accepted that implementors were allowed to do just this. I wonder
whether that's an intentional change in response to some issue, or just
a side-effect of some other change.
Nowhere do I read that this object type *internals* must be disclosed...
See 6.2.5:
Types are partitioned into object types (types that fully describe
objects), function types (types that describe functions), and
incomplete types (types that describe objects but lack information
needed to determine their sizes).
If you can't do sizeof(*stdin), so far as I can tell, you're not providing
an object type.
jacob said:
Richard Heathfield a écrit :
Well, that was it. I will leave it at that. Non conformant but I can't
the FILE type since there are many things that can (and will) change. I
rewrite that later, when some (paying) customer complains
Entirely your choice.
Of course, you could do something like...
typedef unsigned char FILE[__FILESIZE];
Then, in your implementation of the C library, simply cast it to the
correct type. This would hide all the details whilst still meeting the
Of course, one disadvantage to hiding the details is that your getc/putc
macros cannot as easily take advantage of the freedoms they have, since
it is rather harder for them to directly access the buffer!
Ben Bacarisse said:
Phil Carmody said:
Ben Bacarisse said:
John Taylor wrote:
) pete wrote:
)> extern int arr[];
) I didn't know you can create arrays of unspecified size. How can the
) compiler know how much space to allocate for such an object?
The array is not being created there. It's only being declared.
Basically it's saying "During linking, some other module will define
an array of int called 'arr' of a size we don't know right now"
Although I'm not quite sure this is legal; what happens to
sizeof(arr) ?
It's "legal".
arr is a unary expression that has an incomplete type, so it's a
contraint violation, surely?
Yes. Why did you snip the part where i said that it was a constraint
violation (the very next few words, IIRC)?
Because meaning should be delivered in a forward direction. Forward
context should be unnecessary.
That, and he mentioned "sizeof(arr)", and you later mentioned "sizeof arr".
Syntactically these are different things.
Because meaning should be delivered in a forward direction. Forward
context should be unnecessary.
? communicate normally you polish notation in
Richard said:
You may or may not consider non-conformance to be a practical problem.
I think you're addressing the wrong question. I suspect he was asking
about what the practical consequences would be if the standard removed
that requirement, so that it would no longer be a conformance issue.
The following program is strictly conforming:
#include <stdio.h>
#include <stdlib.h>
int main(void)
return sizeof(FILE) > 0 ? EXIT_SUCCESS : EXIT_FAILURE;
This program /must/ return EXIT_SUCCESS. But if FILE is an incomplete
type, then the program won't even compile. I think that's a big deal.
Considered in terms of a possible relaxation of the standard's
requirements, I don't think it's a big deal. Because of 7.19.3p6 "The
address of the FILE object used to control a stream may be significant;
a copy of a FILE object need not serve in place of the original.".
Primarily as a result of that clause, there's very little, if anything,
that you can usefully do with FILE objects that would require knowledge
of their size.
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Diagnostic Tests | Solution Center
What are they and why do my students need to take them?
Most administrators and teachers use a baseline test to determine what students know before instruction begins. Then, they use the same test to ascertain how much students have learned during and
after instruction is completed. This baseline test is what Typing Agent refers to as its Diagnostic Tests. Before students begin their keyboarding lessons, all of them, even those in kindergarten,
take a baseline or Diagnostic Test. As students complete their keyboarding lessons, the same test appears at various times during the program to track their growth or improvement over time.
When students in Grades 3 and above begin, their test will look something like this:
When students in Grades K-2 get their first diagnostic test, they are only given one letter at a time, so they are not overwhelmed. Their test will look like this:
How are the Diagnostic Tests administered?
For students using the Keyboarding Foundations K2 Curriculum, Diagnostic Test 1 is one minute long. One letter at a time appears on the screen and students must type that letter. If they get that
letter incorrect five times in a row, testing stops immediately and the students move on to their keyboarding curriculum. Should students get the letter correct, the next letter appears. The test
continues until either one minute is up or the students type incorrectly the on-screen letter five times consecutively – whichever happens first.
The Diagnostic Tests for the Keyboarding Foundations 3+ Curriculum follows a different format. With Diagnostic Test: World 0, students get two minutes to type. Should they type a letter incorrectly,
they can’t move forward until they correct the error. Once they’ve completed the test or 2 minutes have passed, students get feedback on how well they did.
Where can I see how my students performed in the Diagnostic Tests?
Results and grades for these tests are found in the Reports section. We detail the Accuracy, Speed and Grade Earned for all Diagnostics Tests students. In total, K2 students get four Diagnostic Tests
but students in grades 3 and higher get 28 Diagnostic Tests.
Can I skip this first diagnostic test?
Since the Diagnostic Test is part of the pedagogy of Typing Agent, there is no option to skip the test.
How are Diagnostic Tests different from Scheduled Tests?
Diagnostic Tests are controlled completely by Typing Agent. They are given at set intervals as students go through their keyboarding curriculum. On the other hand, the teacher or administrator must
set up and determine when and how Scheduled Tests are be administered. They may use their own customized texts or one of the many supplied by Typing Agent. For more information on Scheduled Tests,
click here. | {"url":"https://help.typingagent.com/en/articles/3506237-diagnostic-tests","timestamp":"2024-11-07T19:02:21Z","content_type":"text/html","content_length":"55926","record_id":"<urn:uuid:a5ce3c2d-26c8-47e6-afee-5af316924488>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00273.warc.gz"} |