John R. Bowles Thesis A
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The Number of Dissimilar Supergraphs of a Linear Graph
Pacific Journal of Mathematics THE NUMBER OF DISSIMILAR SUPERGRAPHS OF A LINEAR GRAPH FRANK HARARY Vol. 7, No. 1 January 1957 THE NUMBER OF DISSIMILAR SUPERGRAPHS OF A LINEAR GRAPH FRANK HARARY 1. Introduction* A (p, q) graph is one with p vertices and q lines. A formula is obtained for the number of dissimilar occurrences of a given (α, β) graph H as a subgraph of all (p, q) graphs G, oc<ip, β <: q, that is, for the number of dissimilar (p, q) supergraphs of H. The enumeration methods are those of Pόlya [7]. This result is then appli- ed to obtain formulas for the number of dissimilar complete subgraphs (cliques) and cycles among all (p, q) graphs. The formula for the num- ber of rooted graphs in [2] is a special case of the number of dissimilar cliques. This note complements [3] in which the number of dissimilar {p, k) subgraphs of a given (p, q) graph is found. We conclude with a discussion of two unsolved problems. A {linear) graph G (see [5] as a general reference) consists of a finite set V of vertices together with a prescribed subset W of the col- lection of all unordered pairs of distinct vertices. The members of W are called lines and two vertices vu v% are adjacent if {vlt v2} e W, that is, if there is a line joining them. By the complement Gr of a graph G, we mean the graph whose vertex-set coincides with that of G, in which two vertices are adjacent if and only if they are not adjacent in G. -
Remembering Frank Harary
Discrete Mathematics Letters Discrete Math. Lett. 6 (2021) 1–7 www.dmlett.com DOI: 10.47443/dml.2021.s101 Editorial Remembering Frank Harary On March 11, 2005, at a special session of the 36th Southeastern International Conference on Combinatorics, Graph The- ory, and Computing held at Florida Atlantic University in Boca Raton, the famous mathematician Ralph Stanton, known for his work in combinatorics and founder of the Institute of Combinatorics and Its Applications, stated that the three mathematicians who had the greatest impact on modern graph theory have now all passed away. Stanton was referring to Frenchman Claude Berge of France, Canadian William Tutte, originally from England, and a third mathematician, an American, who had died only 66 days earlier and to whom this special session was being dedicated. Indeed, that day, March 11, 2005, would have been his 84th birthday. This third mathematician was Frank Harary. Let’s see what led Harary to be so recognized by Stanton. Frank Harary was born in New York City on March 11, 1921. He was the oldest child of Jewish immigrants from Syria and Russia. He earned a B.A. degree from Brooklyn College in 1941, spent a graduate year at Princeton University from 1943 to 1944 in theoretical physics, earned an M.A. degree from Brooklyn College in 1945, spent a year at New York University from 1945 to 1946 in applied mathematics, and then moved to the University of California at Berkeley, where he wrote his Ph.D. Thesis on The Structure of Boolean-like Rings, in 1949, under Alfred Foster. -
Leverages and Constraints for Turkish Foreign Policy in Syrian War: a Structural Balance Approach
Instructions for authors, permissions and subscription information: E-mail: [email protected] Web: www.uidergisi.com.tr Leverages and Constraints for Turkish Foreign Policy in Syrian War: A Structural Balance Approach Serdar Ş. GÜNER* and Dilan E. KOÇ** * Assoc. Prof. Dr., Department of International Relations, Bilkent University ** Student, Department of International Relations, Bilkent University To cite this article: Güner, Serdar Ş. and Koç, Dilan E., “Leverages and Constraints for Turkish Foreign Policy in Syrian War: A Structural Balance Approach”, Uluslararası İlişkiler, Volume 15, No. 59, 2018, pp. 89-103. Copyright @ International Relations Council of Turkey (UİK-IRCT). All rights reserved. No part of this publication may be reproduced, stored, transmitted, or disseminated, in any form, or by any means, without prior written permission from UİK, to whom all requests to reproduce copyright material should be directed, in writing. References for academic and media coverages are beyond this rule. Statements and opinions expressed in Uluslararası İlişkiler are the responsibility of the authors alone unless otherwise stated and do not imply the endorsement by the other authors, the Editors and the Editorial Board as well as the International Relations Council of Turkey. Uluslararası İlişkiler Konseyi Derneği | Uluslararası İlişkiler Dergisi Web: www.uidergisi.com.tr | E- Mail: [email protected] Leverages and Constraints for Turkish Foreign Policy in Syrian War: A Structural Balance Approach Serdar Ş. GÜNER Assoc. Prof. Dr., Department of International Relations, Bilkent University, Ankara, Turkey. E-mail: [email protected] Dilan E. KOÇ Student, Department of International Relations, Bilkent University, Ankara, Turkey. E-mail: [email protected] The authors thank participants of the Seventh Eurasian Peace Science Network Meeting of 2018 and anonymous referees for their comments and suggestions. -
Introduction to Graph Theory: a Discovery Course for Undergraduates
Introduction to Graph Theory: A Discovery Course for Undergraduates James M. Benedict Augusta State University Contents 1 Introductory Concepts 1 1.1 BasicIdeas ...................................... 1 1.2 Graph Theoretic Equality . 2 1.3 DegreesofVertices .................................. 4 1.4 Subgraphs....................................... 6 1.5 The Complement of a Graph . 7 2 Special Subgraphs 9 2.1 Walks ......................................... 9 2.2 Components...................................... 10 2.3 BlocksofaGraph................................... 11 3 Three Famous Results and One Famous Graph 14 3.1 The Four-Color Theorem . 14 3.2 PlanarGraphs..................................... 16 3.3 ThePetersenGraph ................................. 18 3.4 TraceableGraphs ................................... 18 K(3;3;3) = H1 H2 Removing the edge w1v2 destroys the only C4 v 3 u1 H1: H2: w3 v v2 3 u w1 u 2 u u 2 v 1 3 w 1 w 2 2 w3 u3 w1 v2 v1 Place any edge of H1 into H2 or (vice versa) and a C4 is created. i Remarks By reading through this text one can acquire a familiarity with the elementary topics of Graph Theory and the associated (hopefully standard) notation. The notation used here follows that used by Gary Chartrand at Western Michigan University in the last third of the 20th century. His usage of notation was in‡uenced by that of Frank Harary at the University of Michigan beginning in the early 1950’s. The text’s author was Chartrand’s student at WMU from 1973 to 1976. In order to actually learn any graph theory from this text, one must work through and solve the problems found within it. Some of the problems are very easy. -
National Film Registry
National Film Registry Title Year EIDR ID Newark Athlete 1891 10.5240/FEE2-E691-79FD-3A8F-1535-F Blacksmith Scene 1893 10.5240/2AB8-4AFC-2553-80C1-9064-6 Dickson Experimental Sound Film 1894 10.5240/4EB8-26E6-47B7-0C2C-7D53-D Edison Kinetoscopic Record of a Sneeze 1894 10.5240/B1CF-7D4D-6EE3-9883-F9A7-E Rip Van Winkle 1896 10.5240/0DA5-5701-4379-AC3B-1CC2-D The Kiss 1896 10.5240/BA2A-9E43-B6B1-A6AC-4974-8 Corbett-Fitzsimmons Title Fight 1897 10.5240/CE60-6F70-BD9E-5000-20AF-U Demolishing and Building Up the Star Theatre 1901 10.5240/65B2-B45C-F31B-8BB6-7AF3-S President McKinley Inauguration Footage 1901 10.5240/C276-6C50-F95E-F5D5-8DCB-L The Great Train Robbery 1903 10.5240/7791-8534-2C23-9030-8610-5 Westinghouse Works 1904 1904 10.5240/F72F-DF8B-F0E4-C293-54EF-U A Trip Down Market Street 1906 10.5240/A2E6-ED22-1293-D668-F4AB-I Dream of a Rarebit Fiend 1906 10.5240/4D64-D9DD-7AA2-5554-1413-S San Francisco Earthquake and Fire, April 18, 1906 1906 10.5240/69AE-11AD-4663-C176-E22B-I A Corner in Wheat 1909 10.5240/5E95-74AC-CF2C-3B9C-30BC-7 Lady Helen’s Escapade 1909 10.5240/0807-6B6B-F7BA-1702-BAFC-J Princess Nicotine; or, The Smoke Fairy 1909 10.5240/C704-BD6D-0E12-719D-E093-E Jeffries-Johnson World’s Championship Boxing Contest 1910 10.5240/A8C0-4272-5D72-5611-D55A-S White Fawn’s Devotion 1910 10.5240/0132-74F5-FC39-1213-6D0D-Z Little Nemo 1911 10.5240/5A62-BCF8-51D5-64DB-1A86-H A Cure for Pokeritis 1912 10.5240/7E6A-CB37-B67E-A743-7341-L From the Manger to the Cross 1912 10.5240/5EBB-EE8A-91C0-8E48-DDA8-Q The Cry of the Children 1912 10.5240/C173-A4A7-2A2B-E702-33E8-N -
Why Bad Teacher Is a Bad Movie and Where the Real Crisis Is: Implications for Teachers and Teacher Education
Georgia State University ScholarWorks @ Georgia State University Middle and Secondary Education Faculty Publications Department of Middle and Secondary Education 2016 Why Bad Teacher is a Bad Movie and Where the Real Crisis Is: Implications for Teachers and Teacher Education J. Patrick McGrail Jacksonville State University Ewa McGrail Georgia State University Follow this and additional works at: https://scholarworks.gsu.edu/mse_facpub Part of the Curriculum and Instruction Commons, and the Junior High, Intermediate, Middle School Education and Teaching Commons Recommended Citation McGrail, J. P., & McGrail, E. (2016). Why Bad Teacher is a bad movie and where the real crisis is: Implications for teachers and teacher education. In Shoffner, M. (Ed.), Teachers in fiction & film (pp. 192-202). New York, NY: Routledge. This Book Chapter is brought to you for free and open access by the Department of Middle and Secondary Education at ScholarWorks @ Georgia State University. It has been accepted for inclusion in Middle and Secondary Education Faculty Publications by an authorized administrator of ScholarWorks @ Georgia State University. For more information, please contact [email protected]. Final Draft 10/2/15 Why Bad Teacher is a Bad Movie and Where the Real Crisis Is: Implications for Teachers and Teacher Education J. P. McGrail and Ewa McGrail In this chapter, we analyze and critique the film Bad Teacher (Miller & Kasdan, 2011). In our view, it cynically panders to the worst aspects of contemporary pessimism toward educational outcomes in the US (Beck, 2012; Thomsen, 1993; Vandermeersche, Soetaert, &; Rutten, 2013). We argue, however, that Bad Teacher is actually consonant with Hollywood’s well-known narrative memes of redemption of the fallen (Carter, 2009; Reyes & Rios, 2003). -
National Film Registry Titles Listed by Release Date
National Film Registry Titles 1989-2017: Listed by Year of Release Year Year Title Released Inducted Newark Athlete 1891 2010 Blacksmith Scene 1893 1995 Dickson Experimental Sound Film 1894-1895 2003 Edison Kinetoscopic Record of a Sneeze 1894 2015 The Kiss 1896 1999 Rip Van Winkle 1896 1995 Corbett-Fitzsimmons Title Fight 1897 2012 Demolishing and Building Up the Star Theatre 1901 2002 President McKinley Inauguration Footage 1901 2000 The Great Train Robbery 1903 1990 Life of an American Fireman 1903 2016 Westinghouse Works 1904 1904 1998 Interior New York Subway, 14th Street to 42nd Street 1905 2017 Dream of a Rarebit Fiend 1906 2015 San Francisco Earthquake and Fire, April 18, 1906 1906 2005 A Trip Down Market Street 1906 2010 A Corner in Wheat 1909 1994 Lady Helen’s Escapade 1909 2004 Princess Nicotine; or, The Smoke Fairy 1909 2003 Jeffries-Johnson World’s Championship Boxing Contest 1910 2005 White Fawn’s Devotion 1910 2008 Little Nemo 1911 2009 The Cry of the Children 1912 2011 A Cure for Pokeritis 1912 2011 From the Manger to the Cross 1912 1998 The Land Beyond the Sunset 1912 2000 Musketeers of Pig Alley 1912 2016 Bert Williams Lime Kiln Club Field Day 1913 2014 The Evidence of the Film 1913 2001 Matrimony’s Speed Limit 1913 2003 Preservation of the Sign Language 1913 2010 Traffic in Souls 1913 2006 The Bargain 1914 2010 The Exploits of Elaine 1914 1994 Gertie The Dinosaur 1914 1991 In the Land of the Head Hunters 1914 1999 Mabel’s Blunder 1914 2009 1 National Film Registry Titles 1989-2017: Listed by Year of Release Year Year -
2012 Twenty-Seven Years of Nominees & Winners FILM INDEPENDENT SPIRIT AWARDS
2012 Twenty-Seven Years of Nominees & Winners FILM INDEPENDENT SPIRIT AWARDS BEST FIRST SCREENPLAY 2012 NOMINEES (Winners in bold) *Will Reiser 50/50 BEST FEATURE (Award given to the producer(s)) Mike Cahill & Brit Marling Another Earth *The Artist Thomas Langmann J.C. Chandor Margin Call 50/50 Evan Goldberg, Ben Karlin, Seth Rogen Patrick DeWitt Terri Beginners Miranda de Pencier, Lars Knudsen, Phil Johnston Cedar Rapids Leslie Urdang, Dean Vanech, Jay Van Hoy Drive Michel Litvak, John Palermo, BEST FEMALE LEAD Marc Platt, Gigi Pritzker, Adam Siegel *Michelle Williams My Week with Marilyn Take Shelter Tyler Davidson, Sophia Lin Lauren Ambrose Think of Me The Descendants Jim Burke, Alexander Payne, Jim Taylor Rachael Harris Natural Selection Adepero Oduye Pariah BEST FIRST FEATURE (Award given to the director and producer) Elizabeth Olsen Martha Marcy May Marlene *Margin Call Director: J.C. Chandor Producers: Robert Ogden Barnum, BEST MALE LEAD Michael Benaroya, Neal Dodson, Joe Jenckes, Corey Moosa, Zachary Quinto *Jean Dujardin The Artist Another Earth Director: Mike Cahill Demián Bichir A Better Life Producers: Mike Cahill, Hunter Gray, Brit Marling, Ryan Gosling Drive Nicholas Shumaker Woody Harrelson Rampart In The Family Director: Patrick Wang Michael Shannon Take Shelter Producers: Robert Tonino, Andrew van den Houten, Patrick Wang BEST SUPPORTING FEMALE Martha Marcy May Marlene Director: Sean Durkin Producers: Antonio Campos, Patrick Cunningham, *Shailene Woodley The Descendants Chris Maybach, Josh Mond Jessica Chastain Take Shelter -
Combinatorics: a First Encounter
Combinatorics: a first encounter Darij Grinberg Thursday 10th January, 2019at 9:29pm (unfinished draft!) Contents 1. Preface1 1.1. Acknowledgments . .4 2. What is combinatorics?4 2.1. Notations and conventions . .4 1. Preface These notes (which are work in progress and will remain so for the foreseeable fu- ture) are meant as an introduction to combinatorics – the mathematical discipline that studies finite sets (roughly speaking). When finished, they will cover topics such as binomial coefficients, the principles of enumeration, permutations, parti- tions and graphs. The emphasis falls on enumerative combinatorics, meaning the art of computing sizes of finite sets (“counting”), and graph theory. I have tried to keep the presentation as self-contained and elementary as possible. The reader is assumed to be familiar with some basics such as induction proofs, equivalence relations and summation signs, as well as have some experience with mathematical proofs. One of the best places to catch up on these basics and to gain said experience is the MIT lecture notes [LeLeMe16] (particularly their first five chapters). Two other resources to familiarize oneself with proofs are [Hammac15] and [Day16]. Generally, most good books about “reading and writing mathemat- ics” or “introductions to abstract mathematics” should convey these skills, although the extent to which they actually do so may differ. These notes are accompanying two classes on combinatorics (Math 4707 and 4990) I am giving at the University of Minneapolis in Fall 2017. Here is a (subjective and somewhat random) list of recommended texts on the kinds of combinatorics that will be considered in these notes: • Enumerative combinatorics (aka counting): 1 Notes on graph theory (Thursday 10th January, 2019, 9:29pm) page 2 – The very basics of the subject can be found in [LeLeMe16, Chapters 14– 15]. -
Structural Balance: a Generalization of Heider's Theory'
VOL. 63, No. 5 SEPTEMBER, 1956 THE PSYCHOLOGICAL REVIEW STRUCTURAL BALANCE: A GENERALIZATION OF HEIDER'S THEORY' DORWIN CARTWRIGHT AND FRANK HARARY Research Center for Group Dynamics, University of Michigan A persistent problem of psychology will arise to change it toward a state has been how to deal conceptually of balance. These pressures may with patterns of interdependent prop- work to change the relation of affec- erties. This problem has been cen- tion between P and 0, the relation of tral, of course, in the theoretical responsibility between 0 and X, or the treatment by Gestalt psychologists of relation of evaluation between P phenomenal or neural configurations andX. or fields (12, 13, 15). It has also The purpose of this paper is to been of concern to social psychologists present and develop the consequences and sociologists who attempt to em- of a formal definition of balance which ploy concepts referring to social sys- is consistent with Heider's conception tems (18). and which may be employed in a more Heider (19), reflecting the general general treatment of empirical con- field-theoretical approach, has con- figurations. The definition is stated sidered certain aspects of cognitive in terms of the mathematical theory fields which contain perceived people of linear graphs (8, 14) and makes use and impersonal objects or events. of a distinction between a given rela- His analysis focuses upon what he calls tion and its opposite relation. Some the P-O-X unit of a cognitive field, of the ramifications of this definition consisting of P (one person), 0 (an- are then examined by means of other person), and X (an impersonal theorems derivable from the definition entity). -
Los Angeles Education Films and the Rhetoric of Nation at Risk, No Child Left Behind, and Race to the Top
Los Angeles Education Films and the Rhetoric of Nation at Risk, No Child Left Behind, and Race To The Top Bernie Sapir The perception of Los Angeles’s public school system reflects the predominant way our populace views public schools—negatively. Urban schools, such as the Los Angeles Unified School District, acknowledge that public education is struggling with key problems: high dropout rates, overworked teachers, and underperforming students. At the same time, public school teachers and administrators are attempting to accomplish more and more with less and less resources. While public school representatives—such as the Los Angeles public school teachers—would argue for reform efforts that would garner greater funds being allocated to the school system, others—including Republican George Bush and Democrat Barack Obama—argue that the increase of charter schools and a voucher system is a better resolution. I argue that part of this debate has been shaped on the federal level, and this federal rhetoric has influenced not only the public, but also popular culture. In 1983, President Ronald Reagan’s Secretary of Education, Terrel H. Bell, alarmed the American public with the Nation at Risk Report (NAR), putting our educational system under scrutiny and adopting rhetoric critical of the public education system. Subsequent federal educational policies have adopted its ideology, beginning with President George W. Bush’s No Child Left Behind Law (NCLB) followed by President Obama’s Race To The Top Program (RTTT). This paper argues that these federal educational policies influence Americans’ perspectives of public education, and these presidential mandates’ impact is acutely evident in the Los Angeles Greater Metropolis’s school system, where the UTLA—the United Teachers of Los Angeles— has been the target of the public’s angst. -
Memories of the Golden State
Issue 135 December 2016/January 2017 A NEWSLETTER OF THE ROCKEFELLER UNIVERSITY COMMUNITY Memories of the Golden State O WEN C LARK Armed with a DSLR camera, travel guitar, two Haight and Ashbury-acquired shawl- cardigans, and three of my oldest friends, I left the perpetual fog of the San Francisco Bay. Having played out the scene a thousand times in my head, I had romanticized the drive down California’s scenic Pacific Coast Highway to levels approaching cliché. But despite trading the flashy convertibles of Entourage’s Vincent Chase or Californica- tion’s Hank Moody for a grey Hyundai So- nata rental car, it still failed to disappoint. /NATURAL SELECTIONS Practically every bend on that winding road greeted me with a stunning scene of pure, rugged beauty. California’s jagged cliffs are lined with earthy hues of bright red and orange, while each inlet of the vast Pacific OWEN CLARK Ocean contains a perfectly balanced array of turquoise and green pastels that one might have found on Winslow Homer’s palette. Despite navigating hairpin turns sur- rounded by 300-foot drops under cover of by All Photos total darkness, we made it safely to Big Sur. A smokestack towers above Mono Lake. My friends liked to joke that being the ob- Though I had fallen in love with the Cal- Tuolumne Meadows area of the park. After sessive ball of neuroses that I am, I had al- ifornia coast, we had to move on to the next returning to my friends relaxing by the lake, ready lived out the entire trip through the stop on our long list.