Teledyne and Dr. Henry Singleton, Case Study in Capital Allocation
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Fuzzy Logic : Introduction
Fuzzy Logic : Introduction Debasis Samanta IIT Kharagpur [email protected] 07.01.2015 Debasis Samanta (IIT Kharagpur) Soft Computing Applications 07.01.2015 1 / 69 What is Fuzzy logic? Fuzzy logic is a mathematical language to express something. This means it has grammar, syntax, semantic like a language for communication. There are some other mathematical languages also known • Relational algebra (operations on sets) • Boolean algebra (operations on Boolean variables) • Predicate logic (operations on well formed formulae (wff), also called predicate propositions) Fuzzy logic deals with Fuzzy set. Debasis Samanta (IIT Kharagpur) Soft Computing Applications 07.01.2015 2 / 69 A brief history of Fuzzy Logic First time introduced by Lotfi Abdelli Zadeh (1965), University of California, Berkley, USA (1965). He is fondly nick-named as LAZ Debasis Samanta (IIT Kharagpur) Soft Computing Applications 07.01.2015 3 / 69 A brief history of Fuzzy logic 1 Dictionary meaning of fuzzy is not clear, noisy etc. Example: Is the picture on this slide is fuzzy? 2 Antonym of fuzzy is crisp Example: Are the chips crisp? Debasis Samanta (IIT Kharagpur) Soft Computing Applications 07.01.2015 4 / 69 Example : Fuzzy logic vs. Crisp logic Yes or No Crisp answer True or False Milk Yes Water A liquid Crisp Coca No Spite Is the liquid colorless? Debasis Samanta (IIT Kharagpur) Soft Computing Applications 07.01.2015 5 / 69 Example : Fuzzy logic vs. Crisp logic May be May not be Fuzzy answer Absolutely Partially etc Debasis Samanta (IIT Kharagpur) Soft Computing Applications -
Mathematics Is Megethology
17 Mathematics is megethology Mereology is the theory of the relation of part to whole, and kindred notions. Megethology is the result of adding plural quantification, as advocated by George Boolos in [1] and [2], to the language of mere ology. It is so-called because it turns out to have enough expressive power to let us express interesting hypotheses about the size of Reality. It also has the power, as John P. Burgess and A. P. Hazen have shown in [3], to simulate quantification over relations. It is generally accepted that mathematics reduces to set theory. In my book Parts of Classes, [6], I argued that set theory in turn reduces, with the aid of mereology, to the theory of singleton functions. I also argued (somewhat reluctantly) for a 'structuralist' approach to the theory of singleton functions. We need not think we have somehow achieved a primitive grasp of some one special singleton function. Rather, we can take the theory of singleton functions, and hence set theory, and hence mathematics, to consist of generalisations about all singleton functions. We need only assume, to avoid vacuity, that there exists at least one singleton function. But we need not assume even that. For it now turns out that if the size of Reality is right, there must exist a singleton function. All we need as a foundation for mathematics, apart from the framework of megethology, are some hypotheses about the size of Reality. First published in this form in Philosophia Mathematila 3 (1993), 3--23. This paper consists in part of near-verbatim excerpts from David Lewis, Parts of Classes (Oxford, Blackwell, 1991). -
Definiteness and Determinacy
Linguistics and Philosophy manuscript No. (will be inserted by the editor) Definiteness and Determinacy Elizabeth Coppock · David Beaver the date of receipt and acceptance should be inserted later Abstract This paper distinguishes between definiteness and determinacy. Defi- niteness is seen as a morphological category which, in English, marks a (weak) uniqueness presupposition, while determinacy consists in denoting an individual. Definite descriptions are argued to be fundamentally predicative, presupposing uniqueness but not existence, and to acquire existential import through general type-shifting operations that apply not only to definites, but also indefinites and possessives. Through these shifts, argumental definite descriptions may become either determinate (and thus denote an individual) or indeterminate (functioning as an existential quantifier). The latter option is observed in examples like `Anna didn't give the only invited talk at the conference', which, on its indeterminate reading, implies that there is nothing in the extension of `only invited talk at the conference'. The paper also offers a resolution of the issue of whether posses- sives are inherently indefinite or definite, suggesting that, like indefinites, they do not mark definiteness lexically, but like definites, they typically yield determinate readings due to a general preference for the shifting operation that produces them. Keywords definiteness · descriptions · possessives · predicates · type-shifting We thank Dag Haug, Reinhard Muskens, Luca Crniˇc,Cleo Condoravdi, Lucas -
Solutions Are Available
Math 436 Introduction to Topology Spring 2018 Examination 1 1. Define (a) the concept of the closure of a set, and (b) the concept of a basis for a given topology. Solution. The closure of a set A can be defined as the smallest closed set containing A, or as the intersection of all closed sets containing A, or as the union of A with the set of limit points of A. A basis for a given topology is a subset of such that every element of can be obtained as a union of elements of . In alternative language, a basis for a given topology is a collection of open sets such that every open set can be obtained by taking a union of some open sets belonging to the basis. 2. Give an example of a separable Hausdorff topological space .X; / with the property that X has no limit points. Solution. A point x is a limit point of X when every neighborhood of x intersects X ⧵ ^x`. This property evidently holds unless the singleton set ^x` is an open set. Saying that X has no limit points is equivalent to saying that every singleton set is an open set. In other words, the topology on X is the discrete topology. The discrete topology is automatically Hausdorff, for if x and y are distinct points, then the sets ^x` and ^y` are disjoint open sets that separate x from y. A minimal basis for the discrete topology consists of all singletons, so the discrete topology is separable if and only if the space X is countable. -
Ring (Mathematics) 1 Ring (Mathematics)
Ring (mathematics) 1 Ring (mathematics) In mathematics, a ring is an algebraic structure consisting of a set together with two binary operations usually called addition and multiplication, where the set is an abelian group under addition (called the additive group of the ring) and a monoid under multiplication such that multiplication distributes over addition.a[›] In other words the ring axioms require that addition is commutative, addition and multiplication are associative, multiplication distributes over addition, each element in the set has an additive inverse, and there exists an additive identity. One of the most common examples of a ring is the set of integers endowed with its natural operations of addition and multiplication. Certain variations of the definition of a ring are sometimes employed, and these are outlined later in the article. Polynomials, represented here by curves, form a ring under addition The branch of mathematics that studies rings is known and multiplication. as ring theory. Ring theorists study properties common to both familiar mathematical structures such as integers and polynomials, and to the many less well-known mathematical structures that also satisfy the axioms of ring theory. The ubiquity of rings makes them a central organizing principle of contemporary mathematics.[1] Ring theory may be used to understand fundamental physical laws, such as those underlying special relativity and symmetry phenomena in molecular chemistry. The concept of a ring first arose from attempts to prove Fermat's last theorem, starting with Richard Dedekind in the 1880s. After contributions from other fields, mainly number theory, the ring notion was generalized and firmly established during the 1920s by Emmy Noether and Wolfgang Krull.[2] Modern ring theory—a very active mathematical discipline—studies rings in their own right. -
Arxiv:Cs/0410053V1 [Cs.DB] 20 Oct 2004 Oe.Teesrcue R Xeso of Extension Are Structures These Model
An Extended Generalized Disjunctive Paraconsistent Data Model for Disjunctive Information Haibin Wang, Hao Tian and Rajshekhar Sunderraman Department of Computer Science Georgia State University Atlanta, GA 30302 email: {hwang17,htian1}@student.gsu.edu, [email protected] Abstract. This paper presents an extension of generalized disjunctive paraconsistent relational data model in which pure disjunctive positive and negative information as well as mixed disjunctive positive and nega- tive information can be represented explicitly and manipulated. We con- sider explicit mixed disjunctive information in the context of disjunctive databases as there is an interesting interplay between these two types of information. Extended generalized disjunctive paraconsistent relation is introduced as the main structure in this model. The relational algebra is appropriately generalized to work on extended generalized disjunctive paraconsistent relations and their correctness is established. 1 Introduction Relational data model was proposed by Ted Codd’s pioneering paper [1]. Re- lational data model is value-oriented and has rich set of simple, but powerful algebraic operators. Moreover, a strong theoretical foundation for the model is provided by the classical first-order logic [2]. This combination of a respectable theoretical platform, ease of implementation and the practicality of the model resulted in its immediate success, and the model has enjoyed being used by many database management systems. One limitation of the relational data model, however, is its lack of applicabil- arXiv:cs/0410053v1 [cs.DB] 20 Oct 2004 ity to nonclassical situations. These are situations involving incomplete or even inconsistent information. Several types of incomplete information have been extensively studied in the past such as null values [3,4,5], partial values [6], fuzzy and uncertain values [7,8], and disjunctive information [9,10,11]. -
October 1, 2001
“Don’t mistake activity for achievement.” –John Wooden April 22, 2021 «Title» «First_Name» «Last_Name» «Job_Title» «Company» «Address1» «Address2» «City» «State_» «Postal_Code» Dear «Salutation»: If Hollywood made a movie based on the events that drove financial markets during 1Q 2021, most viewers would find the plotline too farfetched. (Then again, the same could probably be said for most of 2020’s major headlines!) The year started out with the Georgia senate runoff races securing Democratic control of Congress (via the Vice President’s Senate tiebreaking authority), paving the way for more fiscal stimulus than would have occurred with divided government. Then, on January 6, protesters in support of then-President Donald Trump stormed the Capitol as Congress met to confirm President-elect Joe Biden’s election victory. The protests turned violent, causing lawmakers to shelter in place. Ultimately more than 140 people were injured, and 5 people died, including a police officer. And all this occurred within the first seven days of the year! Then the Reddit/WallStreetBets crowd burst on the scene, with nonprofessional investors informally banding together to buy stocks that in many cases were heavily shorted (presumably by hedge funds), causing a “short squeeze” in certain stocks, most notably mall-based video game retailer GameStop. At one point during January, GameStop shares had advanced 1,741% for the year! This short squeeze destroyed some hedge funds and left former star hedge fund manager Gabe Plotkin of Melvin Capital nursing a 53% loss for January, causing him to seek a capital injection from his former boss, Steven Cohen, and Citadel Securities’ Ken Griffin. -
Arxiv:1806.09506V1 [Cs.AI] 20 Jun 2018 Piiain Ed Efrpiain Pc Robotics
OPTIMAL SEEDING AND SELF-REPRODUCTION FROM A MATHEMATICAL POINT OF VIEW. RITA GITIK Abstract. P. Kabamba developed generation theory as a tool for studying self-reproducing systems. We provide an alternative definition of a generation system and give a complete solution to the problem of finding optimal seeds for a finite self-replicating system. We also exhibit examples illustrating a connection between self-replication and fixed-point theory. Keywords Algorithm, directed labeled graph, fixed point, generation theory, optimization, seed, self-replication, space robotics. Introduction. Recent research for space exploration, such as [3], considers creating robot colonies on extraterrestrial planets for mining and manufacturing. However, sending such colonies through space is expensive [14], so it would be efficient to transport just one colony capable of self-replication. Once such a colony is designed, a further effort should be made to identify its optimal seeds, where a seed is a subset of the colony capable of manufacturing the whole colony. The optimization parameters might include the number of robots, the mass of robots, the cost of building robots on an extraterrestrial planet versus shipping them there, the time needed to man- ufacture robots at the destination, etc. Menezes and Kabamba gave a background and several algorithms for determining optimal seeds for some special cases of such colonies in [7], [8], and [9]. They also gave a lengthy discussion of the merits of the problem and an extensive reference list in [9]. In this paper, which originated in [5], we provide an alternative definition of a generation system, show how this definition simplifies and allows one to solve the problem of finding optimal seeds for a finite self-replicating system, and exhibit a connection between self-replication and fixed-point theory. -
Introduction: the Carried Interest Loophole 7
Simply stated, the carried interest loophole is the mistreatment of hedge fund and private equity fees as capital gains, rather than ordinary income. CONTENTS 3 | Introduction: the Carried Interest Loophole 7 | What is the Carried Interest Loophole? 10 | The Fight to Hold New Jersey Billionaires Accountable 11 | Meet The Billionaires – MFP Investors, Michael Price – Omega Advisors, Leon Cooperman – Redwood Capital Management, Jonathan Kolatch – Glenview Capital, Larry Robbins 19 | Methodology 22 | Who Are the Hedge Clippers? 23 | Press + General Inquiry Contacts INTRODUCTION: THE CARRIED INTEREST LOOPHOLE Understanding what the Instead, with last year’s new federal tax law, Trump and Republicans chose to increase the trillions of Carried Interest Loophole dollars going to billionaires and corporations while is and why Trump and threatening vital investments in housing, education 2 Congressional Republicans and healthcare. During his presidential campaign, President Donald kept it alive in the Federal Trump pledged to close the loophole, saying that “the Tax Law. hedge fund guys are getting away with murder...I have hedge fund guys that are making a lot of money The carried interest loophole is that aren’t paying anything.” among the most costly and wasteful Now, of course, many of those “hedge fund guys” are tax loopholes out there. in the Trump administration or otherwise advising or funding Trump. It’s a massive giveaway to hedge fund and private equity firms that costs federal taxpayers $18 billion each year. Here’s how it works: These firms charge their investors fees for managing their money, but rather than classifying this as income they deem it carried interest, allowing them to pay lower tax rates. -
The Uptick Rule 3.96 Background Briefing –Is A
defending a market attack - the uptick rule 3.96 CLEARED FOR RELEASE 07/16/2020 [Economic Battle PlanTM points: 100) Background Briefing –Is a planned stock market attack in the works? What we must do now to stop it! A stock market crash can determine an election’s outcome. It has happened before…. On September 11, there was a naked short-selling attack on Lehman Brothers, triggering the worst market collapse since the Great Depression. It was done right before the 2008 election and it literally shifted the outcome. The stock market has been a strength for the Trump administration, but there are indications history could repeat itself soon. Economic Warfare expert Kevin Freeman reviews how the stock market can be used as a secret weapon to influence the 2020 Presidential election. Statistically, the stock market performance in the last three months before an election determines who wins the White House 87% of the time. July through November is the critical point in the financial markets and our adversaries recognize it. Even George Soros warns Trump of a potential economic doom before election. In this briefing Kevin Freeman explains potential attacks adversaries have considered and a simple rule that could prevent a timed economic attack on the US stock market. It is critical action is taken to reinstate this rule now! Your Mission: To understand the economic tactics adversaries have used against the US in the past and to help avoid another economic attack on the US stock market. Also, to help us take on Wall Street to: 1. Reinstate the Uptick Rule 2. -
Axioms of Set Theory and Equivalents of Axiom of Choice Farighon Abdul Rahim Boise State University, [email protected]
Boise State University ScholarWorks Mathematics Undergraduate Theses Department of Mathematics 5-2014 Axioms of Set Theory and Equivalents of Axiom of Choice Farighon Abdul Rahim Boise State University, [email protected] Follow this and additional works at: http://scholarworks.boisestate.edu/ math_undergraduate_theses Part of the Set Theory Commons Recommended Citation Rahim, Farighon Abdul, "Axioms of Set Theory and Equivalents of Axiom of Choice" (2014). Mathematics Undergraduate Theses. Paper 1. Axioms of Set Theory and Equivalents of Axiom of Choice Farighon Abdul Rahim Advisor: Samuel Coskey Boise State University May 2014 1 Introduction Sets are all around us. A bag of potato chips, for instance, is a set containing certain number of individual chip’s that are its elements. University is another example of a set with students as its elements. By elements, we mean members. But sets should not be confused as to what they really are. A daughter of a blacksmith is an element of a set that contains her mother, father, and her siblings. Then this set is an element of a set that contains all the other families that live in the nearby town. So a set itself can be an element of a bigger set. In mathematics, axiom is defined to be a rule or a statement that is accepted to be true regardless of having to prove it. In a sense, axioms are self evident. In set theory, we deal with sets. Each time we state an axiom, we will do so by considering sets. Example of the set containing the blacksmith family might make it seem as if sets are finite. -
From the Collections of the Seeley G. Mudd Manuscript Library, Princeton, NJ
From the collections of the Seeley G. Mudd Manuscript Library, Princeton, NJ These documents can only be used for educational and research purposes (“Fair use”) as per U.S. Copyright law (text below). By accessing this file, all users agree that their use falls within fair use as defined by the copyright law. They further agree to request permission of the Princeton University Library (and pay any fees, if applicable) if they plan to publish, broadcast, or otherwise disseminate this material. This includes all forms of electronic distribution. Inquiries about this material can be directed to: Seeley G. Mudd Manuscript Library 65 Olden Street Princeton, NJ 08540 609-258-6345 609-258-3385 (fax) [email protected] U.S. Copyright law test The copyright law of the United States (Title 17, United States Code) governs the making of photocopies or other reproductions of copyrighted material. Under certain conditions specified in the law, libraries and archives are authorized to furnish a photocopy or other reproduction. One of these specified conditions is that the photocopy or other reproduction is not to be “used for any purpose other than private study, scholarship or research.” If a user makes a request for, or later uses, a photocopy or other reproduction for purposes in excess of “fair use,” that user may be liable for copyright infringement. The Princeton Mathematics Community in the 1930s Transcript Number 27 (PMC27) © The Trustees of Princeton University, 1985 ROBERT SINGLETON (with ALBERT TUCKER) This is an interview of Robert Singleton at the Cromwell Inn on 6 June 1984. The interviewer is Albert Tucker.