Higher Spin Fields in Hyperspace. a Review
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H. G. Wells Time Traveler
Items on Exhibit 1. H. G. Wells – Teacher to the World 11. H. G. Wells. Die Zeitmaschine. (Illustrierte 21. H. G. Wells. Picshua [sketch] ‘Omaggio to 1. H. G. Wells (1866-1946). Text-book of Klassiker, no. 46) [Aachen: Bildschriftenverlag, P.C.B.’ [1900] Biology. London: W.B. Clive & Co.; University 196-]. Wells Picshua Box 1 H. G. Wells Correspondence College Press, [1893]. Wells Q. 823 W46ti:G Wells 570 W46t, vol. 1, cop. 1 Time Traveler 12. H. G. Wells. La machine à explorer le temps. 7. Fantasias of Possibility 2. H. G. Wells. The Outline of History, Being a Translated by Henry-D. Davray, illustrated by 22. H. G. Wells. The World Set Free [holograph Plain History of Life and Mankind. London: G. Max Camis. Paris: R. Kieffer, [1927]. manuscript, ca. 1913]. Simon J. James is Head of the Newnes, [1919-20]. Wells 823 W46tiFd Wells WE-001, folio W-3 Wells Q. 909 W46o 1919 vol. 2, part. 24, cop. 2 Department of English Studies, 13. H. G. Wells. Stroz času : Neviditelný. 23. H. G. Wells to Frederick Wells, ‘Oct. 27th 45’ Durham University, UK. He has 3. H. G. Wells. ‘The Idea of a World Translated by Pavla Moudrá. Prague: J. Otty, [Holograph letter]. edited Wells texts for Penguin and Encyclopedia.’ Nature, 138, no. 3500 (28 1905. Post-1650 MS 0667, folder 75 November 1936) : 917-24. Wells 823 W46tiCzm. World’s Classics and The Wellsian, the Q. 505N 24. H. G. Wells’ Things to Come. Produced by scholarly journal of the H. G. Wells Alexander Korda, directed by William Cameron Society. -
Interaction of the Past of Parallel Universes
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server Interaction of the Past of parallel universes Alexander K. Guts Department of Mathematics, Omsk State University 644077 Omsk-77 RUSSIA E-mail: [email protected] October 26, 1999 ABSTRACT We constructed a model of five-dimensional Lorentz manifold with foliation of codimension 1 the leaves of which are four-dimensional space-times. The Past of these space-times can interact in macroscopic scale by means of large quantum fluctuations. Hence, it is possible that our Human History consists of ”somebody else’s” (alien) events. In this article the possibility of interaction of the Past (or Future) in macroscopic scales of space and time of two different universes is analysed. Each universe is considered as four-dimensional space-time V 4, moreover they are imbedded in five- dimensional Lorentz manifold V 5, which shall below name Hyperspace. The space- time V 4 is absolute world of events. Consequently, from formal standpoints any point-event of this manifold V 4, regardless of that we refer it to Past, Present or Future of some observer, is equally available to operate with her.Inotherwords, modern theory of space-time, rising to Minkowsky, postulates absolute eternity of the World of events in the sense that all events exist always. Hence, it is possible interaction of Present with Past and Future as well as Past can interact with Future. Question is only in that as this is realized. The numerous articles about time machine show that our statement on the interaction of Present with Past is not fantasy, but is subject of the scientific study. -
Projective Geometry: a Short Introduction
Projective Geometry: A Short Introduction Lecture Notes Edmond Boyer Master MOSIG Introduction to Projective Geometry Contents 1 Introduction 2 1.1 Objective . .2 1.2 Historical Background . .3 1.3 Bibliography . .4 2 Projective Spaces 5 2.1 Definitions . .5 2.2 Properties . .8 2.3 The hyperplane at infinity . 12 3 The projective line 13 3.1 Introduction . 13 3.2 Projective transformation of P1 ................... 14 3.3 The cross-ratio . 14 4 The projective plane 17 4.1 Points and lines . 17 4.2 Line at infinity . 18 4.3 Homographies . 19 4.4 Conics . 20 4.5 Affine transformations . 22 4.6 Euclidean transformations . 22 4.7 Particular transformations . 24 4.8 Transformation hierarchy . 25 Grenoble Universities 1 Master MOSIG Introduction to Projective Geometry Chapter 1 Introduction 1.1 Objective The objective of this course is to give basic notions and intuitions on projective geometry. The interest of projective geometry arises in several visual comput- ing domains, in particular computer vision modelling and computer graphics. It provides a mathematical formalism to describe the geometry of cameras and the associated transformations, hence enabling the design of computational ap- proaches that manipulates 2D projections of 3D objects. In that respect, a fundamental aspect is the fact that objects at infinity can be represented and manipulated with projective geometry and this in contrast to the Euclidean geometry. This allows perspective deformations to be represented as projective transformations. Figure 1.1: Example of perspective deformation or 2D projective transforma- tion. Another argument is that Euclidean geometry is sometimes difficult to use in algorithms, with particular cases arising from non-generic situations (e.g. -
The Future of Robotics an Inside View on Innovation in Robotics
The Future of Robotics An Inside View on Innovation in Robotics FEATURE Robots, Humans and Work Executive Summary Robotics in the Startup Ecosystem The automation of production through three industrial revolutions has increased global output exponentially. Now, with machines increasingly aware and interconnected, Industry 4.0 is upon us. Leading the charge are fleets of autonomous robots. Built by major multinationals and increasingly by innovative VC-backed companies, these robots have already become established participants in many areas of the economy, from assembly lines to farms to restaurants. Investors, founders and policymakers are all still working to conceptualize a framework for these companies and their transformative Austin Badger technology. In this report, we take a data-driven approach to emerging topics in the industry, including business models, performance metrics, Director, Frontier Tech Practice and capitalization trends. Finally, we review leading theories of how automation affects the labor market, and provide quantitative evidence for and against them. It is our view that the social implications of this industry will be massive and will require a continual examination by those driving this technology forward. The Future of Robotics 2 Table of Contents 4 14 21 The Landscape VC and Robots Robots, Humans and Work Industry 4.0 and the An Emerging Framework Robotics Ecosystem The Interplay of Automation and Labor The Future of Robotics 3 The Landscape Industry 4.0 and the Robotics Ecosystem The Future of Robotics 4 COVID-19 and US Manufacturing, Production and Nonsupervisory Workers the Next 12.8M Automation Wave 10.2M Recessions tend to reduce 9.0M employment, and some jobs don’t come back. -
Representations of Certain Semidirect Product Groups* H
JOURNAL OF FUNCTIONAL ANALYSIS 19, 339-372 (1975) Representations of Certain Semidirect Product Groups* JOSEPH A. WOLF Department of Mathematics, University of California, Berkeley, California 94720 Communicated by the Editovs Received April I, 1974 We study a class of semidirect product groups G = N . U where N is a generalized Heisenberg group and U is a generalized indefinite unitary group. This class contains the Poincare group and the parabolic subgroups of the simple Lie groups of real rank 1. The unitary representations of G and (in the unimodular cases) the Plancherel formula for G are written out. The problem of computing Mackey obstructions is completely avoided by realizing the Fock representations of N on certain U-invariant holomorphic cohomology spaces. 1. INTRODUCTION AND SUMMARY In this paper we write out the irreducible unitary representations for a type of semidirect product group that includes the Poincare group and the parabolic subgroups of simple Lie groups of real rank 1. If F is one of the four finite dimensional real division algebras, the corresponding groups in question are the Np,Q,F . {U(p, 4; F) xF+}, where FP~*: right vector space F”+Q with hermitian form h(x, y) = i xiyi - y xipi ) 1 lJ+1 N p,p,F: Im F + F”q* with (w. , ~o)(w, 4 = (w, + 7.0+ Im h(z, ,4, z. + 4, U(p, Q; F): unitary group of Fp,q, F+: subgroup of the group generated by F-scalar multiplication on Fp>*. * Research partially supported by N.S.F. Grant GP-16651. 339 Copyright 0 1975 by Academic Press, Inc. -
A NEW SOCIAL COMPACT for Work and Workers
FUTURE OF WORK IN CALIFORNIA A NEW SOCIAL COMPACT for work and workers RE OF W TU OR FU K CO N M MISSIO E OF W TUR OR FU K CO N M MISSIO Commissioners Produced by Institute for the Future (IFTF) for the California Future of Members of the Future of Work Commission were appointed by Governor Work Commission, with the support Gavin Newsom to help create inclusive, long-term economic growth and ensure from The James Irvine Foundation, Californians share in that success. Blue Shield of California Foundation, the Ford Foundation and Lumina Mary Kay Henry, Co-Chair Ash Kalra Foundation. President, Service Employees State Assemblymember, California International Union District 27 James Manyika, Co-Chair Stephane Kasriel Chairman & Director, McKinsey Former CEO, Upwork Global Institute Commission Staff Fei-Fei Li Roy Bahat Professor & Co-Director, Human- Anmol Chaddha, Head, Bloomberg Beta Centered Artificial Intelligence Manager Institute, Stanford Doug Bloch Alyssa Andersen Political Director, Teamsters Joint John Marshall Julie Ericsson Council 7 Senior Capital Markets Economist, United Food and Commercial Ben Gansky Soraya Coley Workers President, California Polytechnic Georgia Gillan State University, Pomona Art Pulaski Executive Secretary-Treasurer Marina Gorbis Lloyd Dean & Chief Officer, California Labor CEO, CommonSpirit Health Jean Hagan Federation Jennifer Granholm* Lyn Jeffery Maria S. Salinas Former Governor, State of Michigan President & CEO, Los Angeles Area *Resigned from Commission Ilana Lipsett Chamber of Commerce upon nomination -
Arxiv:1910.10745V1 [Cond-Mat.Str-El] 23 Oct 2019 2.2 Symmetry-Protected Time Crystals
A Brief History of Time Crystals Vedika Khemania,b,∗, Roderich Moessnerc, S. L. Sondhid aDepartment of Physics, Harvard University, Cambridge, Massachusetts 02138, USA bDepartment of Physics, Stanford University, Stanford, California 94305, USA cMax-Planck-Institut f¨urPhysik komplexer Systeme, 01187 Dresden, Germany dDepartment of Physics, Princeton University, Princeton, New Jersey 08544, USA Abstract The idea of breaking time-translation symmetry has fascinated humanity at least since ancient proposals of the per- petuum mobile. Unlike the breaking of other symmetries, such as spatial translation in a crystal or spin rotation in a magnet, time translation symmetry breaking (TTSB) has been tantalisingly elusive. We review this history up to recent developments which have shown that discrete TTSB does takes place in periodically driven (Floquet) systems in the presence of many-body localization (MBL). Such Floquet time-crystals represent a new paradigm in quantum statistical mechanics — that of an intrinsically out-of-equilibrium many-body phase of matter with no equilibrium counterpart. We include a compendium of the necessary background on the statistical mechanics of phase structure in many- body systems, before specializing to a detailed discussion of the nature, and diagnostics, of TTSB. In particular, we provide precise definitions that formalize the notion of a time-crystal as a stable, macroscopic, conservative clock — explaining both the need for a many-body system in the infinite volume limit, and for a lack of net energy absorption or dissipation. Our discussion emphasizes that TTSB in a time-crystal is accompanied by the breaking of a spatial symmetry — so that time-crystals exhibit a novel form of spatiotemporal order. -
The Fractal Dimension of Product Sets
THE FRACTAL DIMENSION OF PRODUCT SETS A PREPRINT Clayton Moore Williams Brigham Young University [email protected] Machiel van Frankenhuijsen Utah Valley University [email protected] February 26, 2021 ABSTRACT Using methods from nonstandard analysis, we define a nonstandard Minkowski dimension which exists for all bounded sets and which has the property that dim(A × B) = dim(A) + dim(B). That is, our new dimension is “product-summable”. To illustrate our theorem we generalize an example of Falconer’s1 to show that the standard upper Minkowski dimension, as well as the Hausdorff di- mension, are not product-summable. We also include a method for creating sets of arbitrary rational dimension. Introduction There are several notions of dimension used in fractal geometry, which coincide for many sets but have important, distinct properties. Indeed, determining the most proper notion of dimension has been a major problem in geometric measure theory from its inception, and debate over what it means for a set to be fractal has often reduced to debate over the propernotion of dimension. A classical example is the “Devil’s Staircase” set, which is intuitively fractal but which has integer Hausdorff dimension2. As Falconer notes in The Geometry of Fractal Sets3, the Hausdorff dimension is “undoubtedly, the most widely investigated and most widely used” notion of dimension. It can, however, be difficult to compute or even bound (from below) for many sets. For this reason one might want to work with the Minkowski dimension, for which one can often obtain explicit formulas. Moreover, the Minkowski dimension is computed using finite covers and hence has a series of useful identities which can be used in analysis. -
Near-Death Experiences and the Theory of the Extraneuronal Hyperspace
Near-Death Experiences and the Theory of the Extraneuronal Hyperspace Linz Audain, J.D., Ph.D., M.D. George Washington University The Mandate Corporation, Washington, DC ABSTRACT: It is possible and desirable to supplement the traditional neu rological and metaphysical explanatory models of the near-death experience (NDE) with yet a third type of explanatory model that links the neurological and the metaphysical. I set forth the rudiments of this model, the Theory of the Extraneuronal Hyperspace, with six propositions. I then use this theory to explain three of the pressing issues within NDE scholarship: the veridicality, precognition and "fear-death experience" phenomena. Many scholars who write about near-death experiences (NDEs) are of the opinion that explanatory models of the NDE can be classified into one of two types (Blackmore, 1993; Moody, 1975). One type of explana tory model is the metaphysical or supernatural one. In that model, the events that occur within the NDE, such as the presence of a tunnel, are real events that occur beyond the confines of time and space. In a sec ond type of explanatory model, the traditional model, the events that occur within the NDE are not at all real. Those events are merely the product of neurobiochemical activity that can be explained within the confines of current neurological and psychological theory, for example, as hallucination. In this article, I supplement this dichotomous view of explanatory models of the NDE by proposing yet a third type of explanatory model: the Theory of the Extraneuronal Hyperspace. This theory represents a Linz Audain, J.D., Ph.D., M.D., is a Resident in Internal Medicine at George Washington University, and Chief Executive Officer of The Mandate Corporation. -
Back Or to the Future? Preferences of Time Travelers
Judgment and Decision Making, Vol. 7, No. 4, July 2012, pp. 373–382 Back or to the future? Preferences of time travelers Florence Ettlin∗ Ralph Hertwig† Abstract Popular culture reflects whatever piques our imagination. Think of the myriad movies and books that take viewers and readers on an imaginary journey to the past or the future (e.g., Gladiator, The Time Machine). Despite the ubiquity of time travel as a theme in cultural expression, the factors that underlie people’s preferences concerning the direction of time travel have gone unexplored. What determines whether a person would prefer to visit the (certain) past or explore the (uncertain) future? We identified three factors that markedly affect people’s preference for (hypothetical) travel to the past or the future, respectively. Those who think of themselves as courageous, those with a more conservative worldview, and—perhaps counterintuitively—those who are advanced in age prefer to travel into the future. We discuss implications of these initial results. Keywords: time travel; preferences; age; individual differences; conservative Weltanschauung. 1 Introduction of the future. But what determines whether the cultural time machine’s lever is pushed forward to an unknown 1.1 Hypothetical time traveling: A ubiqui- future or back to a more certain past? tous yet little understood activity Little is known about the factors that determine peo- ple’s preferences with regard to the “direction” of time “I drew a breath, set my teeth, gripped the starting lever travel. Past investigations of mental time travel have typ- with both hands, and went off with a thud” (p. -
Arxiv:1902.02232V1 [Cond-Mat.Mtrl-Sci] 6 Feb 2019
Hyperspatial optimisation of structures Chris J. Pickard∗ Department of Materials Science & Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom and Advanced Institute for Materials Research, Tohoku University 2-1-1 Katahira, Aoba, Sendai, 980-8577, Japan (Dated: February 7, 2019) Anticipating the low energy arrangements of atoms in space is an indispensable scientific task. Modern stochastic approaches to searching for these configurations depend on the optimisation of structures to nearby local minima in the energy landscape. In many cases these local minima are relatively high in energy, and inspection reveals that they are trapped, tangled, or otherwise frustrated in their descent to a lower energy configuration. Strategies have been developed which attempt to overcome these traps, such as classical and quantum annealing, basin/minima hopping, evolutionary algorithms and swarm based methods. Random structure search makes no attempt to avoid the local minima, and benefits from a broad and uncorrelated sampling of configuration space. It has been particularly successful in the first principles prediction of unexpected new phases of dense matter. Here it is demonstrated that by starting the structural optimisations in a higher dimensional space, or hyperspace, many of the traps can be avoided, and that the probability of reaching low energy configurations is much enhanced. Excursions into the extra dimensions are progressively eliminated through the application of a growing energetic penalty. This approach is tested on hard cases for random search { clusters, compounds, and covalently bonded networks. The improvements observed are most dramatic for the most difficult ones. Random structure search is shown to be typically accelerated by two orders of magnitude, and more for particularly challenging systems. -
SUPERSYMMETRY 1. Introduction the Purpose
SUPERSYMMETRY JOSH KANTOR 1. Introduction The purpose of these notes is to give a short and (overly?)simple description of supersymmetry for Mathematicians. Our description is far from complete and should be thought of as a first pass at the ideas that arise from supersymmetry. Fundamental to supersymmetry is the mathematics of Clifford algebras and spin groups. We will describe the mathematical results we are using but we refer the reader to the references for proofs. In particular [4], [1], and [5] all cover spinors nicely. 2. Spin and Clifford Algebras We will first review the definition of spin, spinors, and Clifford algebras. Let V be a vector space over R or C with some nondegenerate quadratic form. The clifford algebra of V , l(V ), is the algebra generated by V and 1, subject to the relations v v = v, vC 1, or equivalently v w + w v = 2 v, w . Note that elements of· l(V ) !can"b·e written as polynomials· in V · and this! giv"es a splitting l(V ) = l(VC )0 l(V )1. Here l(V )0 is the set of elements of l(V ) which can bCe writtenC as a linear⊕ C combinationC of products of even numbers ofCvectors from V , and l(V )1 is the set of elements which can be written as a linear combination of productsC of odd numbers of vectors from V . Note that more succinctly l(V ) is just the quotient of the tensor algebra of V by the ideal generated by v vC v, v 1.