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Complexity and Second Moment of the Mathematical Theory of Communication [article]

Hsin-Po Wang
2021 arXiv   pre-print
The performance of an error correcting code is evaluated by its error probability, rate, and en/decoding complexity.  ...  The framework that generates codes and the machinery that evaluates codes can be extended to many other scenarios in network information theory.  ...  Shannon founded the theory of information with an article titled A Mathematical Theory of Communication, which was later republished under the name The Mathematical Theory of Communication to reflect its  ... 
arXiv:2107.06420v1 fatcat:q35kl44i45b5xcybodesjaxzwy

Page 1143 of Mathematical Reviews Vol. 12, Issue 11 [page]

1951 Mathematical Reviews  
The reader who has mastered the book will comprehend the use of complex analysis in physics and related fields; he will also be well equipped for further study of complex function theory.  ...  . $7.00 A combined text and reference work, this book presents basic statistical theory, including the elementary princi- ples of probability, population and sampling theory with moment-generating functions  ... 

Page 564 of American Mathematical Society. Transactions of the American Mathematical Society Vol. 85, Issue 2 [page]

1957 American Mathematical Society. Transactions of the American Mathematical Society  
Chern, Department of Mathematics, University of Chicago, Chicago 37, Ill. All other communications to the editors should be ad to the Managing Editor, W. S.  ...  REID On singularities of solutions of certain differential equations in three variables. By STEFAN BERGMAN The differential equations of birth-and-death processes, and the Stieltjes moment problem.  ... 

Preface to the Special Issue Mathematical modelling for complex systems: multi-agents methods

Elena De Angelis
2018 Communications in Applied and Industrial Mathematics  
New ideas and new mathematical methods are needed to understand the main features of the behaviour of such living, and hence, complex systems: as a consequence, the interest of mathematicians in new structures  ...  The modeling approach is based on the tools of the so called kinetic theory of active particles.  ...  Acknowledgements I would like to point out here the continuous support and the very helpful assistance that I and all the Authors have received from Giorgio Fotia and the whole CAIM editorial board.  ... 
doi:10.2478/caim-2018-0019 fatcat:hjvtenue6fb4pdhpc5tx7yyiva

Special issues on moment methods in kinetic gas theory

Manuel Torrilhon
2009 Continuum Mechanics and Thermodynamics  
The first moments are the conservative variables of gas dynamics, the density, the momentum density and total energy density. Obviously, the motivation is that Communicated by M. Torrilhon M.  ...  This two-volume special issue of 'Continuum Mechanics and Thermodynamics' is the result of an international meeting on moment methods in kinetic gas theory that took place in November 2008 at ETH Zurich  ...  They also demonstrate a close link between moment equations and the constitutive theory of thermodynamics based on the exploitation of the entropy law.  ... 
doi:10.1007/s00161-009-0129-x fatcat:a6dgo5ukbre5fdccr5cjcjcgau

Page 1231 of Mathematical Reviews Vol. , Issue 95b [page]

1995 Mathematical Reviews  
(A) (Hermite’s parameter) and the shaping gain y,(A) (or equivalently the normalized second moment G(A)) are geometrical invariants of a lattice A that are figures of merit for coding and quantizing, respectively  ...  “These quantities appear in low-order terms of the series ex- 94A .Communication, information 95b:94008 pansions of the normalized (relevant) theta series of A and the normalized moment-generating function  ... 

Semiotics in Theory and Practice in Mathematics Education [chapter]

Norma Presmeg, Luis Radford, Wolff-Michael Roth, Gert Kadunz
2016 ICME-13 Topical Surveys  
(González Rey 2011b, p. 259) The second moment goes roughly from 1927 to 1931. It is in the second moment that we find Vygotsky elaborating his concept of sign.  ...  We can turn now to the second semiotic dimension in the theory of objectification.  ... 
doi:10.1007/978-3-319-31370-2_2 fatcat:c4i3c66r5zb5hgzy3chsfbakmm

Page 260 of Mathematical Reviews Vol. 9, Issue 5 [page]

1948 Mathematical Reviews  
These second order equations involve terms describing the magnetic moment of the meson.  ...  In addition to the proceedings of the Congress, this volume contains forty-one lectures, which have been re- viewed separately in Mathematical Reviews. Communications on Applied Mathematics.  ... 

Page 3116 of Mathematical Reviews Vol. 58, Issue 4 [page]

1979 Mathematical Reviews  
Yao, K. 58 #20778 Moment space error bounds in digital communication systems. Communication systems and random process theory (Proc. 2nd NATO Advanced Study Inst., Darlington, 1977), pp. 605-618.  ...  We consider # bounding technique based on an isomorphism theorem from the } theory of moment spaces to evaluate upper and lower bounds W0 the error probability.  ... 

Page 610 of Mathematical Reviews Vol. 26, Issue 3 [page]

1963 Mathematical Reviews  
In both papers the statistical theory of the dis- tribution of the complex random vector £’ =(Z, ---, Zp) is developed.  ...  In the second paper the distribution of the determinant of z, is derived.  ... 

Analyzing the Impact of Video Representation Complexity on Preservice Teacher Noticing of Children's Thinking

Alison Superfine, John Bragelman
2018 Eurasia Journal of Mathematics, Science and Technology Education  
Drawing from cognitive load theory, we developed a rubric to code the complexity of the salient teaching and learning events captured in video, and analyzed the relationship between video complexity and  ...  Despite the growing research base on preservice teacher noticing of children's mathematical thinking in video, few, if any studies consider the complex nature of the video representations themselves.  ...  The mathematical content includes place value, whole and rational number operations, proportional reasoning, and certain aspects of number theory.  ... 
doi:10.29333/ejmste/99501 fatcat:akhkn2nh3vfcfkxl4givp6ymza

Proof, Proving, and Teacher-Student Interaction: Theories and Contexts [chapter]

Keith Jones, Patricio Herbst
2011 New ICMI Studies Series  
Balacheff goes on to consider the didactical complexity of learning and teaching mathematical proof by analyzing the gap between knowing mathematics and proving in mathematics.  ...  As such, mathematics classroom communities involve students in communicating their reasoning and in building norms and representations that provide the necessary structures for mathematical proof to have  ...  Thus, the second key hypothesis is that the work of the teacher includes managing activities and objects within two different timescales: the work done moment-to-moment (at the scale of the utterance)  ... 
doi:10.1007/978-94-007-2129-6_11 fatcat:o6mqtijp65hsbmcat5jmtxqnne

Ronald R. Kline, The Cybernetics Moment: or Why We Call Our Age the Information Age

Lukas Miller
2017 Canadian Journal of Academic Librarianship  
, and the highly mathematical targeting computer as a singular cohesive entity.  ...  This new way of thinking and looking at the world enabled a new conceptualization of organisms and machines (or technology) as information-feedback systems, each with varying methods of communication and  ...  Kline uses clear wording and provides simple models to explain many of the complex mathematical formulas and theories that form the basis of cybernetics (Wiener's Cybernetics is described by Kline as "  ... 
doi:10.33137/cjal-rcbu.v2.27267 fatcat:lesoygazs5cphplrat6hzydycu

The Construction and Globalization of the Knowlege Base in Interhuman Communication Systems

Loet Leydesdorff
2003 Canadian Journal of Communication  
Abstract: The relationship between the knowledge base and the globalization of communication systems is discussed from the perspective of communication theory.  ...  At the first level information is exchanged and provided with meaning, and at the second level meaning can reflexively be communicated.  ...  Shannon (1948) defined the uncertainty of information as equal to the probabilistic entropy of the communication system.  ... 
doi:10.22230/cjc.2003v28n3a1372 fatcat:2wfny3illra4fmmw45u5wczym4

Page 301 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 6, Issue [page]

1900 American Mathematical Society. Bulletin of the American Mathematical Society  
The chapter considers in turn projec- tions, moments, systems of segments, couples, the theory of the right line, and concludes with a beautiful application of the theory of complexes to systems of segments  ...  theory of linear complexes and that of the displacement of a solid, determination of a continuous motion when the rotations are known, and inverse move- ment.  ... 
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