Journal ArticleDOI
The theory of information and coding: A mathematical framework for communication
G. Longo
- Vol. 67, Iss: 10, pp 1467-1468
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The stochastic integral with respect to processes with values in a reflexive Banach space, Theor.Abstract:
14. M. Metivier, The stochastic integral with respect to processes with values in a reflexive Banach space, Theor. Probability 19 (1974), 758-787. 15. M. Metivier and G. Pistone, Une formule d'isométrie pour r intégrale stochastique Hilbertienne et équations d'évolution linéaires stochastiques, Z. Wahrscheinlicnkeitstheorie und Verw. Gebiete 33 (1975), 1-18. 16. P. A. Meyer, A decomposition theorem for supermartingales, Illinois J. Math. 6 (1962), 193-205. 17. , Intégrales stochastiques. IV, Lecture Notes in Math., vol. 39, Springer-Verlag, Berlin and New York, 1967, pp. 142-162. 18. , Un cours sur les intégrales stochastiques, Lecture Notes in Math., vol. 511, Springer-Verlag, Berlin and New York, 1976, pp. 245-400. 19. , Intégrales Hilbertiennes, Lecture Notes in Math., vol. 581, Springer-Verlag, Berlin and New York, 1977, pp. 446-461. 20. R. E. A. C. Paley, N. Wiener and A. Zygmund, Notes on random functions, Math. Z. 37 (1933), 647-668. 21. J. Pellaumail, Sur lintégrale stochastique et la décomposition de Doob-Meyer, Asterique 9 (1973), 1-125. 22. P. E. Protter, Markov solutions of stochastic differential equations, TL Wahrscheinlichkeitstheorie und Verw. Gebiete 41 (1977), 39-58. 23. , A comparison of stochastic integrals, Ann. Probability (to appear). 24. R. L. Stratonovich, A new representation for stochastic integrals and equations, SIAM. J. Control 4 (1966), 362-371. 25. N. Wiener, Differential-space, J. Math, and Physics 2 (1923), 131-174.read more
Citations
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Journal ArticleDOI
Giving form to social cloud storage through experimentation: Issues and insights
Raul Gracia-Tinedo,Marc Sanchez-Artigas,Aleix Ramírez,Adrián Moreno-Martínez,Xavier León,Pedro García-López +5 more
TL;DR: This paper proposes to leverage digital relationships between individuals to form a dynamic ''social cloud'' for storage and proposes to the members of the social cloud the use of online storage services like Amazon S3 to store data and improve data availability.
Posted Content
Partitions and Objective Indefiniteness in Quantum Mechanics
TL;DR: In this paper, the authors show how the mathematics of set partitions can be transported in a natural way to complex vector spaces where it yields the mathematical machinery of quantum mechanics, and then the machinery of QM can be transferred the other way down to set-like vector spaces over ℤ₂ yielding a rather fulsome "toy" or pedagogical model of "quantum mechanics over sets."
Posted Content
The Quantum Logic of Direct-Sum Decompositions
TL;DR: In this article, the quantum logic of direct-sum decompositions of a finite-dimensional vector space is studied in the context of quantum mechanics over sets (QM/Sets).
Journal ArticleDOI
Quantum Mechanics Over Sets
TL;DR: In this article, a theory of quantum mechanics over sets is proposed, which is based on the notion of "objective indefiniteness", a program that grew out the recent development of the logic of partitions mathematically dual to the usual Boolean logic of subsets.
Journal ArticleDOI
The capacity-cost function of discrete additive noise channels with and without feedback
Fady Alajaji,N. Whalen +1 more
TL;DR: It is shown that for a particular feedback encoding strategy and a class of Markov noise sources, the lower bound to C/sub FB/(/spl beta/) is strictly greater than C( /spl beta/), demonstrating that feedback can increase the capacity-cost function of discrete channels with memory.
References
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Book
Elements of information theory
Thomas M. Cover,Joy A. Thomas +1 more
TL;DR: The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.
Journal ArticleDOI
Good error-correcting codes based on very sparse matrices
TL;DR: It is proved that sequences of codes exist which, when optimally decoded, achieve information rates up to the Shannon limit, and experimental results for binary-symmetric channels and Gaussian channels demonstrate that practical performance substantially better than that of standard convolutional and concatenated codes can be achieved.
Journal ArticleDOI
Vector quantization in speech coding
John Makhoul,S. Roucos,H. Gish +2 more
TL;DR: This tutorial review presents the basic concepts employed in vector quantization and gives a realistic assessment of its benefits and costs when compared to scalar quantization, and focuses primarily on the coding of speech signals and parameters.
Journal ArticleDOI
Finding the Number of Clusters in a Dataset
TL;DR: A simple, yet powerful nonparametric method for choosing the number of clusters based on distortion, a quantity that measures the average distance, per dimension, between each observation and its closest cluster center, is developed.
Journal ArticleDOI
On channel capacity per unit cost
TL;DR: It is shown that, if the input alphabet contains a zero-cost symbol, then the capacity per unit cost admits a simple expression as the maximum normalized divergence between two conditional output distributions.