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K-theory for operator algebras

by Bruce Blackadar - Mathematical Sciences Research Institute Publications , 1998
"... p. XII line-5: since p. 1-2: I blew this simple formula: should be α = −〈ξ, η〉/〈η, η〉. p. 2 I.1.1.4: The Riesz-Fischer Theorem is often stated this way today, but neither Riesz nor Fischer (who worked independently) phrased it in terms of completeness of the orthogonal system {e int}. If [a, b] is a ..."
Abstract - Cited by 558 (0 self) - Add to MetaCart
space is not σ-finite. p. 13: add after I.2.6.16: I.2.6.17. If X is a compact subset of C not containing 0, and k ∈ N, there is in general no bound on the norm of T −1 as T ranges over all operators with ‖T ‖ ≤ k and σ(T) ⊆ X. For example, let Sn ∈ L(l 2) be the truncated shift: Sn(α1, α2,...) = (0

The fundamental properties of natural numbers

by Grzegorz Bancerek - Journal of Formalized Mathematics , 1989
"... Summary. Some fundamental properties of addition, multiplication, order relations, exact division, the remainder, divisibility, the least common multiple, the greatest common divisor are presented. A proof of Euclid algorithm is also given. MML Identifier:NAT_1. WWW:http://mizar.org/JFM/Vol1/nat_1.h ..."
Abstract - Cited by 688 (73 self) - Add to MetaCart
.html The articles [4], [6], [1], [2], [5], and [3] provide the notation and terminology for this paper. A natural number is an element of N. For simplicity, we use the following convention: x is a real number, k, l, m, n are natural numbers, h, i, j are natural numbers, and X is a subset of R

The irreducibility of the space of curves of given genus

by P. Deligne, D. Mumford - Publ. Math. IHES , 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~- ..."
Abstract - Cited by 506 (2 self) - Add to MetaCart
finite algebraic extension L of K such

An introduction to Kolmogorov Complexity and its Applications: Preface to the First Edition

by Ming Li, Paul Vitanyi , 1997
"... This document has been prepared using the L a T E X system. We thank Donald Knuth for T E X, Leslie Lamport for L a T E X, and Jan van der Steen at CWI for online help. Some figures were prepared by John Tromp using the xpic program. The London Mathematical Society kindly gave permission to reproduc ..."
Abstract - Cited by 2138 (120 self) - Add to MetaCart
This document has been prepared using the L a T E X system. We thank Donald Knuth for T E X, Leslie Lamport for L a T E X, and Jan van der Steen at CWI for online help. Some figures were prepared by John Tromp using the xpic program. The London Mathematical Society kindly gave permission

Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition

by Y. C. Pati, R. Rezaiifar, P. S. Krishnaprasad - in Conference Record of The Twenty-Seventh Asilomar Conference on Signals, Systems and Computers , 1993
"... In this paper we describe a recursive algorithm to compute representations of functions with respect to nonorthogonal and possibly overcomplete dictionaries of elementary building blocks e.g. aiEne (wa.velet) frames. We propoeea modification to the Matching Pursuit algorithm of Mallat and Zhang (199 ..."
Abstract - Cited by 637 (1 self) - Add to MetaCart
recursively. where fk is the current approximation, and Rkf the current residual (error). Using initial values ofR0f = 1, fo = 0, and k = 1, the MP algorithm is comprised of the following steps,.,.41) Compute the inner-products {(Rkf,z)}. (H) Find flki such that (III) Set, I(R*f,1:n 1+,)l asupl

The rate-distortion function for source coding with side information at the decoder

by Aaron D. Wyner, Jacob Ziv - IEEE Trans. Inform. Theory , 1976
"... Abstract-Let {(X,, Y,J}r = 1 be a sequence of independent drawings of a pair of dependent random variables X, Y. Let us say that X takes values in the finite set 6. It is desired to encode the sequence {X,} in blocks of length n into a binary stream*of rate R, which can in turn be decoded as a seque ..."
Abstract - Cited by 1060 (1 self) - Add to MetaCart
sequence { 2k}, where zk E %, the reproduction alphabet. The average distorjion level is (l/n) cl = 1 E[D(X,,z&, where D(x, $ 2 0, x E I, 2 E J, is a pre-assigned distortion measure. The special assumption made here is that the decoder has access to the side information {Yk}. In this paper we determine

Loopy belief propagation for approximate inference: An empirical study. In:

by Kevin P Murphy , Yair Weiss , Michael I Jordan - Proceedings of Uncertainty in AI, , 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" -the use of Pearl's polytree algorithm in a Bayesian network with loops -can perform well in the context of error-correcting codes. The most dramatic instance of this is the near Shannon-limit performanc ..."
Abstract - Cited by 676 (15 self) - Add to MetaCart
X passes to its parent U; is given by: and the message X sends to its child Y j is given by: k;Cj For noisy-or links between parents and children, there exists an analytic expression for 1r( x) and Ax ( u;) that avoids the exhaustive enumeration over parent config urations We made a slight

On the bursty evolution of Blogspace

by Ravi Kumar, Jasmine Novak, Prabhakar Raghavan, Andrew Tomkins , 2003
"... O)( 1 #$ #+&PQ+&,0,/RP 2 ":9:0/ +%&P &.F0, )& ;)S O)( 1 #$ #+&PQ+&,0,/RP 2 ":9:0/ +% # O,<&7& =1 P &7"U;(Z ;>A@CB;D,[\D]K,D?^_ B`Bba]@C>Ac >AG8H$^2d)@C]E 9='0,*+82 &e " & Q (T0 U;Ub%&7*',#$ %& :3 Q ..."
Abstract - Cited by 365 (8 self) - Add to MetaCart
Q+ #$ f" L ;&Vg"L0 ,M' (Fhji_E KkI+H$^2D9" 0 O (` lV P gmA)fn i_E K/o3qpr%+N8%+*s&#$ V# t /M- &U5u 7*wv x)y z{V&.+L U; P| x)z}l P 3~10/)O&U; P)2 "; b" l P l*` 5)% U5u&0 =)7*& ( U; 28900-33320 3 &U;r82 U; 3!j" L8%=+*b

On the geometry and cohomology of some simple Shimura varieties

by Michael Harris, Richard Taylor , 1999
"... This paper has twin aims. On the one hand we prove the local Langlands conjecture for GL n over a p-adic field. On the other hand in many cases we are able to identify the action of the decomposition group at a prime of bad reduction on the l-adic cohomology of the "simple" Shimura varieti ..."
Abstract - Cited by 333 (19 self) - Add to MetaCart
This paper has twin aims. On the one hand we prove the local Langlands conjecture for GL n over a p-adic field. On the other hand in many cases we are able to identify the action of the decomposition group at a prime of bad reduction on the l-adic cohomology of the "simple" Shimura

Alternative implementations of two-level adaptive branch prediction

by Tse-yu Yeh, Yale N. Patt - In Proceedings of the 19th International Symposium on Computer Architecture (ISCA-19 , 1992
"... As the issue rate and depth of pipelining of high performance Superscalar processors increase, the importance of an excellent branch predictor becomes more vital to delivering the potential performance of a wide-issue, deep pipelined microarchitecture. We propose a new dynamic branch predictor (Two- ..."
Abstract - Cited by 327 (22 self) - Add to MetaCart
-Level Adaptive Branch Prediction) that achieves substantially higher accuracy than any other scheme reported in the literature. The mechanism uses two levels of branch history information to make predictions, the history of the last L branches encountered, and the branch behavior for the last s occurrences
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