A connection between multiresolution wavelet theory of scale N and representations of the Cuntz algebra O_N

In this paper we give a short survey of a connection between the theory of wavelets in L^2(R) and certain representations of the Cuntz algebra on L^2(T).Comment: 13 pages, AMS-TeX version 2.1, uses LaTeX circle font lcircle10. To appear in J. Roberts, ed., Proceedings of the Rome Conference on Operator Algebras and Quantum Field Theory. Survey article; for complete proofs see funct-an/9612002 and funct-an/9612003 by the same author

Convergence of the cascade algorithm at irregular scaling functions

The spectral properties of the Ruelle transfer operator which arises from a given polynomial wavelet filter are related to the convergence question for the cascade algorithm for approximation of the corresponding wavelet scaling function.Comment: AMS-LaTeX; 38 pages, 10 figures comprising 42 EPS diagrams; some diagrams are bitmapped at 75 dots per inch; for full-resolution bitmaps see ftp://ftp.math.uiowa.edu/pub/jorgen/convcasc

Wavelet filters and infinite-dimensional unitary groups

In this paper, we study wavelet filters and their dependence on two numbers, the scale N and the genus g. We show that the wavelet filters, in the quadrature mirror case, have a harmonic analysis which is based on representations of the C^*-algebra O_N. A main tool in our analysis is the infinite-dimensional group of all maps T -> U(N) (where U(N) is the group of all unitary N-by-N matrices), and we study the extension problem from low-pass filter to multiresolution filter using this group.Comment: AMS-LaTeX; 30 pages, 2 tables, 1 picture. Invited lecture by Jorgensen at International Conference on Wavelet Analysis and Its Applications, Zhongshan University, Guangzhou, China, in November 1999. Changes: Some references have been added and some technical points in several proofs have been clarified in this new revised versio

Iterated function systems and permutation representations of the Cuntz algebra

We study a class of representations of the Cuntz algebras O_N, N=2,3,..., acting on L^2(T) where T=R/2\pi Z. The representations arise in wavelet theory, but are of independent interest. We find and describe the decomposition into irreducibles, and show how the O_N-irreducibles decompose when restricted to the subalgebra UHF_N\subset O_N of gauge-invariant elements; and we show that the whole structure is accounted for by arithmetic and combinatorial properties of the integers Z. We have general results on a class of representations of O_N on Hilbert space H such that the generators S_i as operators permute the elements in some orthonormal basis for H. We then use this to extend our results from L^2(T) to L^2(T^d), d>1 ; even to L^2(\mathbf{T}) where \mathbf{T} is some fractal version of the torus which carries more of the algebraic information encoded in our representations.Comment: 84 pages, 11 figures, AMS-LaTeX v1.2b, full-resolution figures available at ftp://ftp.math.uiowa.edu/pub/jorgen/PermRepCuntzAlg in eps files with the same names as the low-resolution figures included her

Spectral asymptotics of periodic elliptic operators

We demonstrate that the structure of complex second-order strongly elliptic operators $H$ on ${\bf R}^d$ with coefficients invariant under translation by ${\bf Z}^d$ can be analyzed through decomposition in terms of versions $H_z$, $z\in{\bf T}^d$, of $H$ with $z$-periodic boundary conditions acting on $L_2({\bf I}^d)$ where ${\bf I}=[0,1>$. If the semigroup $S$ generated by $H$ has a H\"older continuous integral kernel satisfying Gaussian bounds then the semigroups $S^z$ generated by the $H_z$ have kernels with similar properties and $z\mapsto S^z$ extends to a function on ${\bf C}^d\setminus\{0\}$ which is analytic with respect to the trace norm. The sequence of semigroups $S^{(m),z}$ obtained by rescaling the coefficients of $H_z$ by $c(x)\to c(mx)$ converges in trace norm to the semigroup $\hat{S}^z$ generated by the homogenization $\hat{H}_z$ of $H_z$. These convergence properties allow asymptotic analysis of the spectrum of $H$.Comment: 27 pages, LaTeX article styl

Tournaments with prize-setting agents

In many tournaments it is the contestants themselves who determine reward allocation. Labor-union members bargain over wage distribution, and many firms allow self-managed teams to freely determine internal resource allocation, incentive structure, and division of labour. We analyze, and test experimentally, a rank-order tournament where heterogenous agents determine the spread between winner prize and looser prize. We investigate the relationship between prize spread, uncertainty (i.e. noise between e¤ort and performance), heterogeneity and effort. The paper challenges well-known results from tournament theory. We find that a large prize spread is associated with low degree of uncertainty and high degree of heterogeneity, and that heterogeneity triggers effort. By and large, our real-effort experiment supports the theoretical predictions.Rank-order tournament; prize spread; ability-difference

New oral antithrombotics: focus on dabigatran, an oral, reversible direct thrombin inhibitor for the prevention and treatment of venous and arterial thromboembolic disorders

Venous thromboembolism, presenting as deep vein thrombosis or pulmonary embolism, is a major challenge for health care systems. It is the third most common vascular disease after coronary heart disease and stroke, and many hospitalized patients have at least one risk factor. In particular, patients undergoing hip or knee replacement are at risk, with an incidence of asymptomatic deep vein thrombosis of 40%–60% without thromboprophylaxis. Venous thromboembolism is associated with significant mortality and morbidity, with patients being at risk of recurrence, post-thrombotic syndrome, and chronic thromboembolic pulmonary hypertension. Arterial thromboembolism is even more frequent, and atrial fibrillation, the most common embolic source (cardiac arrhythmia), is associated with a five-fold increase in the risk of stroke. Strokes due to atrial fibrillation tend to be more severe and disabling and are more often fatal than strokes due to other causes. Currently, recommended management of both venous and arterial thromboembolism involves the use of anticoagulants such as coumarin and heparin derivatives. These agents are effective, although have characteristics that prevent them from providing optimal anticoagulation and convenience. Hence, new improved oral anticoagulants are being investigated. Dabigatran is a reversible, direct thrombin inhibitor, which is administered as dabigatran etexilate, the oral prodrug. Because it is the first new oral anticoagulant that has been licensed in many countries worldwide for thromboprophylaxis following orthopedic surgery and for stroke prevention in patients with atrial fibrillation, this compound will be the main focus of this review. Dabigatran has been investigated for the treatment of established venous thromboembolism and prevention of recurrence in patients undergoing hip or knee replacement, as well as for stroke prevention in atrial fibrillation patients with a moderate and high risk of stroke

Non-stationarity of isomorphism between AF algebras defined by stationary Bratteli diagrams

We first study situations where the stable AF-algebras defined by two square primitive nonsingular incidence matrices with nonnegative integer matrix elements are isomorphic even though no powers of the associated automorphisms of the corresponding dimension groups are isomorphic. More generally we consider neccessary and sufficient conditions for two such matrices to determine isomorphic dimension groups. We give several examples.Comment: 16 page