Construction of Parseval wavelets from redundant filter systems

We consider wavelets in L^2(R^d) which have generalized multiresolutions. This means that the initial resolution subspace V_0 in L^2(R^d) is not singly generated. As a result, the representation of the integer lattice Z^d restricted to V_0 has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on R^d can be constructed directly from the generalized wavelet filters.Comment: 34 pages, AMS-LaTeX ("amsproc" document class) v2 changes minor typos in Sections 1 and 4, v3 adds a number of references on GMRA theory and wavelet multiplicity analysis; v4 adds material on pages 2, 3, 5 and 10, and two more reference

The existence problem for dynamics of dissipative systems in quantum probability

Motivated by existence problems for dissipative systems arising naturally in lattice models from quantum statistical mechanics, we consider the following $C^{\ast}$-algebraic setting: A given hermitian dissipative mapping $\delta$ is densely defined in a unital $C^{\ast}$-algebra $\mathfrak{A}$. The identity element in ${\frak A}$ is also in the domain of $\delta$. Completely dissipative maps $\delta$ are defined by the requirement that the induced maps, $(a_{ij})\to (\delta (a_{ij}))$, are dissipative on the $n$ by $n$ complex matrices over ${\frak A}$ for all $n$. We establish the existence of different types of maximal extensions of completely dissipative maps. If the enveloping von Neumann algebra of ${\frak A}$ is injective, we show the existence of an extension of $\delta$ which is the infinitesimal generator of a quantum dynamical semigroup of completely positive maps in the von Neumann algebra. If $\delta$ is a given well-behaved *-derivation, then we show that each of the maps $\delta$ and $-\delta$ is completely dissipative.Comment: 24 pages, LaTeX/REVTeX v. 4.0, submitted to J. Math. Phys.; PACS 02., 02.10.Hh, 02.30.Tb, 03.65.-w, 05.30.-

Discovery of widespread transcription initiation at microsatellites predictable by sequence-based deep neural network

Using the Cap Analysis of Gene Expression (CAGE) technology, the FANTOM5 consortium provided one of the most comprehensive maps of transcription start sites (TSSs) in several species. Strikingly, ~72% of them could not be assigned to a specific gene and initiate at unconventional regions, outside promoters or enhancers. Here, we probe these unassigned TSSs and show that, in all species studied, a significant fraction of CAGE peaks initiate at microsatellites, also called short tandem repeats (STRs). To confirm this transcription, we develop Cap Trap RNA-seq, a technology which combines cap trapping and long read MinION sequencing. We train sequence-based deep learning models able to predict CAGE signal at STRs with high accuracy. These models unveil the importance of STR surrounding sequences not only to distinguish STR classes, but also to predict the level of transcription initiation. Importantly, genetic variants linked to human diseases are preferentially found at STRs with high transcription initiation level, supporting the biological and clinical relevance of transcription initiation at STRs. Together, our results extend the repertoire of non-coding transcription associated with DNA tandem repeats and complexify STR polymorphism

Phase equilibria in the metal-sulfur-oxygen system and selective reduction of metal oxides and sulfides : Part I. The carbothermic reduction and calcination of complex mineral sulfides

Copyright 2006 Elsevier B.V., All rights reserved.The difference in the standard Gibbs free energy for the formation of any two oxides or sulfides is the chemical potential for selective reduction of metals from complex minerals. The magnitude of the Gibbs free energy difference is shown by plotting the univariant relationships for relevant sulfides and oxides. In this investigation, three examples of mineral sulfides are considered, and the experimental results are compared with the predicted thermodynamic calculations. These examples include the reduction conditions for nickel and iron sulfides and pentlandite (Fe,Ni)S and chalcopyrite (CuFeS) minerals. The reduction behavior of mineral sulfides, such as those of nickel, cobalt, iron, and copper, is illustrated by referring to both the sulfide and alloy phase equilibria. In particular, the solution thermodynamic properties of the metallic phase equilibria are featured for determining the physical chemistry of preferential or selective reduction of the metal oxides and sulfides. The mechanism for the reduction of the aforementioned sulfide minerals is explained with the aid of the governing phase equilibria for the calcination process. The results from the carbothermic reduction of sulfide minerals are also compared. The important roles of lime and calcium sulfate in controlling the emission of sulfurous gases during the reduction reaction are explained. A qualitative analysis of reduction reactions of nickel and iron sulfides is reviewed to provide a comparison of the mechanism for complex nickel-bearing minerals. The importance of these results in producing alloy and pure metallic phases is also examined.Peer reviewe