Nearly tight frames and space-frequency analysis on compact manifolds

Let M be a smooth compact oriented Riemannian manifold of dimension n without boundary, and let Δ be the Laplace–Beltrami operator on M. Say , and that f (0)  =  0. For t  >  0, let K _t (x, y) denote the kernel of f (t ² Δ). Suppose f satisfies Daubechies’ criterion, and b  >  0. For each j, write M as a disjoint union of measurable sets E _j,k with diameter at most ba ^j , and measure comparable to if ba ^j is sufficiently small. Take x _j,k ∈ E _j,k . We then show that the functions form a frame for (I  −  P)L ²(M), for b sufficiently small (here P is the projection onto the constant functions). Moreover, we show that the ratio of the frame bounds approaches 1 nearly quadratically as the dilation parameter approaches 1, so that the frame quickly becomes nearly tight (for b sufficiently small). Moreover, based upon how well-localized a function F ∈ (I  −  P)L ² is in space and in frequency, we can describe which terms in the summation are so small that they can be neglected. If n  =  2 and M is the torus or the sphere, and f (s)  =  se ^−s (the “Mexican hat” situation), we obtain two explicit approximate formulas for the φ _j,k , one to be used when t is large, and one to be used when t is small. A. Mayeli was partially supported by the Marie Curie Excellence Team Grant MEXT-CT-2004-013477, Acronym MAMEBIA.     

Joint QoS control for video streaming over wireless multihop networks: A cross-layer approach

In this paper, we propose a novel cross-layer framework for jointly controlling and coding for multiple video streams in wireless multihop networks. At first, we develop a cross-layer flow control algorithm that works at the medium access control (MAC) layer to adjust each link's persistence probability and at the transport layer to adjust flow rates. This proposal is designed in a distributed manner that is amenable to online implementation for wireless networks, and then, a rate-distortion optimized joint source-channel coding (JSCC) approach for error-resilient scalable encoded video is presented, in which the video is encoded into multiple independent streams and each stream is assigned forward error correction (FEC) codes to avoid error propagation. Furthermore, we integrate the JSCC with the specific flow control algorithm, which optimally applies the appropriate channel coding rate given the constraints imposed by the transmission rate obtained from the proposed flow control algorithm and the prevailing channel condition. Simulation results demonstrate the merits and the need for joint quality of service (QoS) control in order to provide an efficient solution for video streaming over wireless multihop networks.     

Accurate first-principles detailed-balance determination of auger recombination and impact ionization rates in semiconductors

The technologically important prediction of Auger recombination lifetimes in semiconductors is addressed by means of a fully first-principles formalism, based on precise energy bands and wave functions provided by the full-potential linearized augmented plane wave code. The minority carrier Auger lifetime is determined by two related approaches: (i) a direct evaluation within Fermi's golden rule, and (ii) an indirect evaluation, based on a detailed balance formulation combining Auger recombination and its inverse process, impact ionization, in a unified framework. Lifetimes determined with the direct and indirect methods show excellent consistency between them (i) for n-doped GaAs and (ii) with measured values for GaAs and InGaAs. This indicates the computational formalism as a new sensitive tool for use in materials performance optimization.     

The crystal structure of the Cu+ ion conductor, (C5H5NH)2Cu5Br7

(C₅H₅NH)₂Cu₅Br₇, in which (C₅H₅NH)⁺ is the pyridinium ion, belongs to space group P2₁2₁2₁ with Z = 4 and a = 13.09 ± 0.03 Å, b = 14.04 ± 0.03 Å, c = 11.78 ± 0.02Å. The 20 Cu⁺ ions are distributed non-uniformly over 52 tetrahedral sites. The bromide tetrahedra share faces in such a manner that undulating channels are formed in the [100] and [010] directions, and right- and left-handed helical channels are formed in the c-direction. The channels are interconnected, thereby forming a three-dimensional solid electrolyte. A detailed examination of the conduction pathways and of Cu⁺ ion site occupancies leads to the predictions that σ₂ (|b) should be somewhat greater than σ₁ (|a) but σ₃ (|c) should be substantially less than σ₁. (σ_i is the specific conductivity in the ith direction.) The ratio of available sites to current carriers and the percentage of unit cell volume attributable to the conduction pathways are both rather low and the average conductivity is rather high relative to AgI-based solid electrolytes.     

Government policy as to AT&T and the BOCs: the next 5 years

The author discusses the transition caused by the advent of competition and divestiture of AT&T. He predicts that in the next five years, that transitional period will probably end for AT&T, which would then be effectively deregulated, and that difficult transitional problems with the regional Bell Operating Companies (BOCs) will continue. He argues that US governmental policy in dealing with those problems will continue to be diffused and confused     

K(A,B,I): II

The KABI conjecture states that double relative K-theory and cyclic homology agree, at least in characteristic zero. We show that K ₂(A, B, I) maps onto HC ₁ (A, B, I) whenever A B is a map of Q-algebras and I BIB. We also reinterpret the KABI conjecture in terms of the injectivity of the inverse limit of the map from NK(A, B, I) to the inverse limit of the truncated polynomial versions of NK(A, B, I).Supported by National Science Foundation Grant RII — 8700009.Partially supported by National Science Foundation Grants DMS — 8503018 and 8803497.     

Inhibition of cell proliferation,invasion and migration by the cardenolides digitoxigenin monodigitoxoside and convallatoxin in human lung cancer cell line

Cardiac glycosides consist of a large family of naturally derived compounds that are clinically used to treat congestive heart failure, and also present anticancer properties. In this study, the cytotoxic effects of two cardenolides, digitoxigenin monodigitoxoside (DGX) and convallatoxin (CON) were screened in four human tumour cell lines. Both compounds showed anti-proliferative effects in all tumour cells, at nanomolar concentrations. Since the human lung cancer cell line A549 was the most sensitive, we investigated the anti-proliferative, anti-migratory and anti-invasive effects of these cardenolides. DGX and CON reduced A549 cell migration, being able to reduce more than 90% of cell invasion. Their effects on the expression of key regulators of metastatic mechanism showed decreased levels of MMP-2, MMP-9 and p-FAK. Both compounds also presented low toxicity for healthy cells. Finally, this work provides the first insights into the effects of these cardenolides on key steps of lung cancer metastasis.     

Low-temperature phase transitions in (C5H5NH)Ag5I6

The solid electrolyte (C₅H₅NH)Ag₅I₆ undergoes two low-temperature transitions, probably associated with the ordering of the pyridinium ions. The two phases are monoclinic and have structures closely related to that of the hexagonal phase at 240°K. The transition to the γ-phase at 230°K is second order, and that from the γ- to the δ-phase at 180°K, first order. In the γ-phase, the monoclinic a and b axes correspond to the orthohexagonal B and A axes, respectively; in the δ-phase, the correspondence is reversed. If the pyridinium ions order in the γ-phase, its space group is most probably Cc. If the pyridinium ions are ordered in the δ-phase, the N atoms must lie on twofold axes in $\text{C2}\text{c}$, but the space group Cc is also possible for this phase.