Approximate decoding approaches for network coded correlated data

This paper considers a framework where data from correlated sources are transmitted with the help of network coding in ad hoc network topologies. The correlated data are encoded independently at sensors and network coding is employed in the intermediate nodes in order to improve the data delivery performance. In such settings, we focus on the problem of reconstructing the sources at decoder when perfect decoding is not possible due to losses or bandwidth variations. We show that the source data similarity can be used at decoder to permit decoding based on a novel and simple approximate decoding scheme. We analyze the influence of the network coding parameters and in particular the size of finite coding fields on the decoding performance. We further determine the optimal field size that maximizes the expected decoding performance as a trade-off between information loss incurred by limiting the resolution of the source data and the error probability in the reconstructed data. Moreover, we show that the performance of the approximate decoding improves when the accuracy of the source model increases even with simple approximate decoding techniques. We provide illustrative examples showing how the proposed algorithm can be deployed in sensor networks and distributed imaging applications.

A stochastic principle behind polar properties of condensed molecular matter

A statistical mechanics view leads to the conclusion that polar molecules allowed to populate a degree of freedom for orientational disorder in a condensed phase thermalize into a bi-polar state featuring zero net polarity. In cases of orientational disorder polar order of condensed molecular matter can only exist in corresponding sectors of opposite average polarities. Channel type inclusion compounds, single component molecular crystals, solid solutions, optically anomalous crystals, inorganic ionic crystals, biomimetic crystals and biological tissues investigated by scanning pyroelectric and phase sensitive second harmonic generation microscopy all showed domains of opposite polarities in their final grown state. For reported polar molecular crystal structures it is assumed that kinetic hindrance along one direction of the polar axis is preventing the formation of a bi-polar state, thus allowing for a kinetically controlled mono-domain state. In this review we summarize theoretical and experimental findings leading to far reaching conclusions on the polar state of solid molecular matter. “… no stationary state … of a system has an electrical dipole moment.” P. W. Anderson, Science, 1972, 177, 393.

Involvement of a region of 23S ribosomal RNA of {\it E. coli\/} in decoding of termination codons

Involvement of E. coli 23S ribosomal RNA (rRNA) in decoding of termination codons was first indicated by the characterization of a 23S rRNA mutant that causes UGA-specific nonsense suppression. The work described here was begun to test the hypothesis that more 23S rRNA suppressors of specific nonsense mutations can be isolated and that they would occur non-randomly in the rRNA genes and be clustered in specific, functionally significant regions of rRNA.^ Approximately 2 kilobases of the gene for 23S rRNA were subjected to PCR random mutagenesis and the amplified products screened for suppression of nonsense mutations in trpA. All of the suppressor mutations obtained were located in a thirty-nucleotide part of the GTPase center, a conserved rRNA sequence and structure, and they and others made in that region by site-directed mutagenesis were shown to be UGA-specific in their suppression of termination codon mutations. These results proved the initial hypothesis and demonstrated that a group of nucleotides in this region are involved in decoding of the UGA termination codon. Further, it was shown that limitation of cellular availability or synthesis of L11, a ribosomal protein that binds to the GTPase center rRNA, resulted in suppression of termination codon mutations, suggesting the direct involvement of L11 in termination in vivo.^ Finally, in vivo analysis of certain site-specific mutations made in the GTPase center RNA demonstrated that (a) the G$\cdot$A base pair closing the hexanucleotide hairpin loop was not essential for normal termination, (b) the "U-turn" structure in the 1093 to 1098 hexaloop is critical for normal termination, (c) nucleotides A1095 and A1067, necessary for the binding to ribosomes of thiostrepton, an antibiotic that inhibits polypeptide release factor binding to ribosomes in vitro, are also necessary for normal peptide chain termination in vivo, and (d) involvement of this region of rRNA in termination is determined by some unique subset structure that includes particular nucleotides rather than merely by a general structural feature of the GTPase center.^ This work advances the understanding of peptide chain termination by demonstrating that the GTPase region of 23S rRNA participates in recognition of termination codons, through an associated ribosomal protein and specific conserved nucleotides and structural motifs in its RNA. ^

Functions and intramolecular interactions of ribosomal RNA in decoding of termination codons

Two regions in the 3$\prime$ domain of 16S rRNA (the RNA of the small ribosomal subunit) have been implicated in decoding of termination codons. Using segment-directed PCR random mutagenesis, I isolated 33 translational suppressor mutations in the 3$\prime$ domain of 16S rRNA. Characterization of the mutations by both genetic and biochemical methods indicated that some of the mutations are defective in UGA-specific peptide chain termination and that others may be defective in peptide chain termination at all termination codons. The studies of the mutations at an internal loop in the non-conserved region of helix 44 also indicated that this structure, in a non-conserved region of 16S rRNA, is involved in both peptide chain termination and assembly of 16S rRNA.^ With a suppressible trpA UAG nonsense mutation, a spontaneously arising translational suppressor mutation was isolated in the rrnB operon cloned into a pBR322-derived plasmid. The mutation caused suppression of UAG at two codon positions in trpA but did not suppress UAA or UGA mutations at the same trpA positions. The specificity of the rRNA suppressor mutation suggests that it may cause a defect in UAG-specific peptide chain termination. The mutation is a single nucleotide deletion (G2484$\Delta$) in helix 89 of 23S rRNA (the large RNA of the large ribosomal subunit). The result indicates a functional interaction between two regions of 23S rRNA. Furthermore, it provides suggestive in vivo evidence for the involvement of the peptidyl-transferase center of 23S rRNA in peptide chain termination. The $\Delta$2484 and A1093/$\Delta$2484 (double) mutations were also observed to alter the decoding specificity of the suppressor tRNA lysT(U70), which has a mutation in its acceptor stem. That result suggests that there is an interaction between the stem-loop region of helix 89 of 23S rRNA and the acceptor stem of tRNA during decoding and that the interaction is important for the decoding specificity of tRNA.^ Using gene manipulation procedures, I have constructed a new expression vector to express and purify the cellular protein factors required for a recently developed, realistic in vitro termination assay. The gene for each protein was cloned into the newly constructed vector in such a way that expression yielded a protein with an N-terminal affinity tag, for specific, rapid purification. The amino terminus was engineered so that, after purification, the unwanted N-terminal tag can be completely removed from the protein by thrombin cleavage, yielding a natural amino acid sequence for each protein. I have cloned the genes for EF-G and all three release factors into this new expression vector and the genes for all the other protein factors into a pCAL-n expression vector. These constructs will allow our laboratory group to quickly and inexpensively purify all the protein factors needed for the new in vitro termination assay. (Abstract shortened by UMI.) ^

Decoding Delay Minimization in Inter-Session Network Coding

Intra-session network coding has been shown to offer significant gains in terms of achievable throughput and delay in settings where one source multicasts data to several clients. In this paper, we consider a more general scenario where multiple sources transmit data to sets of clients over a wireline overlay network. We propose a novel framework for efficient rate allocation in networks where intermediate network nodes have the opportunity to combine packets from different sources using randomized network coding. We formulate the problem as the minimization of the average decoding delay in the client population and solve it with a gradient-based stochastic algorithm. Our optimized inter-session network coding solution is evaluated in different network topologies and is compared with basic intra-session network coding solutions. Our results show the benefits of proper coding decisions and effective rate allocation for lowering the decoding delay when the network is used by concurrent multicast sessions.

Computed Ultrasound Tomography in Echo Mode for Imaging Speed of Sound Using Pulse-Echo Sonography: Proof of Principle

The limitations of diagnostic echo ultrasound have motivated research into novel modalities that complement ultrasound in a multimodal device. One promising candidate is speed of sound imaging, which has been found to reveal structural changes in diseased tissue. Transmission ultrasound tomography shows speed of sound spatially resolved, but is limited to the acoustically transparent breast. We present a novel method by which speed-of-sound imaging is possible using classic pulse-echo equipment, facilitating new clinical applications and the combination with state-of-the art diagnostic ultrasound. Pulse-echo images are reconstructed while scanning the tissue under various angles using transmit beam steering. Differences in average sound speed along different transmit directions are reflected in the local echo phase, which allows a 2-D reconstruction of the sound speed. In the present proof-of-principle study, we describe a contrast resolution of 0.6% of average sound speed and a spatial resolution of 1 mm (laterally) × 3 mm (axially), suitable for diagnostic applications.

An Oka principle for equivariant isomorphisms

Let G be a reductive complex Lie group acting holomorphically on normal Stein spaces X and Y, which are locally G-biholomorphic over a common categorical quotient Q. When is there a global G-biholomorphism X → Y? If the actions of G on X and Y are what we, with justification, call generic, we prove that the obstruction to solving this local-to-global problem is topological and provide sufficient conditions for it to vanish. Our main tool is the equivariant version of Grauert's Oka principle due to Heinzner and Kutzschebauch. We prove that X and Y are G-biholomorphic if X is K-contractible, where K is a maximal compact subgroup of G, or if X and Y are smooth and there is a G-diffeomorphism ψ : X → Y over Q, which is holomorphic when restricted to each fibre of the quotient map X → Q. We prove a similar theorem when ψ is only a G-homeomorphism, but with an assumption about its action on G-finite functions. When G is abelian, we obtain stronger theorems. Our results can be interpreted as instances of the Oka principle for sections of the sheaf of G-biholomorphisms from X to Y over Q. This sheaf can be badly singular, even for a low-dimensional representation of SL2(ℂ). Our work is in part motivated by the linearisation problem for actions on ℂn. It follows from one of our main results that a holomorphic G-action on ℂn, which is locally G-biholomorphic over a common quotient to a generic linear action, is linearisable.

Testing the Weak Equivalence Principle with an antimatter beam at CERN

The goal of the AEgIS experiment is to measure the gravitational acceleration of antihydrogen – the simplest atom consisting entirely of antimatter – with the ultimate precision of 1%. We plan to verify the Weak Equivalence Principle (WEP), one of the fundamental laws of nature, with an antimatter beam. The experiment consists of a positron accumulator, an antiproton trap and a Stark accelerator in a solenoidal magnetic field to form and accelerate a pulsed beam of antihydrogen atoms towards a free-fall detector. The antihydrogen beam passes through a moir ́e deflectometer to measure the vertical displacement due to the gravitational force. A position and time sensitive hybrid detector registers the annihilation points of the antihydrogen atoms and their time-of-flight. The detection principle has been successfully tested with antiprotons and a miniature moir ́e deflectometer coupled to a nuclear emulsion detector.