On the Growth Rate of the Weight Distribution of Irregular Doubly-Generalized LDPC Codes

In this paper, an expression for the asymptotic growth rate of the number of small linear-weight codewords of irregular doubly-generalized LDPC (D-GLDPC) codes is derived. The expression is compact and generalizes existing results for LDPC and generalized LDPC (GLDPC) codes. Assuming that there exist check and variable nodes with minimum distance 2, it is shown that the growth rate depends only on these nodes. An important connection between this new result and the stability condition of D-GLDPC codes over the BEC is highlighted. Such a connection, previously observed for LDPC and GLDPC codes, is now extended to the case of D-GLDPC codes.Comment: 10 pages, 1 figure, presented at the 46th Annual Allerton Conference on Communication, Control and Computing (this version includes additional appendix

The roles and regulation of ubiquitin/ubiquitin-like protein conjugation pathways in responses to oxidative stress in Schizosaccharomyces pombe

PhD ThesisUbiquitin and ubiquitin-like proteins (Ubls) are conjugated to proteins to regulate activity, stability, localisation or function. Ubiquitin/Ubl conjugation pathways are highly conserved in eukaryotes, and usually involve activating enzymes (E1s) and conjugating enzymes (E2s) specific for each ubiquitin/Ubl. Many studies have suggested that ubiquitin/Ubl conjugation pathways are important for oxidative stress resistance. However, there is much to learn regarding the roles of these pathways in oxidative stress responses. Additionally, limited studies in mammalian cells and yeast have indicated that certain E1s and E2s are redox-regulated, although how this relates to stress resistance is largely unclear, and these regulatory mechanisms have never been shown to be conserved in eukaryotes. Here, the roles and regulation of ubiquitin/Ubl conjugation pathways in responses to oxidative stress are investigated in Schizosaccharomyces pombe. Firstly, while our previous research has shown that the budding yeast E2, Cdc34, is redox-regulated, it was unclear whether ubiquitination is redox-regulated in other organisms. Results presented here show that the fission yeast Cdc34 homologue, Ubc15, is redox-regulated, suggesting that redox regulation of specific ubiquitination events may be conserved. Furthermore, Ubc15 is important for resistance to oxidative stress in S. pombe. Secondly, the Ubl Urm1 is found to be important for resistance to a range of stress conditions in S. pombe, as in S. cerevisiae, thus demonstrating for the first time that urmylation has conserved roles in stress resistance in eukaryotes. Additionally, urmylation controls the activation of a conserved mitogen-activated protein kinase during exposure to H2O2. Finally, although autophagic Ubl conjugation is not important for oxidative stress responses in S. pombe, these investigations have identified an E2 with roles in oxidative stress responses and cell cycle control. Taken together, these findings advance the study of the roles of ubiquitin/Ubl conjugation pathways in responses to oxidative stress, and offer exciting prospects for future investigations

Vacuum Instability in Chern-Simons Gravity

We explore perturbations about a Friedmann-Robertson-Walker background in Chern-Simons gravity. At large momenta one of the two circularly polarized tensor modes becomes ghostlike. We argue that nevertheless the theory does not exhibit classical runaway solutions, except possibly in the relativistic nonlinear regime. However, the ghost modes cause the vacuum state to be quantum mechanically unstable, with a decay rate that is naively infinite. The decay rate can be made finite only if one interprets the theory as an effective quantum field theory valid up to some momentum cutoff, which violates Lorentz invariance. By demanding that the energy density in photons created by vacuum decay over the lifetime of the Universe not violate observational bounds, we derive strong constraints on the two dimensional parameter space of the theory, consisting of the cutoff and the Chern-Simons mass.Comment: 8 pages, 2 figures; final published versio

Spectral Shape of Check-Hybrid GLDPC Codes

This paper analyzes the asymptotic exponent of both the weight spectrum and the stopping set size spectrum for a class of generalized low-density parity-check (GLDPC) codes. Specifically, all variable nodes (VNs) are assumed to have the same degree (regular VN set), while the check node (CN) set is assumed to be composed of a mixture of different linear block codes (hybrid CN set). A simple expression for the exponent (which is also referred to as the growth rate or the spectral shape) is developed. This expression is consistent with previous results, including the case where the normalized weight or stopping set size tends to zero. Furthermore, it is shown how certain symmetry properties of the local weight distribution at the CNs induce a symmetry in the overall weight spectral shape function.Comment: 6 pages, 3 figures. Presented at the IEEE ICC 2010, Cape Town, South Africa. A minor typo in equation (9) has been correcte

Growth Rate of the Weight Distribution of Doubly-Generalized LDPC Codes: General Case and Efficient Evaluation

The growth rate of the weight distribution of irregular doubly-generalized LDPC (D-GLDPC) codes is developed and in the process, a new efficient numerical technique for its evaluation is presented. The solution involves simultaneous solution of a 4 x 4 system of polynomial equations. This represents the first efficient numerical technique for exact evaluation of the growth rate, even for LDPC codes. The technique is applied to two example D-GLDPC code ensembles.Comment: 6 pages, 1 figure. Proc. IEEE Globecom 2009, Hawaii, USA, November 30 - December 4, 200

Stability of Iterative Decoding of Multi-Edge Type Doubly-Generalized LDPC Codes Over the BEC

Using the EXIT chart approach, a necessary and sufficient condition is developed for the local stability of iterative decoding of multi-edge type (MET) doubly-generalized low-density parity-check (D-GLDPC) code ensembles. In such code ensembles, the use of arbitrary linear block codes as component codes is combined with the further design of local Tanner graph connectivity through the use of multiple edge types. The stability condition for these code ensembles is shown to be succinctly described in terms of the value of the spectral radius of an appropriately defined polynomial matrix.Comment: 6 pages, 3 figures. Presented at Globecom 2011, Houston, T

Transnational Dealings - Morrison Continues to Make Waves

Morrison v. National Australia Bank Ltd. drastically altered the landscape for transnational securities litigation and the way that courts determine proper application of a statute concerning a transnational claim. The Supreme Court’s characterization of extraterritoriality under the Securities Exchange Act as a merits-based inquiry has led to a reexamination of limitations under other federal statutes that were previously thought to be jurisdictional issues. Significantly, Morrison created a road map for courts to follow when the extraterritoriality of a statute is brought into question. The key to proper application of a statute is to decipher the minimum U.S. contacts required to state a transnational claim. The tests developed addressing this inquiry are critical in discerning the boundaries of U.S. law at a time when transnational dealings are prevalent

Spectral Shape of Doubly-Generalized LDPC Codes: Efficient and Exact Evaluation

This paper analyzes the asymptotic exponent of the weight spectrum for irregular doubly-generalized LDPC (D-GLDPC) codes. In the process, an efficient numerical technique for its evaluation is presented, involving the solution of a 4 x 4 system of polynomial equations. The expression is consistent with previous results, including the case where the normalized weight or stopping set size tends to zero. The spectral shape is shown to admit a particularly simple form in the special case where all variable nodes are repetition codes of the same degree, a case which includes Tanner codes; for this case it is also shown how certain symmetry properties of the local weight distribution at the CNs induce a symmetry in the overall weight spectral shape function. Finally, using these new results, weight and stopping set size spectral shapes are evaluated for some example generalized and doubly-generalized LDPC code ensembles.Comment: 17 pages, 6 figures. To appear in IEEE Transactions on Information Theor