The distribution of cycles in breakpoint graphs of signed permutations

Breakpoint graphs are ubiquitous structures in the field of genome rearrangements. Their cycle decomposition has proved useful in computing and bounding many measures of (dis)similarity between genomes, and studying the distribution of those cycles is therefore critical to gaining insight on the distributions of the genomic distances that rely on it. We extend here the work initiated by Doignon and Labarre, who enumerated unsigned permutations whose breakpoint graph contains $k$ cycles, to signed permutations, and prove explicit formulas for computing the expected value and the variance of the corresponding distributions, both in the unsigned case and in the signed case. We also compare these distributions to those of several well-studied distances, emphasising the cases where approximations obtained in this way stand out. Finally, we show how our results can be used to derive simpler proofs of other previously known results

Step fluctuations and random walks

The probability distribution p(l) of an atom to return to a step at distance l from the detachment site, with a random walk in between, is exactly enumerated. In particular, we study the dependence of p(l) on step roughness, presence of other reflecting or absorbing steps, interaction between steps and diffusing atom, as well as concentration of defects on the terrace neighbouring the step. Applying Monte Carlo techniques, the time evolution of equilibrium step fluctuations is computed for specific forms of return probabilities. Results are compared to previous theoretical and experimental findings.Comment: 16 pages, 6 figure

Designability of alpha-helical Proteins

A typical protein structure is a compact packing of connected alpha-helices and/or beta-strands. We have developed a method for generating the ensemble of compact structures a given set of helices and strands can form. The method is tested on structures composed of four alpha-helices connected by short turns. All such natural four-helix bundles that are connected by short turns seen in nature are reproduced to closer than 3.6 Angstroms per residue within the ensemble. Since structures with no natural counterpart may be targets for ab initio structure design, the designability of each structure in the ensemble -- defined as the number of sequences with that structure as their lowest energy state -- is evaluated using a hydrophobic energy. For the case of four alpha-helices, a small set of highly designable structures emerges, most of which have an analog among the known four-helix fold families, however several novel packings and topologies are identified.Comment: 21 pages, 6 figures, to appear in PNA

A Scalable VLSI Architecture for Soft-Input Soft-Output Depth-First Sphere Decoding

Multiple-input multiple-output (MIMO) wireless transmission imposes huge challenges on the design of efficient hardware architectures for iterative receivers. A major challenge is soft-input soft-output (SISO) MIMO demapping, often approached by sphere decoding (SD). In this paper, we introduce the - to our best knowledge - first VLSI architecture for SISO SD applying a single tree-search approach. Compared with a soft-output-only base architecture similar to the one proposed by Studer et al. in IEEE J-SAC 2008, the architectural modifications for soft input still allow a one-node-per-cycle execution. For a 4x4 16-QAM system, the area increases by 57% and the operating frequency degrades by 34% only.Comment: Accepted for IEEE Transactions on Circuits and Systems II Express Briefs, May 2010. This draft from April 2010 will not be updated any more. Please refer to IEEE Xplore for the final version. *) The final publication will appear with the modified title "A Scalable VLSI Architecture for Soft-Input Soft-Output Single Tree-Search Sphere Decoding