Enumeration of generalized polyominoes

As a generalization of polyominoes we consider edge-to-edge connected nonoverlapping unions of regular $k$-gons. For $n\le 4$ we determine formulas for the number $a_k(n)$ of generalized polyominoes consisting of $n$ regular $k$-gons. Additionally we give a table of the numbers $a_k(n)$ for small $k$ and $n$ obtained by computer enumeration. We finish with some open problems for $k$-polyominoes.Comment: 10 pages, 6 figures, 3 table

Compatible solute influence on nucleic acids: Many questions but few answers

Compatible solutes are small organic osmolytes including but not limited to sugars, polyols, amino acids, and their derivatives. They are compatible with cell metabolism even at molar concentrations. A variety of organisms synthesize or take up compatible solutes for adaptation to extreme environments. In addition to their protective action on whole cells, compatible solutes display significant effects on biomolecules in vitro. These include stabilization of native protein and nucleic acid structures. They are used as additives in polymerase chain reactions to increase product yield and specificity, but also in other nucleic acid and protein applications

Higher-order hadronic and heavy-lepton contributions to the anomalous magnetic moment

We report about recent results obtained for the muon anomalous magnetic moment. Three-loop kernel functions have been computed to obtain the next-to-next-to-leading-order hadronic vacuum polarization contributions. The numerical result, $a_\mu^{\rm{had,NNLO}}=1.24\pm 0.01 \times 10^{-10}$, is of the same order of magnitude as the current uncertainty from the hadronic contributions. For heavy-lepton corrections, analytical results are obtained at four-loop order and compared with the known results.Comment: Contribution to the proceedings of Loops and Legs in Quantum Field Theory, 27 April - 2 May 2014, Weimar, German

Hadronic contribution to the muon anomalous magnetic moment to next-to-next-to-leading order

We compute the next-to-next-to-leading order hadronic contribution to the muon anomalous magnetic moment originating from the photon vacuum polarization. The corresponding three-loop kernel functions are calculated using asymptotic expansion techniques which lead to analytic expressions. Our final result, $a_\mu^{\rm had,NNLO} = 1.24 \pm 0.01 \times 10^{-10}$, has the same order of magnitude as the current uncertainty of the leading order hadronic contribution and should thus be included in future analyses.Comment: 9 pages,v2: note on NLO hadronic light-by-light contribution added, matches published version, Physics Letters B 734 (2014) 144-14

Detecting Invalid Map Merges in Lifelong SLAM

For Lifelong SLAM, one has to deal with temporary localization failures, e.g., induced by kidnapping. We achieve this by starting a new map and merging it with the previous map as soon as relocalization succeeds. Since relocalization methods are fallible, it can happen that such a merge is invalid, e.g., due to perceptual aliasing. To address this issue, we propose methods to detect and undo invalid merges. These methods compare incoming scans with scans that were previously merged into the current map and consider how well they agree with each other. Evaluation of our methods takes place using a dataset that consists of multiple flat and office environments, as well as the public MIT Stata Center dataset. We show that methods based on a change detection algorithm and on comparison of gridmaps perform well in both environments and can be run in real-time with a reasonable computational cost.Comment: Accepted at IROS 202