Approximately Counting Embeddings into Random Graphs

Let H be a graph, and let C_H(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C_H(G). Previous results cover only a few specific instances of this general problem, for example, the case when H has degree at most one (monomer-dimer problem). In this paper, we present the first general subcase of the subgraph isomorphism counting problem which is almost always efficiently approximable. The results rely on a new graph decomposition technique. Informally, the decomposition is a labeling of the vertices such that every edge is between vertices with different labels and for every vertex all neighbors with a higher label have identical labels. The labeling implicitly generates a sequence of bipartite graphs which permits us to break the problem of counting embeddings of large subgraphs into that of counting embeddings of small subgraphs. Using this method, we present a simple randomized algorithm for the counting problem. For all decomposable graphs H and all graphs G, the algorithm is an unbiased estimator. Furthermore, for all graphs H having a decomposition where each of the bipartite graphs generated is small and almost all graphs G, the algorithm is a fully polynomial randomized approximation scheme. We show that the graph classes of H for which we obtain a fully polynomial randomized approximation scheme for almost all G includes graphs of degree at most two, bounded-degree forests, bounded-length grid graphs, subdivision of bounded-degree graphs, and major subclasses of outerplanar graphs, series-parallel graphs and planar graphs, whereas unbounded-length grid graphs are excluded.Comment: Earlier version appeared in Random 2008. Fixed an typo in Definition 3.

Failed targeted muscle reinnervation: Findings at revision surgery and concepts for success

Although it was initially described for improved myoelectric control, targeted muscle reinnervation (TMR) has quickly gained popularity as a technique for neuroma control. With this rapid increase in utilization has come broadening indications and variability in the described technique. As a result, it becomes difficult to interpret published outcomes. Furthermore, there is no literature discussing the management of failed cases which are undoubtedly occurring. Methods: This is a retrospective case series of two patients who underwent revision surgery for failed TMR. The authors also review the current literature on TMR and outline technical and conceptual pitfalls and pearls based on our local experience. Results: Excessive donor nerve redundancy, kinking, donor-recipient nerve size mismatch, superficial placement of the nerve coaptation, inappropriate target selection, and incomplete target muscle denervation were identified as technical pitfalls of TMR surgery. Techniques to avoid these pitfalls were described. Conclusions: Although TMR has been a major development in amputee care for both pain management and improved myoelectric control, it is important to acknowledge that it is not a foolproof surgery and does not provide a guaranteed result. Failed cases of TMR represent opportunities to learn about factors contributing to unfavorable outcomes and refine our techniques empirically

Revision of Carpal Tunnel Surgery

Carpal tunnel release is one of the most commonly performed upper extremity procedures. The majority of patients experience significant improvement or resolution of their symptoms. However, a small but important subset of patients will experience the failure of their initial surgery. These patients can be grouped into persistent, recurrent, and new symptom categories. The approach to these patients starts with a thorough clinical examination and is supplemented with electrodiagnostic studies. The step-wise surgical management of revision carpal tunnel surgery consists of the proximal exploration of the median nerve, Guyon’s release with neurolysis, the rerelease of the transverse retinaculum, evaluation of the nerve injury, treatment of secondary sites of compression, and potential ancillary procedures. The approach and management of failed carpal tunnel release are reviewed in this article

Cholecystocutaneous Fistula after Percutaneous Gallbladder Drainage

Cases of cholecystocutaneous fistulas are now a rare occurrence as a result of rapid diagnosis and treatment. We present a case of cholecystocutaneous fistula developing after the removal of a percutaneous drain for the treatment of acute cholecystitis. Re-occurring infection and presence of gallstones led to fistulization of the gallbladder fundus and the development of a tract along the path created by the drain. The patient presented with re-occurring right upper quadrant abdominal pain, purulent discharge from the fistulous opening and expulsion of multiple gallstones. She underwent laparoscopic cholecystectomy and fistula excision

Revision of Carpal Tunnel Surgery

Carpal tunnel release is one of the most commonly performed upper extremity procedures. The majority of patients experience significant improvement or resolution of their symptoms. However, a small but important subset of patients will experience the failure of their initial surgery. These patients can be grouped into persistent, recurrent, and new symptom categories. The approach to these patients starts with a thorough clinical examination and is supplemented with electrodiagnostic studies. The step-wise surgical management of revision carpal tunnel surgery consists of the proximal exploration of the median nerve, Guyon’s release with neurolysis, the rerelease of the transverse retinaculum, evaluation of the nerve injury, treatment of secondary sites of compression, and potential ancillary procedures. The approach and management of failed carpal tunnel release are reviewed in this article

Effect of point mutations on the secondary structure and membrane interaction of antimicrobial peptide anoplin

Anoplin (GLLKRIKTLL-NH2) is the smallest linear α-helical antimicrobial peptide found naturally to date. Antibacterial and hemolytic properties of anoplin depend strongly on physicochemical properties. Two anoplin derivatives, anoplin-8K (Ano8K, GLLKTIKKLL-NH2) and anoplin-1K5 V8K (Ano1K5 V8K, KLLKVIKLL-NH2), were found to have increased bacterial and low hemolytic activity. In the present work physicochemical properties of these three peptides were studied by UV resonance Raman (UVRR) spectroscopy, Langmuir-Blodgett monolayer technique, and carboxyfluorescein (CF) leakage assay. UVRR data indicated that all three peptides adopt predominantly unordered conformation in aqueous buffer solution. In membrane-mimicking trifluoroethanol, the α-helical content increases for all three peptides with Ano1K5 V8K having the highest α-helix percentage, followed by Ano8K and anoplin. Critical micelle concentrations were found to be similar for all three peptides, and the saturation pressure decreases in the sequence Ano1K5 V8K, anoplin, Ano8K. Critical pressure of insertion was found to be greater for anionic lipid monolayer DPPG than for zwitterionic lipid DPPC indicating preferential adsorption of all three peptides to DPPG. Finally, membrane lytic activities of all three peptides toward various model lipid vesicles were compared through CF leakage assay. Overall the data indicate that antimicrobial activity of anoplin increases with charge, whereas membrane lytic activity correlates with peptides helicity and amphipathicity