On the Complexity of Searching in Trees: Average-case Minimization

We focus on the average-case analysis: A function w : V -> Z+ is given which defines the likelihood for a node to be the one marked, and we want the strategy that minimizes the expected number of queries. Prior to this paper, very little was known about this natural question and the complexity of the problem had remained so far an open question. We close this question and prove that the above tree search problem is NP-complete even for the class of trees with diameter at most 4. This results in a complete characterization of the complexity of the problem with respect to the diameter size. In fact, for diameter not larger than 3 the problem can be shown to be polynomially solvable using a dynamic programming approach. In addition we prove that the problem is NP-complete even for the class of trees of maximum degree at most 16. To the best of our knowledge, the only known result in this direction is that the tree search problem is solvable in O(|V| log|V|) time for trees with degree at most 2 (paths). We match the above complexity results with a tight algorithmic analysis. We first show that a natural greedy algorithm attains a 2-approximation. Furthermore, for the bounded degree instances, we show that any optimal strategy (i.e., one that minimizes the expected number of queries) performs at most O(\Delta(T) (log |V| + log w(T))) queries in the worst case, where w(T) is the sum of the likelihoods of the nodes of T and \Delta(T) is the maximum degree of T. We combine this result with a non-trivial exponential time algorithm to provide an FPTAS for trees with bounded degree

Effects of local infiltration of peripheral blood mononuclear cells with phonophoresis on wound healing in dogs

A total of six dogs with extensive wounds of 5×5 cm2 size and above were taken with the objective of evaluating the efficacy of autologous peripheral blood mononuclear cells (PBMC) with phonophoresis on wound healing in dogs. Autologous PBMCs were isolated freshly on 0, 7, 14, 21 and 28th day from blood by using density gradient centrifugation. Obtained PBMC was infiltrated around the wounds. Phonophoresis was done using therapeutic ultrasound massage at 0.5 watts/cm2 for 10 min for all the six animals. Clinical evaluation and wound planimetry was performed during post treatment period. Most affected breed was mongrel and main aetiology was automobile accident. The wounds were mostly located on limbs, neck and abdominal region. PBMC was noticed to be compatible to the tissues. No signs of infection were noticed in the wounds after administration of PBMC, rather healthy granulation tissue-formation, increasing values of wound contraction, epithelization and healing were noticed. PBMC-phonophoresis in wound healing of canines in present study was found to be effective in extensive wounds

Compressed Membership for NFA (DFA) with Compressed Labels is in NP (P)

In this paper, a compressed membership problem for finite automata, both deterministic and non-deterministic, with compressed transition labels is studied. The compression is represented by straight-line programs (SLPs), i.e. context-free grammars generating exactly one string. A novel technique of dealing with SLPs is introduced: the SLPs are recompressed, so that substrings of the input text are encoded in SLPs labelling the transitions of the NFA (DFA) in the same way, as in the SLP representing the input text. To this end, the SLPs are locally decompressed and then recompressed in a uniform way. Furthermore, such recompression induces only small changes in the automaton, in particular, the size of the automaton remains polynomial. Using this technique it is shown that the compressed membership for NFA with compressed labels is in NP, thus confirming the conjecture of Plandowski and Rytter and extending the partial result of Lohrey and Mathissen; as it is already known, that this problem is NP-hard, we settle its exact computational complexity. Moreover, the same technique applied to the compressed membership for DFA with compressed labels yields that this problem is in P; for this problem, only trivial upper-bound PSPACE was known

Mortui vivos docent: a modern revival of temporal bone plug harvests

Human temporal bones (HTBs) are invaluable resources for the study of otologic disorders and for evaluating novel treatment approaches. Given the high costs and technical expertise required to collect and process HTBs, there has been a decline in the number of otopathology laboratories. Our objective is to encourage ongoing study of HTBs by outlining the necessary steps to establish a pipeline for collection and processing of HTBs. In this methods manuscript, we: (1) provide the design of a temporal bone plug sawblade that can be used to collect specimens from autopsy donors; (2) establish that decalcification time can be dramatically reduced from 9 to 3 months if ethylenediaminetetraacetic acid is combined with microwave tissue processing and periodic bone trimming; (3) show that serial sections of relatively-rapidly decalcified HTBs can be successfully immunostained for key inner ear proteins; (4) demonstrate how to drill down a HTB to the otic capsule within a few hours so that subsequent decalcification time can be further reduced to only weeks. We include photographs and videos to facilitate rapid dissemination of the developed methods. Collected HTBs can be used for many purposes, including, but not limited to device testing, imaging studies, education, histopathology, and molecular studies. As new technology develops, it is imperative to continue studying HTBs to further our understanding of the cellular and molecular underpinnings of otologic disorders

Rewriting Systems for Reachability in Vector Addition Systems with Pairs

15 pagesInternational audienceWe adapt hypergraph rewriting system to a generalization of Vector Addition Systems with States (VASS) that we call vector addition systems with pairs (VASP). We give rewriting systems and strategies, that allow us to obtain reachability equivalence results between some classes of VASP and VASS. Reachability for the later is well known be equivalent to reachability in Petri nets. VASP generalize also Branching Extension of VASS (BVASS) for which it is unknown if they are more expressive than VASS. We consider here a more restricted notion of reachability for VASP than that for BVASS. However the reachability decision problem corresponding is already equivalent to decidability of the provability in Multiplicative and Exponential Linear Logic (MELL), a question left open for more than 20 years

Aptamers that recognize drug-resistant HIV-1 reverse transcriptase

Drug-resistant variants of HIV-1 reverse transcriptase (RT) are also known to be resistant to anti-RT RNA aptamers. In order to be able to develop diagnostics and therapies that can focus on otherwise drug-resistant viruses, we have isolated two aptamers against a well-known, drug-resistant HIV-1 RT, Mutant 3 (M3) from the multidrug-resistant HIV-1 RT panel. One aptamer, M302, bound M3 but showed no significant affinity for wild-type (WT) HIV-1 RT, while another aptamer, 12.01, bound to both M3 and WT HIV-1 RTs. In contrast to all previously selected anti-RT aptamers, neither of these aptamers showed observable inhibition of either polymerase or RNase H activities. Aptamers M302 and 12.01 competed with one another for binding to M3, but they did not compete with a pseudoknot aptamer for binding to the template/primer cleft of WT HIV-1 RT. These results represent the surprising identification of an additional RNA-binding epitope on the surface of HIV-1 RT. M3 and WT HIV-1 RTs could be distinguished using an aptamer-based microarray. By probing protein conformation as a correlate to drug resistance we introduce an additional and useful measure for determining HIV-1 drug resistance

Genetic overlap between autoimmune diseases and non-Hodgkin lymphoma subtypes

Epidemiologic studies show an increased risk of non-Hodgkin lymphoma (NHL) in patients with autoimmune disease (AD), due to a combination of shared environmental factors and/or genetic factors, or a causative cascade: chronic inflammation/antigen-stimulation in one disease leads to another. Here we assess shared genetic risk in genome-wide-association-studies (GWAS). Secondary analysis of GWAS of NHL subtypes (chronic lymphocytic leukemia, diffuse large B-cell lymphoma, follicular lymphoma, and marginal zone lymphoma) and ADs (rheumatoid arthritis, systemic lupus erythematosus, and multiple sclerosis). Shared genetic risk was assessed by (a) description of regional genetic of overlap, (b) polygenic risk score (PRS), (c)"diseasome", (d)meta-analysis. Descriptive analysis revealed few shared genetic factors between each AD and each NHL subtype. The PRS of ADs were not increased in NHL patients (nor vice versa). In the diseasome, NHLs shared more genetic etiology with ADs than solid cancers (p = .0041). A meta-analysis (combing AD with NHL) implicated genes of apoptosis and telomere length. This GWAS-based analysis four NHL subtypes and three ADs revealed few weakly-associated shared loci, explaining little total risk. This suggests common genetic variation, as assessed by GWAS in these sample sizes, may not be the primary explanation for the link between these ADs and NHLs