Solving One Variable Word Equations in the Free Group in Cubic Time

A word equation with one variable in a free group is given as $U = V$, where both $U$ and $V$ are words over the alphabet of generators of the free group and $X, X^{-1}$, for a fixed variable $X$. An element of the free group is a solution when substituting it for $X$ yields a true equality (interpreted in the free group) of left- and right-hand sides. It is known that the set of all solutions of a given word equation with one variable is a finite union of sets of the form $\{\alpha w^i \beta \: : \: i \in \mathbb Z \}$, where $\alpha, w, \beta$ are reduced words over the alphabet of generators, and a polynomial-time algorithm (of a high degree) computing this set is known. We provide a cubic time algorithm for this problem, which also shows that the set of solutions consists of at most a quadratic number of the above-mentioned sets. The algorithm uses only simple tools of word combinatorics and group theory and is simple to state. Its analysis is involved and focuses on the combinatorics of occurrences of powers of a word within a larger word.Comment: 52 pages, accepted to STACS 202

Imaging study of thoracic outlet syndrome

Universidade Federal de São Paulo (UNIFESP)UNIFESP Departamento de Diagnóstico por ImagemUniversidade Federal do Rio de JaneiroHospital de Caridade São BrásUNIFESP, Depto. de Diagnóstico por ImagemSciEL

Quantitative evaluation of lateral forces on the patella: static and kinematic magnetic resonance imaging

OBJECTIVE: To evaluate the usefulness of combining static and kinematic magnetic resonance imaging in the evaluation of the femoropatellar joint. MATERIALS AND METHODS: Twenty healthy volunteers (40 knees) and 23 patients (43 knees) were submitted to both static and kinematic magnetic resonance imaging on a 1.5 tesla whole-body magnetic resonance scanner. The knees were positioned at 30º flexion with the quadrature knee coil at the inner end of the examination table. The patellar translation was evaluated by measurements of bisect offset, lateral patellar displacement and patellar tilt angle. The nonparametric Wilcoxon test was utilized for statistical analysis of data resulting from the static and kinematic studies in both groups. Nonparametric Mann-Whitney test was utilized in the comparison between healthy volunteers and patients. RESULTS: Statistical analysis demonstrated significant differences (p < 0.05) between static and kinematic magnetic resonance imaging for the three parameters evaluated in both groups. Among the patients the differences between static and kinematic measurements were greater than those found in the volunteers, at 30&deg; and 20&deg; flexion, with bisect offset and lateral patellar displacement. CONCLUSION: Static and kinematic magnetic resonance imaging, when performed in association, demonstrated that the lateral forces being exerted on the patella are higher at a knee flexion at the range between 20&deg; and 30&deg;, particularly in individuals symptomatic for femoropatellar instability.OBJETIVO: Avaliar a validade da ressonância magnética cinemática combinada com a ressonância magnética estática no estudo da articulação femoropatelar. MATERIAIS E MÉTODOS: Foram realizadas ressonância magnética estática e ressonância magnética cinemática em 20 voluntários assintomáticos (40 joelhos) e em 23 pacientes (43 joelhos), em aparelho de configuração fechada de 1,5 tesla de campo. Os indivíduos foram posicionados na extremidade da mesa, em 30&deg; de flexão. A translação patelar foi avaliada medindo-se o desvio da bissetriz, o deslocamento lateral da patela e o ângulo de inclinação da patela. Para a comparação entre os estudos estático e cinemático, foi utilizado o teste não-paramétrico de Wilcoxon. Para a comparação entre os voluntários e os pacientes, foi utilizado o teste de Mann-Whitney. RESULTADOS: Houve diferenças significantes entre a ressonância magnética estática e a ressonância magnética cinemática (p < 0,05) nos três parâmetros utilizados. No grupo dos pacientes, as diferenças entre a ressonância magnética estática e a ressonância magnética cinemática foram maiores que nos voluntários a 20&deg; e a 30&deg; de flexão, com o desvio da bissetriz e com o deslocamento lateral da patela. CONCLUSÃO: A combinação da ressonância magnética estática e ressonância magnética cinemática evidenciou que a força resultante lateral é maior na faixa de 20&deg; e 30&deg; de flexão, especialmente nos indivíduos sintomáticos, para a instabilidade femoropatelar.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Universidade Federal de São Paulo (UNIFESP) Escola Paulista de Medicina Departamento de Diagnóstico por ImagemSociedade Brasileira de Ortopedia e TraumatologiaUniversidade Federal de São Paulo (UNIFESP) Escola Paulista de Medicina Departamento de Ortopedia e TraumatologiaUniversidade Federal de São Paulo (UNIFESP) Escola Paulista de Medicina Departamento de Medicina Preventiva e BioestatísticaUNIFESP, EPM, Depto. de Diagnóstico por ImagemUNIFESP, EPM, Depto. de Ortopedia e TraumatologiaUNIFESP, EPM, Depto. de Medicina Preventiva e BioestatísticaSciEL

Postglacial expansion of the arctic keystone copepod calanus glacialis

Calanus glacialis, a major contributor to zooplankton biomass in the Arctic shelf seas, is a key link between primary production and higher trophic levels that may be sensitive to climate warming. The aim of this study was to explore genetic variation in contemporary populations of this species to infer possible changes during the Quaternary period, and to assess its population structure in both space and time. Calanus glacialis was sampled in the fjords of Spitsbergen (Hornsund and Kongsfjorden) in 2003, 2004, 2006, 2009 and 2012. The sequence of a mitochondrial marker, belonging to the ND5 gene, selected for the study was 1249 base pairs long and distinguished 75 unique haplotypes among 140 individuals that formed three main clades. There was no detectable pattern in the distribution of haplotypes by geographic distance or over time. Interestingly, a Bayesian skyline plot suggested that a 1000-fold increase in population size occurred approximately 10,000 years before present, suggesting a species expansion after the Last Glacial Maximum.GAME from the National Science Centre, the Polish Ministry of Science and Higher Education Iuventus Plus [IP2014 050573]; FCT-PT [CCMAR/Multi/04326/2013]; [2011/03/B/NZ8/02876

Protein disulphide isomerase-mediated grafting of cysteine-containing peptides onto over-bleached hair

The ability of Protein disulphide isomerase (PDI) to promote the grafting of two cysteine-containing peptides onto hair was investigated in order to develop an alternative treatment for over-bleached hair. The studied peptides were designed based on human keratin and human lung surfactant proteins and were linked to a fluorescent dye to facilitate visualisation of the grafting process and to assess hair penetration. The ability of the peptides to restore mechanical and thermal properties lost by repeated bleaching treatments was also studied. After eight bleaching treatments, hair samples displayed 42% less mechanical resistance, coupled with a decrease in α-helix denaturation enthalpies and temperatures. Hair surface damage following bleaching was visualized by scanning electron microscopy. Addition of PDI to the treatment formulations promoted peptide attachment to the hair via disulphide bonds, facilitating their penetration into the hair cortex, as observed by fluorescence microscopy. The proposed peptide treatment resulted in an increase in α-helix denaturation enthalpy in over-bleached hair, as well as an increase in both Young's modulus and tensile strength. Thus, mechanical and thermal properties were improved after the peptide treatment in the presence of PDI; suggesting that the formulations presented in this work are promising candidates for hair-care applications

Self-expanding metal stents in malignant colonic obstruction: experiences from Sweden

<p/> <p>Background</p> <p>Acute surgery in the management of malignant colonic obstruction is associated with high morbidity and mortality. The use of self-expanding metal stents (SEMS) is an alternative method of decompressing colonic obstruction. SEMS may allow time to optimize the patient and to perform preoperative staging, converting acute surgery into elective. SEMS is also proposed as palliative treatment in patients with contraindications to open surgery. Aim: To review our experience of SEMS focusing on clinical outcome and complications. The method used was a review of 75 consecutive trials at SEMS on 71 patients based on stent-protocols and patient charts.</p> <p>Findings</p> <p>SEMS was used for palliation in 64 (85%) cases and as a bridge to surgery in 11 (15%) cases. The majority of obstructions, 53 (71%) cases, were located in the recto-sigmoid. Technical success was achieved in 65 (87%) cases and clinical decompression was achieved in 60 (80%) cases. Reasons for technical failure were inability to cannulate the stricture in 5 (7%) cases and suboptimal SEMS placement in 3 (4%) cases. Complications included 4 (5%) procedure-related bowel perforations of which 2 (3%) patients died in junction to post operative complications. Three cases of bleeding after SEMS occurred, none of which needed invasive treatment. Five of the SEMS occluded. Two cases of stent erosion were diagnosed at the time of surgery. Average survival after palliative SEMS treatment was 6 months.</p> <p>Conclusion</p> <p>Our results correspond well to previously published data and we conclude that SEMS is a relatively safe and effective method of treating malignant colonic obstruction although the risk of SEMS-related perforations has to be taken into account.</p

Therapeutic implications of an enriched cancer stem-like cell population in a human osteosarcoma cell line

<p>Abstract</p> <p>Background</p> <p>Osteosarcoma is a bone-forming tumor of mesenchymal origin that presents a clinical pattern that is consistent with the cancer stem cell model. Cells with stem-like properties (CSCs) have been identified in several tumors and hypothesized as the responsible for the relative resistance to therapy and tumor relapses. In this study, we aimed to identify and characterize CSCs populations in a human osteosarcoma cell line and to explore their role in the responsiveness to conventional therapies.</p> <p>Methods</p> <p>CSCs were isolated from the human MNNG/HOS cell line using the sphere formation assay and characterized in terms of self-renewal, mesenchymal stem cell properties, expression of pluripotency markers and ABC transporters, metabolic activity and tumorigenicity. Cell's sensitivity to conventional chemotherapeutic agents and to irradiation was analyzed and related with cell cycle-induced alterations and apoptosis.</p> <p>Results</p> <p>The isolated CSCs were found to possess self-renewal and multipotential differentiation capabilities, express markers of pluripotent embryonic stem cells Oct4 and Nanog and the ABC transporters P-glycoprotein and BCRP, exhibit low metabolic activity and induce tumors in athymic mice. Compared with parental MNNG/HOS cells, CSCs were relatively more resistant to both chemotherapy and irradiation. None of the treatments have induced significant cell-cycle alterations and apoptosis in CSCs.</p> <p>Conclusions</p> <p>MNNG/HOS osteosarcoma cells contain a stem-like cell population relatively resistant to conventional chemotherapeutic agents and irradiation. This resistant phenotype appears to be related with some stem features, namely the high expression of the drug efflux transporters P-glycoprotein and BCRP and their quiescent nature, which may provide a biological basis for resistance to therapy and recurrence commonly observed in osteosarcoma.</p

End-Tagging of Ultra-Short Antimicrobial Peptides by W/F Stretches to Facilitate Bacterial Killing

BACKGROUND: Due to increasing resistance development among bacteria, antimicrobial peptides (AMPs), are receiving increased attention. Ideally, AMP should display high bactericidal potency, but low toxicity against (human) eukaryotic cells. Additionally, short and proteolytically stable AMPs are desired to maximize bioavailability and therapeutic versatility. METHODOLOGY AND PRINCIPAL FINDINGS: A facile approach is demonstrated for reaching high potency of ultra-short antimicrobal peptides through end-tagging with W and F stretches. Focusing on a peptide derived from kininogen, KNKGKKNGKH (KNK10) and truncations thereof, end-tagging resulted in enhanced bactericidal effect against Gram-negative Escherichia coli and Gram-positive Staphylococcus aureus. Through end-tagging, potency and salt resistance could be maintained down to 4-7 amino acids in the hydrophilic template peptide. Although tagging resulted in increased eukaryotic cell permeabilization at low ionic strength, the latter was insignificant at physiological ionic strength and in the presence of serum. Quantitatively, the most potent peptides investigated displayed bactericidal effects comparable to, or in excess of, that of the benchmark antimicrobial peptide LL-37. The higher bactericidal potency of the tagged peptides correlated to a higher degree of binding to bacteria, and resulting bacterial wall rupture. Analogously, tagging enhanced peptide-induced rupture of liposomes, particularly anionic ones. Additionally, end-tagging facilitated binding to bacterial lipopolysaccharide, both effects probably contributing to the selectivity displayed by these peptides between bacteria and eukaryotic cells. Importantly, W-tagging resulted in peptides with maintained stability against proteolytic degradation by human leukocyte elastase, as well as staphylococcal aureolysin and V8 proteinase. The biological relevance of these findings was demonstrated ex vivo for pig skin infected by S. aureus and E. coli. CONCLUSIONS/SIGNIFICANCE: End-tagging by hydrophobic amino acid stretches may be employed to enhance bactericidal potency also of ultra-short AMPs at maintained limited toxicity. The approach is of general applicability, and facilitates straightforward synthesis of hydrophobically modified AMPs without the need for post-peptide synthesis modifications

Protein disulphide isomerase-assisted functionalization of proteinaceous substrates

Protein disulphide isomerase (PDI) is an enzyme that catalyzes thiol-disulphide exchange reactions among a broad spectrum of substrates, including proteins and low-molecular thiols and disulphides. As the first protein-folding catalyst reported, the study of PDI has mainly involved the correct folding of several cysteine-containing proteins. Its application on the functionalization of protein-based materials has not been extensively reported. Herein, we review the applications of PDI on the modification of proteinaceous substrates and discuss its future potential. The mechanism involved in PDI functionalization of fibrous protein substrates is discussed in detail. These approaches allow innovative applications in textile dyeing and finishing, medical textiles, controlled drug delivery systems and hair or skin care products.We thank to FCT 'Fundacao para a Ciencia e Tecnologia' (scholarship SFRH/BD/38363/2007) for providing Margarida Fernandes the grant for PhD studies