Minimal Hilbert series for quadratic algebras and the Anick conjecture

We study the question on whether the famous Golod–Shafarevich estimate, which gives a lower bound for the Hilbert series of a (noncommutative) algebra, is attained. This question was considered by Anick in his 1983 paper ‘Generic algebras and CW-complexes’, Princeton Univ. Press, where he proved that the estimate is attained for the number of quadratic relations $d\leq n^2/4$
and $d\geq n^2/2$, and conjectured that it is the case for any number of quadratic relations. The particular point where the number of relations is equal to $n(n-1)/2$ was addressed by Vershik. He conjectured that a generic algebra with this number of relations is finite dimensional. We announce here the result that over any infinite field, the Anick conjecture holds for $d \geq 4(n2+n)/9$ and an arbitrary number of generators. We also discuss the result that confirms the Vershik conjecture over any field of characteristic 0, and a series of related
asymptotic results.

Finite dimensional semigroup quadratic algebras with the minimal number of relations

A quadratic semigroup algebra is an algebra over a field given by the generators x_1, . . . , x_n and a finite set of quadratic relations each of which either has the shape x_j x_k = 0 or the shape x_j x_k = x_l x_m . We prove that a quadratic semigroup algebra given by n generators and d=(n^2+n)/4 relations is always infinite dimensional. This strengthens the Golod–Shafarevich estimate for the above class of algebras. Our main result however is that for every n, there is a finite dimensional quadratic semigroup algebra with n generators and d_n relations, where d_n is the first integer greater than (n^2+n)/4 . That is, the above Golod–Shafarevich-type estimate for semigroup algebras is sharp.

Establishing optimal quantitative-polymerase chain reaction assays for routine diagnosis and tracking of minimal residual disease in JAK2-V617F-associated myeloproliferative neoplasms:a joint European LeukemiaNet/MPN&MPNr-EuroNet (COST action BM0902) study

Reliable detection of JAK2-V617F is critical for accurate diagnosis of myeloproliferative neoplasms (MPNs); in addition, sensitive mutation-specific assays can be applied to monitor disease response. However, there has been no consistent approach to JAK2-V617F detection, with assays varying markedly in performance, affecting clinical utility. Therefore, we established a network of 12 laboratories from seven countries to systematically evaluate nine different DNA-based quantitative PCR (qPCR) assays, including those in widespread clinical use. Seven quality control rounds involving over 21,500 qPCR reactions were undertaken using centrally distributed cell line dilutions and plasmid controls. The two best-performing assays were tested on normal blood samples (n=100) to evaluate assay specificity, followed by analysis of serial samples from 28 patients transplanted for JAK2-V617F-positive disease. The most sensitive assay, which performed consistently across a range of qPCR platforms, predicted outcome following transplant, with the mutant allele detected a median of 22 weeks (range 6-85 weeks) before relapse. Four of seven patients achieved molecular remission following donor lymphocyte infusion, indicative of a graft vs MPN effect. This study has established a robust, reliable assay for sensitive JAK2-V617F detection, suitable for assessing response in clinical trials, predicting outcome and guiding management of patients undergoing allogeneic transplant.

Minimal intervention dentistry and older patients part 2: minimally invasive operative interventions

As described in the first paper of this two part series, the expansion of our older population and the concomitant reduction in levels of edentulism will result in an increase in the number of patients presenting in general practice with complex restorative challenges. The application of the concepts of minimal intervention dentistry and minimally invasive operative techniques may offer a powerful armamentarium to the general dentist to provide ethical and conservative treatment to older patients.

Clinical Relevance: When it is unavoidable, operative intervention should be as minimally invasive as practicable in older patients to preserve the longevity of their natural dentition.

Minimal intervention dentistry and older patients Part 1: Risk assessment and caries prevention

Ten million people in the UK today are aged over 65. The latest projections estimate that there will be 5 1/2 million more people aged 65 and older in the next 20 years. This projected pattern of population ageing will have profound consequences for dentistry. Minimal intervention dentistry (MID) is a modern evidence-based approach to caries management in dentate patients that uses the 'medical model' whereby disease is controlled by the 'oral physician'. This approach offers considerable benefits over conventional dentistry for older patients. It encourages patients to be responsible for their oral health through the provision of both knowledge and motivation. MID encompasses risk assessment for dental disease, early detection and control of disease processes, and minimally invasive treatment. 

Clinical Relevance: Risk assessment tools can aid the general dental practitioner and the patient to develop a suitable caries prevention programme for that individual and reduce the need for future operative intervention.

Losses of bioactive polyacetylenes during minimal processing of carrots

Vegetables of the Apiaceae plant family such as carrots, parsnip, celery and parsley,contain in minor quantities, a group of bioactive aliphatic C17-polyacetylenes (falcarinol,falcarindiol, falcarindiol-3- acetate). Recent studies have highlighted important biologicalfunctions in vitro and in vivo (animal studies) although the beneficial effect in humannutrition attributable to an increased in polyacetylenes diet are yet to be confirmed(Lund, 1990).Carrots not only contain relatively high polyacetylene content but also form a significantpart of many countries dietary habits. Carrots are also present in some ready-to-eat foodssuch as chilled freshly prepared salads, as part of the increasingly popular minimallyprocessed foods. Whereas the effect of conventional processing (boiling, vacuum processing) on the levels of polyacetylenes has been relatively well studied, the effect of minimal mechanical operations such as “peeling”, “mechanical cutting” and “chlorine washing” remains unknown.

Minimal residual disease detection in childhood acute lymphoblastic leukaemia patients at multiple time-points reveals high levels of concordance between molecular and immunophenotypic approaches

In this single centre study of childhood acute lymphoblastic leukaemia (ALL) patients treated on the Medical Research Council UKALL 97/99 protocols, it was determined that minimal residual disease (MRD) detected by real time quantitative polymerase chain reaction (RQ-PCR) and 3-colour flow cytometry (FC) displayed high levels of qualitative concordance when evaluated at multiple time-points during treatment (93.38%), and a combined use of both approaches allowed a multi time-point evaluation of MRD kinetics for 90% (53/59) of the initial cohort. At diagnosis, MRD markers with sensitivity of at least 0.01% were identified by RQ-PCR detection of fusion gene transcripts, IGH/TRG rearrangements, and FC. Using a combined RQ-PCR and FC approach, the evaluation of 367 follow-up BM samples revealed that the detection of MRD >1% at Day 15 (P = 0.04), >0.01% at the end of induction (P = 0.02), >0.01% at the end of consolidation (P = 0.01), >0.01% prior to the first delayed intensification (P = 0.01), and >0.1% prior to the second delayed intensification and continued maintenance (P = 0.001) were all associated with relapse and, based on early time-points (end of induction and consolidation) a significant log-rank trend (P = 0.0091) was noted between survival curves for patients stratified into high, intermediate and low-risk MRD groups.

Wilms' tumor gene 1 (WT1) expression in childhood acute lymphoblastic leukemia:a wide range of WT1 expression levels, its impact on prognosis and minimal residual disease monitoring

Wilms' tumor gene 1 (WT1) is overexpressed in the majority (70-90%) of acute leukemias and has been identified as an independent adverse prognostic factor, a convenient minimal residual disease (MRD) marker and potential therapeutic target in acute leukemia. We examined WT1 expression patterns in childhood acute lymphoblastic leukemia (ALL), where its clinical implication remains unclear. Using a real-time quantitative PCR designed according to Europe Against Cancer Program recommendations, we evaluated WT1 expression in 125 consecutively enrolled patients with childhood ALL (106 BCP-ALL, 19 T-ALL) and compared it with physiologic WT1 expression in normal and regenerating bone marrow (BM). In childhood B-cell precursor (BCP)-ALL, we detected a wide range of WT1 levels (5 logs) with a median WT1 expression close to that of normal BM. WT1 expression in childhood T-ALL was significantly higher than in BCP-ALL (P<0.001). Patients with MLL-AF4 translocation showed high WT1 overexpression (P<0.01) compared to patients with other or no chromosomal aberrations. Older children (> or =10 years) expressed higher WT1 levels than children under 10 years of age (P<0.001), while there was no difference in WT1 expression in patients with peripheral blood leukocyte count (WBC) > or =50 x 10(9)/l and lower. Analysis of relapsed cases (14/125) indicated that an abnormal increase or decrease in WT1 expression was associated with a significantly increased risk of relapse (P=0.0006), and this prognostic impact of WT1 was independent of other main risk factors (P=0.0012). In summary, our study suggests that WT1 expression in childhood ALL is very variable and much lower than in AML or adult ALL. WT1, thus, will not be a useful marker for MRD detection in childhood ALL, however, it does represent a potential independent risk factor in childhood ALL. Interestingly, a proportion of childhood ALL patients express WT1 at levels below the normal physiological BM WT1 expression, and this reduced WT1 expression appears to be associated with a higher risk of relapse.

Problems of minimal aerodynamic resistance

Nesta tese estamos preocupados com o problema da resistência mínima primeiro dirigida por I. Newton em seu Principia (1687): encontrar o corpo de resistência mínima que se desloca através de um médio. As partículas do médio não interagem entre si, bem como a interação das partículas com o corpo é perfeitamente elástica. Diferentes abordagens desse modelo foram feitas por vários matemáticos nos últimos 20 anos. Aqui damos uma visão geral sobre estes resultados que representa interesse independente, uma vez que os autores diferentes usam notações diferentes. Apresentamos uma solução do problema de minimização na classe de corpos de revolução geralmente não convexos e simplesmente conexos. Acontece que nessa classe existem corpos com resistência menor do que o mínimo da resistência na classe de corpos convexos de revolução. Encontramos o infimum da resistência nesta classe e construimos uma sequência regular de corpos que aproxima este infimum. Também apresentamos um corpo de resistência nula. Até agora ninguém sabia se tais corpos existem ou não, evidentemente o nosso corpo não pertence a nenhuma classe anteriormente analisado. Este corpo é não convexo e não simplesmente conexo; a forma topológica dele é um toro, parece um UFO extraterrestre. Apresentamos aqui várias famílias de tais corpos e estudamos as suas propriedades. Também apresentamos um corpo que é natural de chamar um corpo "invisíveis em uma direção", uma vez que a trajectória de cada partícula com a certa direcção coincide com a linha recta fora do invólucro convexo do corpo. ABSTRACT: In this thesis we are concerned with the problem of minimal resistance first addressed by I. Newton in his Principia (1687): find the body of minimal resistance moving through a medium. The medium particles do not mutually interact, and the interaction of particles with the body is perfectly elastic. Different approaches to that model have been tried by several mathematicians during the last 20 years. Here we give an overview of these results that represents interest in itself since all authors use different notations. We present a solution of the minimization problem in the class of generally non convex, simply connected bodies of revolution. It happens that in this class there are bodies with smaller resistance than the minimum in the class of convex bodies of revolution. We find the infimum of the resistance in this class, and construct a sequence of bodies which approximates this infimum. Also we present a body of zero resistance. Since earlier it was unknown if such bodies exists or not, evidently our body does not belong to any class previously examined. The zero resistance body found by us is non-convex and non-simply connected; topologically it is a torus, and it looks like an extraterrestrial UFO. We present here several families of such bodies and study their properties. We also present a body which is natural to call a body "invisible in one direction", since the trajectory of each particle with the given direction, outside the convex hull of the body, coincides with a straight line.

Shear strength of adhesively bonded polyolefins with minimal surface preparation

Interest in polyethylene and polypropylene bonding has increased in the last years. However, adhesive joints with adherends which are of low surface energy and which are chemically inert present several difficulties. Generally, their high degree of chemical resistance to solvents and dissimilar solubility parameters limit the usefulness of solvent bonding as a viable assembly technique. One successful approach to adhesive bonding of these materials involves proper selection of surface pre-treatment prior to bonding. With the correct pre-treatment it is possible to glue these materials with one or more of several adhesives required by the applications involved. A second approach is the use of adhesives without surface pre-treatment, such as hot melts, high tack pressure-sensitive adhesives, solvent-based specialty adhesives and, more recently, structural acrylic adhesives as such 3M DP-8005® and Loctite 3030®. In this paper, the shear strengths of two acrylic adhesives were evaluated using the lap shear test method ASTM D3163 and the block shear test method ASTM D4501. Two different industrial polyolefins (polyethylene and polypropylene) were used for adherends. However, the focus of this study was to measure the shear strength of polyethylene joints with acrylic adhesives. The effect of abrasion was also studied. Some test specimens were manually abraded using 180 and 320 grade abrasive paper. An additional goal of this work was to examine the effect of temperature and moisture on mechanical strength of adhesive joints.