A general framework for measuring inconsistency through minimal inconsistent sets

Hunter and Konieczny explored the relationships between measures of inconsistency for a belief base and the minimal inconsistent subsets of that belief base in several of their papers. In particular, an inconsistency value termed MIVC, defined from minimal inconsistent subsets, can be considered as a Shapley Inconsistency Value. Moreover, it can be axiomatized completely in terms of five simple axioms. MinInc, one of the five axioms, states that each minimal inconsistent set has the same amount of conflict. However, it conflicts with the intuition illustrated by the lottery paradox, which states that as the size of a minimal inconsistent belief base increases, the degree of inconsistency of that belief base becomes smaller. To address this, we present two kinds of revised inconsistency measures for a belief base from its minimal inconsistent subsets. Each of these measures considers the size of each minimal inconsistent subset as well as the number of minimal inconsistent subsets of a belief base. More specifically, we first present a vectorial measure to capture the inconsistency for a belief base, which is more discriminative than MIVC. Then we present a family of weighted inconsistency measures based on the vectorial inconsistency measure, which allow us to capture the inconsistency for a belief base in terms of a single numerical value as usual. We also show that each of the two kinds of revised inconsistency measures can be considered as a particular Shapley Inconsistency Value, and can be axiomatically characterized by the corresponding revised axioms presented in this paper.

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.