Ternary Clifford Algebras

Ternary Clifford algebras are an essential ingredient in a cubic factorization of the Laplacian and using a ternary Clifford analysis build on such spaces one obtains a Dirac-type operator D such that D3 = Δ. This paper is a continuation of the work of the authors in describing properties of generalized ternary Clifford algebras. Here we explore a blade decomposition and symmetries of these algebras

Comparative assessment of young learners' foreign language competence in three Eastern European countries

This paper concerns teacher practices in, and beliefs about, the assessment of young learners' progress in English in three Eastern European countries (Slovenia, Croatia, and the Czech Republic). The central part of the paper focuses on an international project involving empirical research into assessment of young learners' foreign language competence in Slovenia, Croatia and the Czech Republic. With the help of an adapted questionnaire, we collected data from a non-random sample of primary and foreign language teachers who teach foreign languages at the primary level in these countries. The research shows that English as a foreign language is taught mostly by young teachers either primary specialists or foreign language teachers. These teachers most frequently use oral assessment/interviews or self-developed tests. Other more authentic types of assessment, such as language portfolios, are rarely used. The teachers most frequently assess speaking and listening skills, and they use assessment involving vocabulary the most frequently of all. However, there are significant differences in practice among the three countries

Genomic correlates of relationship QTL involved in fore-versus hind limb divergence in mice

Divergence of serially homologous elements of organisms is a common evolutionary pattern contributing to increased phenotypic complexity. Here, we study the genomic intervals affecting the variational independence of fore- and hind limb traits within an experimental mouse population. We use an advanced intercross of inbred mouse strains to map the loci associated with the degree of autonomy between fore- and hind limb long bone lengths (loci affecting the relationship between traits, relationship quantitative trait loci [rQTL]). These loci have been proposed to interact locally with the products of pleiotropic genes, thereby freeing the local trait from the variational constraint due to pleiotropic mutations. Using the known polymorphisms (single nucleotide polymorphisms [SNPs]) between the parental strains, we characterized and compared the genomic regions in which the rQTL, as well as their interaction partners (intQTL), reside. We find that these two classes of QTL intervals harbor different kinds of molecular variation. SNPs in rQTL intervals more frequently reside in limb-specific cis-regulatory regions than SNPs in intQTL intervals. The intQTL loci modified by the rQTL, in contrast, show the signature of protein-coding variation. This result is consistent with the widely accepted view that protein-coding mutations have broader pleiotropic effects than cis-regulatory polymorphisms. For both types of QTL intervals, the underlying candidate genes are enriched for genes involved in protein binding. This finding suggests that rQTL effects are caused by local interactions among the products of the causal genes harbored in rQTL and intQTL intervals. This is the first study to systematically document the population-level molecular variation underlying the evolution of character individuation

The importance of early arthritis in patients with rheumatoid arthritis

Rheumatoid arthritis (RA) is a systemic inflammatory disorder that manifests predominantly in the synovial joint, where it causes a chronic inflammatory process, leading to early osteoarticular destructions. These destructions are progressive and irreversible, generating a significant functional deficiency. During the last years, the diagnostic approach of RA has focused on early arthritis. Early arthritis can develop into established RA or another established arthropathy, like systemic lupus erythematosus or psoriatic arthritis. It can have a spontaneous resolution or may remain undifferentiated for indefinite periods of time. The management of early arthritis has changed considerably in the past few years, under the influence of new concepts of diagnosis and new effective therapies. The treatment goal of early arthritis should now be the clinical remission and prevention of joint destruction. Methotrexate is the first line of therapy, used to treat early arthralgia and to reverse or limit impending exacerbation to RA. Biological treatment is used as a second line therapy in patients with severe disease who do not respond or have a contraindication to disease-modifying antirheumatic drugs (DMARDs). Patients with early arthritis should usually be identified and directed to rheumatologists to confirm the presence of arthritis, and to establish the correct diagnosis plus to initiate the proper treatment strategies