The Cohen-Macaulay property of separating invariants of finite groups

In the case of finite groups, a separating algebra is a subalgebra of the ring of invariants which separates the orbits. Although separating algebras are often better behaved than the ring of invariants, we show that many of the criteria which imply that the ring of invariants is non Cohen-Macaulay actually imply that no graded separating algebra is Cohen-Macaulay. For example, we show that, over a field of positive characteristic p, given sufficiently many copies of a faithful modular representation, no graded separating algebra is Cohen-Macaulay. Furthermore, we show that, for a p-group, the existence of a Cohen-Macaulay graded separating algebra implies the group is generated by bireflections. Furthermore, we show that, for a $p$-group, the existence of a Cohen-Macaulay graded separating algebra implies the group is generated by bireflections. Additionally, we give an example which shows that Cohen-Macaulay separating algebras can occur when the ring of invariants is not Cohen-Macaulay.Comment: We removed the conjecture which appeared in previous versions: we give a counter-example. We fixed the proof of Lemma 2.2 (previously Remark 2.2). 16 page

A two-domain elevator mechanism for sodium/proton antiport

Sodium/proton (Na+/H+) antiporters, located at the plasma membrane in every cell, are vital for cell homeostasis1. In humans, their dysfunction has been linked to diseases, such as hypertension, heart failure and epilepsy, and they are well-established drug targets2. The best understood model system for Na+/H+ antiport is NhaA from Escherichia coli1, 3, for which both electron microscopy and crystal structures are available4, 5, 6. NhaA is made up of two distinct domains: a core domain and a dimerization domain. In the NhaA crystal structure a cavity is located between the two domains, providing access to the ion-binding site from the inward-facing surface of the protein1, 4. Like many Na+/H+ antiporters, the activity of NhaA is regulated by pH, only becoming active above pH 6.5, at which point a conformational change is thought to occur7. The only reported NhaA crystal structure so far is of the low pH inactivated form4. Here we describe the active-state structure of a Na+/H+ antiporter, NapA from Thermus thermophilus, at 3 Å resolution, solved from crystals grown at pH 7.8. In the NapA structure, the core and dimerization domains are in different positions to those seen in NhaA, and a negatively charged cavity has now opened to the outside. The extracellular cavity allows access to a strictly conserved aspartate residue thought to coordinate ion binding1, 8, 9 directly, a role supported here by molecular dynamics simulations. To alternate access to this ion-binding site, however, requires a surprisingly large rotation of the core domain, some 20° against the dimerization interface. We conclude that despite their fast transport rates of up to 1,500 ions per second3, Na+/H+ antiporters operate by a two-domain rocking bundle model, revealing themes relevant to secondary-active transporters in general

Recommendations for a core outcome set for measuring standing balance in adult populations: a consensus-based approach

Standing balance is imperative for mobility and avoiding falls. Use of an excessive number of standing balance measures has limited the synthesis of balance intervention data and hampered consistent clinical practice.To develop recommendations for a core outcome set (COS) of standing balance measures for research and practice among adults.A combination of scoping reviews, literature appraisal, anonymous voting and face-to-face meetings with fourteen invited experts from a range of disciplines with international recognition in balance measurement and falls prevention. Consensus was sought over three rounds using pre-established criteria.The scoping review identified 56 existing standing balance measures validated in adult populations with evidence of use in the past five years, and these were considered for inclusion in the COS.Fifteen measures were excluded after the first round of scoring and a further 36 after round two. Five measures were considered in round three. Two measures reached consensus for recommendation, and the expert panel recommended that at a minimum, either the Berg Balance Scale or Mini Balance Evaluation Systems Test be used when measuring standing balance in adult populations.Inclusion of two measures in the COS may increase the feasibility of potential uptake, but poses challenges for data synthesis. Adoption of the standing balance COS does not constitute a comprehensive balance assessment for any population, and users should include additional validated measures as appropriate.The absence of a gold standard for measuring standing balance has contributed to the proliferation of outcome measures. These recommendations represent an important first step towards greater standardization in the assessment and measurement of this critical skill and will inform clinical research and practice internationally

When fast logic meets slow belief: Evidence for a parallel-processing model of belief bias.

Two experiments pitted the default-interventionist account of belief bias against a parallel-processing model. According to the former, belief bias occurs because a fast, belief-based evaluation of the conclusion pre-empts a working-memory demanding logical analysis. In contrast, according to the latter both belief-based and logic-based responding occur in parallel. Participants were given deductive reasoning problems of variable complexity and instructed to decide whether the conclusion was valid on half the trials or to decide whether the conclusion was believable on the other half. When belief and logic conflict, the default-interventionist view predicts that it should take less time to respond on the basis of belief than logic, and that the believability of a conclusion should interfere with judgments of validity, but not the reverse. The parallel-processing view predicts that beliefs should interfere with logic judgments only if the processing required to evaluate the logical structure exceeds that required to evaluate the knowledge necessary to make a belief-based judgment, and vice versa otherwise. Consistent with this latter view, for the simplest reasoning problems (modus ponens), judgments of belief resulted in lower accuracy than judgments of validity, and believability interfered more with judgments of validity than the converse. For problems of moderate complexity (modus tollens and single-model syllogisms), the interference was symmetrical, in that validity interfered with belief judgments to the same degree that believability interfered with validity judgments. For the most complex (three-term multiple-model syllogisms), conclusion believability interfered more with judgments of validity than vice versa, in spite of the significant interference from conclusion validity on judgments of belief

MRI compared to conventional diagnostic work-up in the detection and evaluation of invasive lobular carcinoma of the breast: a review of existing literature

Item does not contain fulltextPURPOSE: The clinical diagnosis and management of invasive lobular carcinoma (ILC) of the breast presents difficulties. Magnetic resonance imaging (MRI) has been proposed as the imaging modality of choice for the evaluation of ILC. Small studies addressing different aspects of MRI in ILC have been presented but no large series to date. To address the usefulness of MRI in the work-up of ILC, we performed a review of the currently published literature. MATERIALS AND METHODS: We performed a literature search using the query "lobular AND (MRI OR MR OR MRT OR magnetic)" in the Cochrane library, PubMed and scholar.google.com, to retrieve all articles that dealt with the use of MRI in patients with ILC. We addressed sensitivity, morphologic appearance, correlation with pathology, detection of additional lesions, and impact of MRI on surgery as different endpoints. Whenever possible we performed meta-analysis of the pooled data. RESULTS: Sensitivity is 93.3% and equal to overall sensitivity of MRI for malignancy in the breast. Morphologic appearance is highly heterogeneous and probably heavily influenced by interreader variability. Correlation with pathology ranges from 0.81 to 0.97; overestimation of lesion size occurs but is rare. In 32% of patients, additional ipsilateral lesions are detected and in 7% contralateral lesions are only detected by MRI. Consequently, MRI induces change in surgical management in 28.3% of cases. CONCLUSION: This analysis indicates MRI to be valuable in the work-up of ILC. It provides additional knowledge that cannot be obtained by conventional imaging modalities which can be helpful in patient treatment

A next-generation liquid xenon observatory for dark matter and neutrino physics

The nature of dark matter and properties of neutrinos are among the most pressing issues in contemporary particle physics. The dual-phase xenon time-projection chamber is the leading technology to cover the available parameter space for weakly interacting massive particles, while featuring extensive sensitivity to many alternative dark matter candidates. These detectors can also study neutrinos through neutrinoless double-beta decay and through a variety of astrophysical sources. A next-generation xenon-based detector will therefore be a true multi-purpose observatory to significantly advance particle physics, nuclear physics, astrophysics, solar physics, and cosmology. This review article presents the science cases for such a detector

The Paracoccus denitrificans NarK-like nitrate and nitrite transporters; probing nitrate uptake and nitrate/nitrite exchange mechanisms

Nitrate and nitrite transport across biological mem branes is often facilitated by protein transporters that are members of the major facilita tor superfamily. Paracoccus denitrificans contains an unusual arrangement whereby two of the se transporters, NarK1 and NarK2, are fused into a single protein, N arK, which delivers nitrate to the respiratory nitrate reductase and transfers the pro duct, nitrite, to the periplasm. Our complementation studies, using a mutant lacking the nitrate/proton symporter NasA from the assimilatory nitrate reductase pathway, su pport that NarK1 functions as a nitrate/proton symporter while NarK2 is a nitrate/n itrite antiporter. Through the same experimental system, we find that Escherichia coli NarK and NarU can complement deletions in both narK and nasA in P. denitrificans , suggesting that, while these proteins are most likely nitrate/nitrite antiporters, they c an also act in the net uptake of nitrate. Finally, we argue that primary sequence analysis an d structural modelling do not readily explain why NasA, NarK1 and NarK2, as well as other transporters from this protein family, have such different functions, ranging from net nitrate uptake to nitrate/nitrite exchange