Multigraded Castelnuovo-Mumford Regularity

We develop a multigraded variant of Castelnuovo-Mumford regularity. Motivated by toric geometry, we work with modules over a polynomial ring graded by a finitely generated abelian group. As in the standard graded case, our definition of multigraded regularity involves the vanishing of graded components of local cohomology. We establish the key properties of regularity: its connection with the minimal generators of a module and its behavior in exact sequences. For an ideal sheaf on a simplicial toric variety X, we prove that its multigraded regularity bounds the equations that cut out the associated subvariety. We also provide a criterion for testing if an ample line bundle on X gives a projectively normal embedding.Comment: 30 pages, 5 figure

Free thyroxine measurement in clinical practice: how to optimize indications, analytical procedures, and interpretation criteria while waiting for global standardization

Thyroid dysfunctions are among the most common endocrine disorders and accurate biochemical testing is needed to confirm or rule out a diagnosis. Notably, true hyperthyroidism and hypothyroidism in the setting of a normal thyroid-stimulating hormone level are highly unlikely, making the assessment of free thyroxine (FT4) inappropriate in most new cases. However, FT4 measurement is integral in both the diagnosis and management of relevant central dysfunctions (central hypothyroidism and central hyperthyroidism) as well as for monitoring therapy in hyperthyroid patients treated with anti-thyroid drugs or radioiodine. In such settings, accurate FT4 quantification is required. Global standardization will improve the comparability of the results across laboratories and allow the development of common clinical decision limits in evidence-based guidelines. The International Federation of Clinical Chemistry and Laboratory Medicine Committee for Standardization of Thyroid Function Tests has undertaken FT4 immunoassay method comparison and recalibration studies and developed a reference measurement procedure that is currently being validated. However, technical and implementation challenges, including the establishment of different clinical decision limits for distinct patient groups, still remain. Accordingly, different assays and reference values cannot be interchanged. Two-way communication between the laboratory and clinical specialists is pivotal to properly select a reliable FT4 assay, establish reference intervals, investigate discordant results, and monitor the analytical and clinical performance of the method over time

Myelofibrosis-Associated Lymphoproliferative Disease: Retrospective Study of 16 Cases and Literature Review

Background. To better describe the clinical, biological, and the outcome of non-Hodgkin's lymphoma (NHL) with, at the initial presentation, bone marrow fibrosis (MF). Patients and Methods. From January 2001 to January 2007, 16 eligible patients with NHL and MF were retrieved from the Pathology Department of the University hospital of Amiens. Median age of patients was 62 years (range 16–74) with a sex ratio male/female of 3. Results. MF is associated with all types of lymphoma predominantly with B-cell phenotype and it seems to be more associated with low-grade NHL. B-symptoms are more frequent at diagnosis and more patients presented with an elevated LDH level. JAK-2 was negative in the 10 patients analysed. Two patients presented with features of primary MF with no evidence of lymphoma. Overall response rate was 94% after the first line of therapy with regression or improvement of MF. Relapse occurred in 8 patients (47%) with recurrence of MF in all of them. After a median follow-up of 42 months, 12 patients were alive with an overall survival rate for the entire group of 75%. Conclusions. MF-associated NHL is a rare manifestation which may be associated with all types of NHL and its presence does not seem to confer a poor prognosis. A search for lymphoproliferation should be considered when the cause of MF is not apparent

Generalized Robba rings

We prove that any projective coadmissible module over the locally analytic distribution algebra of a compact $p$-adic Lie group is finitely generated. In particular, the category of coadmissible modules does not have enough projectives. In the Appendix a "generalized Robba ring" for uniform pro-$p$ groups is constructed which naturally contains the locally analytic distribution algebra as a subring. The construction uses the theory of generalized microlocalization of quasi-abelian normed algebras that is also developed there. We equip this generalized Robba ring with a self-dual locally convex topology extending the topology on the distribution algebra. This is used to show some results on coadmissible modules.Comment: with an appendix by Peter Schneider; revised; new titl

Decomposition of semigroup algebras

Let A \subseteq B be cancellative abelian semigroups, and let R be an integral domain. We show that the semigroup ring R[B] can be decomposed, as an R[A]-module, into a direct sum of R[A]-submodules of the quotient ring of R[A]. In the case of a finite extension of positive affine semigroup rings we obtain an algorithm computing the decomposition. When R[A] is a polynomial ring over a field we explain how to compute many ring-theoretic properties of R[B] in terms of this decomposition. In particular we obtain a fast algorithm to compute the Castelnuovo-Mumford regularity of homogeneous semigroup rings. As an application we confirm the Eisenbud-Goto conjecture in a range of new cases. Our algorithms are implemented in the Macaulay2 package MonomialAlgebras.Comment: 12 pages, 2 figures, minor revisions. Package may be downloaded at http://www.math.uni-sb.de/ag/schreyer/jb/Macaulay2/MonomialAlgebras/html

Interpersonal interactions in instrumental lessons: teacher/students verbal and non-verbal behaviours

This study examined verbal and non-verbal teacher/student interpersonal interactions in higher education instrumental music lessons. Twenty-four lessons were videotaped and teacher/ student behaviours were analysed using a researcher-designed instrument. The findings indicate predominance of student and teacher joke among the verbal behaviours with no substantial gender differences between males and females. Deceit cues were the most frequent among the non-verbal behaviours, with the males displaying more gestures of deceit than the females. Other gender differences include the female students using courting signals towards both teacher groups and the female teachers showing interest towards the male students. The presence of positive verbal and negative non-verbal behaviours highlights the mixed messages present in teaching. Implications for instrumental teaching practice include greater focus on gender differences in interpersonal interactions and visual cues to improve communication and teacher/student relationship in the instrumental studio

Espaces de Berkovich sur Z : \'etude locale

We investigate the local properties of Berkovich spaces over Z. Using Weierstrass theorems, we prove that the local rings of those spaces are noetherian, regular in the case of affine spaces and excellent. We also show that the structure sheaf is coherent. Our methods work over other base rings (valued fields, discrete valuation rings, rings of integers of number fields, etc.) and provide a unified treatment of complex and p-adic spaces.Comment: v3: Corrected a few mistakes. Corrected the proof of the Weierstrass division theorem 7.3 in the case where the base field is imperfect and trivially value

Effects of reducing beta-lactam antibiotic pressure on intestinal colonization of antibiotic-resistant gram-negative bacteria

Background: We determined the effects of two antibiotic policies (predominance of either β-lactam antibiotics or fluroquinolones) on acquisition with third-generation cephalosporin-resistant Enterobacteriaceae (CRE) and fluoroquinolone-resistant CRE (FCRE) in two ICUs, with monitoring of other variables that may influence acquisition. Methods: After an 8-month baseline period, units were randomized to a predominant β-lactam antibiotic regimen (weekly cycling of ceftriaxone, amoxicillin-clavulanic acid and fluroquinolones) or a fluoroquinolone regimen for 3 months, with cross-over for another 3 months. Acquisition of CRE and FCRE was determined by microbiological surveillance. Results: During baseline, acquisition rates for CRE and FCRE were 14/1,000 and 2/1,000 patient days at risk, respectively. Cross-transmission of CRE accounted for ≤25% of acquisitions, and CRE acquisition was associated with the use of β-lactam antibiotics (amoxicillin-clavulanic acid in particular). As compared to baseline, β-lactam antibiotic use [in defined daily dose (DDD)/1,000 patient days] was reduced from 854 to 526 (-39%) and 555 (-35%) during both intervention periods. Fluoroquinolone use was increased from 150 and 129 DDD/1,000 patient days in baseline and the β-lactam period to 514 DDD/1,000 patient days (+243%) in the fluoroquinolone period. Reductions in β-lactam use were not associated with reduced CRE acquisition [adjusted HRs were 1.0 (95% CR: 0.5-2.2) and 1.1 (95% CI: 0.5-2.5) during both periods, respectively]. Increased use of fluoroquinolones was associated with increased acquisition of FCRE [adjusted HR 4.1 (95% CI: 1.4-11.9; p < 0.01]. Infection control variables remained comparable during all periods. Conclusion: A 35-39% reduction of β-lactam exposure was not associated with reduced acquisition of CRE, whereas a 243% increase of fluoroquinolone use increased acquisition of FCRE

Lifting and restricting recollement data

We study the problem of lifting and restricting TTF triples (equivalently, recollement data) for a certain wide type of triangulated categories. This, together with the parametrizations of TTF triples given in "Parametrizing recollement data", allows us to show that many well-known recollements of right bounded derived categories of algebras are restrictions of recollements in the unbounded level, and leads to criteria to detect recollements of general right bounded derived categories. In particular, we give in Theorem 1 necessary and sufficient conditions for a 'right bounded' derived category of a differential graded(=dg) category to be a recollement of 'right bounded' derived categories of dg categories. In Theorem 2 we consider the particular case in which those dg categories are just ordinary algebras.Comment: 29 page

A Horizon Study for Cosmic Explorer: Science, Observatories, and Community

Gravitational-wave astronomy has revolutionized humanity's view of the universe. Investment in the field has rewarded the scientific community with the first direct detection of a binary black hole merger and the multimessenger observation of a neutron-star merger. Each of these was a watershed moment in astronomy, made possible because gravitational waves reveal the cosmos in a way that no other probe can. Since the first detection of gravitational waves in 2015, the National Science Foundation's LIGO and its partner observatory, the European Union's Virgo, have detected over fifty binary black hole mergers and a second neutron star merger -- a rate of discovery that has amazed even the most optimistic scientists.This Horizon Study describes a next-generation ground-based gravitational-wave observatory: Cosmic Explorer. With ten times the sensitivity of Advanced LIGO, Cosmic Explorer will push the gravitational-wave astronomy towards the edge of the observable universe ($z \sim 100$). This Horizon Study presents the science objective for Cosmic Explorer, and describes and evaluates its design concepts for. Cosmic Explorer will continue the United States' leadership in gravitational-wave astronomy in the international effort to build a "Third-Generation" (3G) observatory network that will make discoveries transformative across astronomy, physics, and cosmology