Towards Mixed Gr{\"o}bner Basis Algorithms: the Multihomogeneous and Sparse Case

One of the biggest open problems in computational algebra is the design of efficient algorithms for Gr{\"o}bner basis computations that take into account the sparsity of the input polynomials. We can perform such computations in the case of unmixed polynomial systems, that is systems with polynomials having the same support, using the approach of Faug{\`e}re, Spaenlehauer, and Svartz [ISSAC'14]. We present two algorithms for sparse Gr{\"o}bner bases computations for mixed systems. The first one computes with mixed sparse systems and exploits the supports of the polynomials. Under regularity assumptions, it performs no reductions to zero. For mixed, square, and 0-dimensional multihomogeneous polynomial systems, we present a dedicated, and potentially more efficient, algorithm that exploits different algebraic properties that performs no reduction to zero. We give an explicit bound for the maximal degree appearing in the computations

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

Exceptional collections and D-branes probing toric singularities

We demonstrate that a strongly exceptional collection on a singular toric surface can be used to derive the gauge theory on a stack of D3-branes probing the Calabi-Yau singularity caused by the surface shrinking to zero size. A strongly exceptional collection, i.e., an ordered set of sheaves satisfying special mapping properties, gives a convenient basis of D-branes. We find such collections and analyze the gauge theories for weighted projective spaces, and many of the Y^{p,q} and L^{p,q,r} spaces. In particular, we prove the strong exceptionality for all p in the Y^{p,p-1} case, and similarly for the Y^{p,p-2r} case.Comment: 49 pages, 6 figures; v2 refs added; v3 published versio

Urgent need to clarify the definition of chronic critical limb ischemia - a position paper from the European Society for Vascular Medicine

Chronic critical lower limb ischemia (CLI) has been defined as ischemia that endangers the leg. An attempt was made to give a precise definition of CLI, based on clinical and hemodynamic data (Second European Consensus). CLI may be easily defined from a clinical point of view as rest pain of the distal foot or gangrene or ulceration. It is probably useful to add leg ulcers of other origin which do not heal because of severe ischemia, and to consider the impact of frailty on adverse outcome. From a hemodynamic viewpoint there is no consensus and most of the existing classifications are not based upon evidence. We should thus propose a definition and then validate it in a prospective cohort in order to define the patients at major risk of amputation, and also to define the categories of patients whose prognosis is improved by revascularisation. From today\u27s available data, it seems clear that the patients with a systolic toe pressure (STP) below 30 mmHg must be revascularised whenever possible. However other patients with clinically suspected CLI and STP above 30 mmHg must be evaluated and treated in specialised vascular units and revascularisation has to be discussed on a case by case basis, taking into account other data such as the WiFi classification for ulcers.In conclusion, many useful but at times contradictory definitions of CLI have been suggested. Only a few have taken into account evidence, and none have been validated prospectively. This paper aims to address this and to give notice that a CLI registry within Europe will be set up to prospectively validate, or not, the previous and suggested definitions of CLI

Coarsening of graded local cohomology

Some criteria for graded local cohomology to commute with coarsening functors are proven, and an example is given where graded local cohomology does not commute with coarsening.Comment: minor correction

“Less is more”: A dose-response account of intranasal oxytocin pharmacodynamics in the human brain

Intranasal oxytocin is attracting attention as a potential treatment for several brain disorders due to promising preclinical results. However, translating findings to humans has been hampered by remaining uncertainties about its pharmacodynamics and the methods used to probe its effects in the human brain. Using a dose-response design (9, 18 and 36 IU), we demonstrate that intranasal oxytocin-induced changes in local regional cerebral blood flow (rCBF) in the amygdala at rest, and in the covariance between rCBF in the amygdala and other key hubs of the brain oxytocin system, follow a dose-response curve with maximal effects for lower doses. Yet, the effects on local rCBF might vary by amygdala subdivision, highlighting the need to qualify dose-response curves within subregion. We further link physiological changes with the density of the oxytocin receptor gene mRNA across brain regions, strengthening our confidence in intranasal oxytocin as a valid approach to engage central targets. Finally, we demonstrate that intranasal oxytocin does not disrupt cerebrovascular reactivity, which corroborates the validity of haemodynamic neuroimaging to probe the effects of intranasal oxytocin in the human brain. Data availability: Participants did not consent for open sharing of the data. Therefore, data can only be accessed from the corresponding author upon reasonable reques

Why Are Outcomes Different for Registry Patients Enrolled Prospectively and Retrospectively? Insights from the Global Anticoagulant Registry in the FIELD-Atrial Fibrillation (GARFIELD-AF).

Background: Retrospective and prospective observational studies are designed to reflect real-world evidence on clinical practice, but can yield conflicting results. The GARFIELD-AF Registry includes both methods of enrolment and allows analysis of differences in patient characteristics and outcomes that may result. Methods and Results: Patients with atrial fibrillation (AF) and ≥1 risk factor for stroke at diagnosis of AF were recruited either retrospectively (n = 5069) or prospectively (n = 5501) from 19 countries and then followed prospectively. The retrospectively enrolled cohort comprised patients with established AF (for a least 6, and up to 24 months before enrolment), who were identified retrospectively (and baseline and partial follow-up data were collected from the emedical records) and then followed prospectively between 0-18 months (such that the total time of follow-up was 24 months; data collection Dec-2009 and Oct-2010). In the prospectively enrolled cohort, patients with newly diagnosed AF (≤6 weeks after diagnosis) were recruited between Mar-2010 and Oct-2011 and were followed for 24 months after enrolment. Differences between the cohorts were observed in clinical characteristics, including type of AF, stroke prevention strategies, and event rates. More patients in the retrospectively identified cohort received vitamin K antagonists (62.1% vs. 53.2%) and fewer received non-vitamin K oral anticoagulants (1.8% vs . 4.2%). All-cause mortality rates per 100 person-years during the prospective follow-up (starting the first study visit up to 1 year) were significantly lower in the retrospective than prospectively identified cohort (3.04 [95% CI 2.51 to 3.67] vs . 4.05 [95% CI 3.53 to 4.63]; p = 0.016). Conclusions: Interpretations of data from registries that aim to evaluate the characteristics and outcomes of patients with AF must take account of differences in registry design and the impact of recall bias and survivorship bias that is incurred with retrospective enrolment. Clinical Trial Registration: - URL: http://www.clinicaltrials.gov . Unique identifier for GARFIELD-AF (NCT01090362)

Розрахунок та проектування окремого фундаменту будівлі на природній ґрунтовій основі. Методичні рекомендації до виконання практичних завдань та курсового проекту з дисципліни «Механіка ґрунтів, основи і фундаменти» сту- дентами напрямів підготовки 6.060101 Будівництво та 6.050301 Гірництво

Подано методичні рекомендації до виконання практичних завдань та кур- сового проекту з дисципліни «Механіка ґрунтів, основи і фундаменти» для сту- дентів напрямів підготовки 6.060101 Будівництво та 6.050301 Гірництво. Розглянуто порядок проектування фундаменту будівлі мілкого закладан- ня на природній ґрунтовій основі. Методичні рекомендації передбачають виконання курсового проекту «Розрахунок та проектування окремого фундаменту будівлі на природній ґрун- товій основі» як із викладачем, так і під час самостійної роботи. Можна використовувати також у підготовці курсового та дипломного про- ектування

Antiinflammatory Therapy with Canakinumab for Atherosclerotic Disease

Background: Experimental and clinical data suggest that reducing inflammation without affecting lipid levels may reduce the risk of cardiovascular disease. Yet, the inflammatory hypothesis of atherothrombosis has remained unproved. Methods: We conducted a randomized, double-blind trial of canakinumab, a therapeutic monoclonal antibody targeting interleukin-1β, involving 10,061 patients with previous myocardial infarction and a high-sensitivity C-reactive protein level of 2 mg or more per liter. The trial compared three doses of canakinumab (50 mg, 150 mg, and 300 mg, administered subcutaneously every 3 months) with placebo. The primary efficacy end point was nonfatal myocardial infarction, nonfatal stroke, or cardiovascular death. RESULTS: At 48 months, the median reduction from baseline in the high-sensitivity C-reactive protein level was 26 percentage points greater in the group that received the 50-mg dose of canakinumab, 37 percentage points greater in the 150-mg group, and 41 percentage points greater in the 300-mg group than in the placebo group. Canakinumab did not reduce lipid levels from baseline. At a median follow-up of 3.7 years, the incidence rate for the primary end point was 4.50 events per 100 person-years in the placebo group, 4.11 events per 100 person-years in the 50-mg group, 3.86 events per 100 person-years in the 150-mg group, and 3.90 events per 100 person-years in the 300-mg group. The hazard ratios as compared with placebo were as follows: in the 50-mg group, 0.93 (95% confidence interval [CI], 0.80 to 1.07; P = 0.30); in the 150-mg group, 0.85 (95% CI, 0.74 to 0.98; P = 0.021); and in the 300-mg group, 0.86 (95% CI, 0.75 to 0.99; P = 0.031). The 150-mg dose, but not the other doses, met the prespecified multiplicity-adjusted threshold for statistical significance for the primary end point and the secondary end point that additionally included hospitalization for unstable angina that led to urgent revascularization (hazard ratio vs. placebo, 0.83; 95% CI, 0.73 to 0.95; P = 0.005). Canakinumab was associated with a higher incidence of fatal infection than was placebo. There was no significant difference in all-cause mortality (hazard ratio for all canakinumab doses vs. placebo, 0.94; 95% CI, 0.83 to 1.06; P = 0.31). Conclusions: Antiinflammatory therapy targeting the interleukin-1β innate immunity pathway with canakinumab at a dose of 150 mg every 3 months led to a significantly lower rate of recurrent cardiovascular events than placebo, independent of lipid-level lowering. (Funded by Novartis; CANTOS ClinicalTrials.gov number, NCT01327846.