On positivity of Ehrhart polynomials

Ehrhart discovered that the function that counts the number of lattice points in dilations of an integral polytope is a polynomial. We call the coefficients of this polynomial Ehrhart coefficients, and say a polytope is Ehrhart positive if all Ehrhart coefficients are positive (which is not true for all integral polytopes). The main purpose of this article is to survey interesting families of polytopes that are known to be Ehrhart positive and discuss the reasons from which their Ehrhart positivity follows. We also include examples of polytopes that have negative Ehrhart coefficients and polytopes that are conjectured to be Ehrhart positive, as well as pose a few relevant questions.Comment: 40 pages, 7 figures. To appear in in Recent Trends in Algebraic Combinatorics, a volume of the Association for Women in Mathematics Series, Springer International Publishin

Theoretical analysis of the mechanisms of a gender differentiation in the propensity for orthostatic intolerance after spaceflight

<p>Abstract</p> <p>Background</p> <p>A tendency to develop reentry orthostasis after a prolonged exposure to microgravity is a common problem among astronauts. The problem is 5 times more prevalent in female astronauts as compared to their male counterparts. The mechanisms responsible for this gender differentiation are poorly understood despite many detailed and complex investigations directed toward an analysis of the physiologic control systems involved.</p> <p>Methods</p> <p>In this study, a series of computer simulation studies using a mathematical model of cardiovascular functioning were performed to examine the proposed hypothesis that this phenomenon could be explained by basic physical forces acting through the simple common anatomic differences between men and women. In the computer simulations, the circulatory components and hydrostatic gradients of the model were allowed to adapt to the physical constraints of microgravity. After a simulated period of one month, the model was returned to the conditions of earth's gravity and the standard postflight tilt test protocol was performed while the model output depicting the typical vital signs was monitored.</p> <p>Conclusions</p> <p>The analysis demonstrated that a 15% lowering of the longitudinal center of gravity in the anatomic structure of the model was all that was necessary to prevent the physiologic compensatory mechanisms from overcoming the propensity for reentry orthostasis leading to syncope.</p

Efficacy of α-Blockers on Hemodynamic Control during Pheochromocytoma Resection: A Randomized Controlled Trial

CONTEXT: Pretreatment with α-adrenergic receptor blockers is recommended to prevent hemodynamic instability during resection of a pheochromocytoma or sympathetic paraganglioma (PPGL). OBJECTIVE: To determine which type of α-adrenergic receptor blocker provides the best efficacy. DESIGN: Randomized controlled open-label trial (PRESCRIPT; ClinicalTrials.gov NCT01379898). SETTING: Multicenter study including 9 centers in The Netherlands. PATIENTS: 134 patients with nonmetastatic PPGL. INTERVENTION: Phenoxybenzamine or doxazosin starting 2 to 3 weeks before surgery using a blood pressure targeted titration schedule. Intraoperative hemodynamic management was standardized. MAIN OUTCOME MEASURES: Primary efficacy endpoint was the cumulative intraoperative time outside the blood pressure target range (ie, SBP >160 mmHg or MAP <60 mmHg) expressed as a percentage of total surgical procedure time. Secondary efficacy endpoint was the value on a hemodynamic instability score. RESULTS: Median cumulative time outside blood pressure targets was 11.1% (interquartile range [IQR]: 4.3-20.6] in the phenoxybenzamine group compared to 12.2% (5.3-20.2)] in the doxazosin group (P = .75, r = 0.03). The hemodynamic instability score was 38.0 (28.8-58.0) and 50.0 (35.3-63.8) in the phenoxybenzamine and doxazosin group, respectively (P = .02, r = 0.20). The 30-day cardiovascular complication rate was 8.8% and 6.9% in the phenoxybenzamine and doxazosin group, respectively (P = .68). There was no mortality after 30 days. CONCLUSIONS: The duration of blood pressure outside the target range during resection of a PPGL was not different after preoperative treatment with either phenoxybenzamine or doxazosin. Phenoxybenzamine was more effective in preventing intraoperative hemodynamic instability, but it could not be established whether this was associated with a better clinical outcome

Efficacy of alpha-Blockers on Hemodynamic Control during Pheochromocytoma Resection:A Randomized Controlled Trial

CONTEXT: Pretreatment with α-adrenergic receptor blockers is recommended to prevent hemodynamic instability during resection of a pheochromocytoma or sympathetic paraganglioma (PPGL). OBJECTIVE: To determine which type of α-adrenergic receptor blocker provides the best efficacy. DESIGN: Randomized controlled open-label trial (PRESCRIPT; ClinicalTrials.gov NCT01379898). SETTING: Multicenter study including 9 centers in The Netherlands. PATIENTS: 134 patients with non-metastatic PPGL. INTERVENTION: phenoxybenzamine or doxazosin starting 2-3 weeks before surgery using a blood pressure targeted titration schedule. Intraoperative hemodynamic management was standardized. MAIN OUTCOME MEASURES: Primary efficacy endpoint was the cumulative intraoperative time outside the blood pressure target range (i.e., SBP >160 mmHg or MAP <60 mmHg) expressed as a percentage of total surgical procedure time. Secondary efficacy endpoint was the value on a hemodynamic instability score. RESULTS: Median cumulative time outside blood pressure targets was 11.1% [IQR: 4.3-20.6] in the phenoxybenzamine group compared to 12.2% [5.3-20.2] in the doxazosin group (P=0.75, r=0.03). The hemodynamic instability score was 38.0 [28.8-58.0] and 50.0 [35.3-63.8] in the phenoxybenzamine and doxazosin group, respectively (P=0.02, r=0.20). The 30-day cardiovascular complication rate was 8.8% and 6.9% in the phenoxybenzamine and doxazosin group, respectively (P=0.68). There was no mortality after 30 days. CONCLUSIONS: The duration of blood pressure outside the target range during resection of a PPGL was not different after preoperative treatment with either phenoxybenzamine or doxazosin. Phenoxybenzamine was more effective in preventing intraoperative hemodynamic instability, but it could not be established whether this was associated with a better clinical outcome

Interpersonal psychotherapy (IPT) for late-life depression in general practice: uptake and satisfaction by patients, therapists and physicians

<p>Abstract</p> <p>Background</p> <p>Interpersonal Psychotherapy (IPT) is recommended in most depression treatment guidelines and proved to be a suitable treatment for elderly depressed patients. Despite the favorable results of IPT in research populations, the dissemination to general practice is surprisingly limited. Little is known about uptake and satisfaction when this therapy is introduced into real-life general practice.</p> <p>Methods</p> <p>Motivation and evaluation of patients, GPs and therapists were recorded and organizational barriers described alongside a randomized controlled trial. IPT, given by mental health workers, was compared with usual general practitioner (GP) care. Included were patients (≥55 years) who met the DSM-IV criteria for major depressive disorder.</p> <p>Results</p> <p>Patients were motivated for the psychotherapy intervention: of the 205 eligible patients, 143 (70%) entered the study, and of the 69 patients who were offered IPT, 77% complied with the treatment. IPT proved to be an attractive therapy for patients as well as for therapists from mental health organizations. General practitioners evaluated the intervention positively afterwards, mainly because of the time-limited and structured approach. Organizational barriers: no IPT therapists were available; an IPT trainer and supervisor had to be trained and training materials had to be developed and translated. Additionally, there was a lack of office space in some general practices; for therapists from private practices it was not feasible to participate because of financial reasons. IPT was superior to usual care in patients with moderate to severe depression.</p> <p>Conclusion</p> <p>As we succeeded in delivering IPT in primary care practice, and as IPT was superior to usual care, there are grounds to support the implementation of IPT for depressed elderly patients within general practice, as long as the practices have room for the therapists and financial barriers can be overcome. Consolidation may be achieved by making this intervention available through practice nurses or community psychiatric nurses who deliver IPT as part of a more comprehensive depression management program.</p

Clinical effectiveness of usual care with or without antidepressant medication for primary care patients with minor or mild-major depression: a randomized equivalence trial

<p>Abstract</p> <p>Background</p> <p>Minor and mild-major depression are highly prevalent in primary care. There is insufficient evidence for the effectiveness of antidepressants in the treatment of minor and mild-major depression. We compared the effectiveness of usual primary care treatment, with or without antidepressants, in minor and mild-major depression.</p> <p>Methods</p> <p>A pragmatic patient-randomized equivalence trial with 52 weeks follow-up was conducted in The Netherlands. In total, 59 primary care physicians (PCPs) recruited and treated 181 adult patients with minor or mild-major depression. Patients were randomized to four consultations within 3 months of usual care plus antidepressants (UCandAD) or usual care alone (UCnoAD). The Montgomery Åsberg Depression Rating Scale (MADRS) was used to assess changes in severity of depressive symptoms. The predefined equivalence margin was set at five points. Multilevel analysis was used to analyze the data. Secondary outcome measures were the Short-Form 36 (SF-36), and the Client Satisfaction Questionnaire (CSQ-8).</p> <p>Results</p> <p>Patients received on average 3.0 (SD 1.4) 15-min consultations within 3 months with (n = 85) or without paroxetine (n = 96). Equivalence of UCandAD and UCnoAD was demonstrated in the intention-to-treat analyses as well as the per-protocol analysis after 6 weeks, but not at 13, 26 and 52 weeks follow-up. No statistical differences in effectiveness between treatment groups were found in the intention-to-treat analysis. No differences in the physical and mental functioning (SF-36) were found between the treatment groups. Patients allocated to UCandAD were slightly more satisfied with their treatment at 13 weeks follow-up (but not at 52 weeks follow-up) than patients allocated to UCnoAD. Preliminary analyses suggested that subgroups such as patients with mild-major (instead of a minor) depression might benefit from antidepressant treatment. Patients who were assigned to their preferred treatment (in particular to UCnoAD) were more often compliant and had better clinical outcomes.</p> <p>Conclusion</p> <p>UCandAD was as effective as UCnoAD over the first 6 weeks, but not at 13, 26, and 52 weeks. However, superiority of either treatment could not be demonstrated either. The question whether antidepressants add any clinical effect to usual care remains unresolved. We recommend future studies to look for subgroups of patients who may benefit from antidepressants.</p> <p>Trial registration</p> <p>Dutch Trial Registry ISRCN03007807.</p

Measurement of the cosmic ray spectrum above 4×10184{\times}10^{18} eV using inclined events detected with the Pierre Auger Observatory

A measurement of the cosmic-ray spectrum for energies exceeding $4{\times}10^{18}$ eV is presented, which is based on the analysis of showers with zenith angles greater than $60^{\circ}$ detected with the Pierre Auger Observatory between 1 January 2004 and 31 December 2013. The measured spectrum confirms a flux suppression at the highest energies. Above $5.3{\times}10^{18}$ eV, the "ankle", the flux can be described by a power law $E^{-\gamma}$ with index $\gamma=2.70 \pm 0.02 \,\text{(stat)} \pm 0.1\,\text{(sys)}$ followed by a smooth suppression region. For the energy ($E_\text{s}$) at which the spectral flux has fallen to one-half of its extrapolated value in the absence of suppression, we find $E_\text{s}=(5.12\pm0.25\,\text{(stat)}^{+1.0}_{-1.2}\,\text{(sys)}){\times}10^{19}$ eV.Comment: Replaced with published version. Added journal reference and DO