An Algebra of Pieces of Space -- Hermann Grassmann to Gian Carlo Rota

We sketch the outlines of Gian Carlo Rota's interaction with the ideas that Hermann Grassmann developed in his Ausdehnungslehre of 1844 and 1862, as adapted and explained by Giuseppe Peano in 1888. This leads us past what Rota variously called 'Grassmann-Cayley algebra', or 'Peano spaces', to the Whitney algebra of a matroid, and finally to a resolution of the question "What, really, was Grassmann's regressive product?". This final question is the subject of ongoing joint work with Andrea Brini, Francesco Regonati, and William Schmitt. The present paper was presented at the conference "The Digital Footprint of Gian-Carlo Rota: Marbles, Boxes and Philosophy" in Milano on 17 Feb 2009. It will appear in proceedings of that conference, to be published by Springer Verlag.Comment: 28 page

The cost-effectiveness of the WINGS intervention: a program to prevent HIV and sexually transmitted diseases among high-risk urban women

BACKGROUND: We evaluated the cost-effectiveness of the WINGS project, an intervention to prevent HIV and other sexually transmitted diseases among urban women at high risk for sexual acquisition of HIV. METHODS: We used standard methods of cost-effectiveness analysis. We conducted a retrospective analysis of the intervention's cost and we used a simplified model of HIV transmission to estimate the number of HIV infections averted by the intervention. We calculated cost-effectiveness ratios for the complete intervention and for the condom use skills component of the intervention. RESULTS: Under base case assumptions, the intervention prevented an estimated 0.2195 new cases of HIV at a cost of $215,690 per case of HIV averted. When indirect costs of HIV were excluded from the analysis, the intervention's cost-effectiveness ratios were$357,690 per case of HIV averted and $31,851 per quality-adjusted life year (QALY) saved. Under base case assumptions, the condom use skills component of the intervention prevented an estimated 0.1756 HIV infections and was cost-saving. When indirect HIV costs were excluded, the cost-effectiveness ratios for the condom use skills component of the intervention were$97,404 per case of HIV averted and $8,674 per QALY saved. CONCLUSIONS: The WINGS intervention, particularly the two sessions of the intervention which focussed on condom use skills, could be cost-effective in preventing HIV among women

Image perception and interpretation of abnormalities; can we believe our eyes? Can we do something about it?

The radiologist’s visual impression of images is transmitted, via non-visual means (the report), to the clinician. There are several complex steps from the perception of the images by the radiologist to the understanding of the impression by the clinician. With a process as complex as this, it is no wonder that errors in perception, cognition, interpretation, transmission and understanding are very common. This paper reviews the processes of perception and error generation and possible strategies for minimising them

Quantum field theory and Hopf algebra cohomology

We exhibit a Hopf superalgebra structure of the algebra of field operators of quantum field theory (QFT) with the normal product. Based on this we construct the operator product and the time-ordered product as a twist deformation in the sense of Drinfeld. Our approach yields formulas for (perturbative) products and expectation values that allow for a significant enhancement in computational efficiency as compared to traditional methods. Employing Hopf algebra cohomology sheds new light on the structure of QFT and allows the extension to interacting (not necessarily perturbative) QFT. We give a reconstruction theorem for time-ordered products in the spirit of Streater and Wightman and recover the distinction between free and interacting theory from a property of the underlying cocycle. We also demonstrate how non-trivial vacua are described in our approach solving a problem in quantum chemistry.Comment: 39 pages, no figures, LaTeX + AMS macros; title changed, minor corrections, references update

A Markov computer simulation model of the economics of neuromuscular blockade in patients with acute respiratory distress syndrome

BACKGROUND: Management of acute respiratory distress syndrome (ARDS) in the intensive care unit (ICU) is clinically challenging and costly. Neuromuscular blocking agents may facilitate mechanical ventilation and improve oxygenation, but may result in prolonged recovery of neuromuscular function and acute quadriplegic myopathy syndrome (AQMS). The goal of this study was to address a hypothetical question via computer modeling: Would a reduction in intubation time of 6 hours and/or a reduction in the incidence of AQMS from 25% to 21%, provide enough benefit to justify a drug with an additional expenditure of $267 (the difference in acquisition cost between a generic and brand name neuromuscular blocker)? METHODS: The base case was a 55 year-old man in the ICU with ARDS who receives neuromuscular blockade for 3.5 days. A Markov model was designed with hypothetical patients in 1 of 6 mutually exclusive health states: ICU-intubated, ICU-extubated, hospital ward, long-term care, home, or death, over a period of 6 months. The net monetary benefit was computed. RESULTS: Our computer simulation modeling predicted the mean cost for ARDS patients receiving standard care for 6 months to be$62,238 (5% – 95% percentiles $42,259 –$83,766), with an overall 6-month mortality of 39%. Assuming a ceiling ratio of $35,000, even if a drug (that cost$267 more) hypothetically reduced AQMS from 25% to 21% and decreased intubation time by 6 hours, the net monetary benefit would only equal $137. CONCLUSION: ARDS patients receiving a neuromuscular blocker have a high mortality, and unpredictable outcome, which results in large variability in costs per case. If a patient dies, there is no benefit to any drug that reduces ventilation time or AQMS incidence. A prospective, randomized pharmacoeconomic study of neuromuscular blockers in the ICU to asses AQMS or intubation times is impractical because of the highly variable clinical course of patients with ARDS

Cost-Effectiveness of Genotypic Antiretroviral Resistance Testing in HIV-Infected Patients with Treatment Failure

BACKGROUND: Genotypic antiretroviral resistance testing (GRT) in HIV infection with drug resistant virus is recommended to optimize antiretroviral therapy, in particular in patients with virological failure. We estimated the clinical effect, cost and cost-effectiveness of using GRT as compared to expert opinion in patients with antiretroviral treatment failure. METHODS: We developed a mathematical model of HIV disease to describe disease progression in HIV-infected patients with treatment failure and compared the incremental impact of GRT versus expert opinion to guide antiretroviral therapy. The analysis was conducted from the health care (discount rate 4%) and societal (discount rate 2%) perspective. Outcome measures included life-expectancy, quality-adjusted life-expectancy, health care costs, productivity costs and cost-effectiveness in US Dollars per quality-adjusted life-year (QALY) gained. Clinical and economic data were extracted from the large Swiss HIV Cohort Study and clinical trials. RESULTS: Patients whose treatment was optimized with GRT versus expert opinion had an increase in discounted life-expectancy and quality-adjusted life-expectancy of three and two weeks, respectively. Health care costs with and without GRT were $US 421,000 and$US 419,000, leading to an incremental cost-effectiveness ratio of $US 35,000 per QALY gained. In the analysis from the societal perspective, GRT versus expert opinion led to an increase in discounted life-expectancy and quality-adjusted life-expectancy of three and four weeks, respectively. Health care costs with and without GRT were$US 551,000 and $US 549,000, respectively. When productivity changes were included in the analysis, GRT was cost-saving. CONCLUSIONS: GRT for treatment optimization in HIV-infected patients with treatment failure is a cost-effective use of scarce health care resources and beneficial to the society at large

Cost-effectiveness of In-home Automated External Defibrillators for Individuals at Increased Risk of Sudden Cardiac Death

In-home automated external defibrillators (AEDs) are increasingly recommended as a means for improving survival of cardiac arrests that occur at home. The current study was conducted to explore the relationship between individuals' risk of cardiac arrest and cost-effectiveness of in-home AED deployment. Design : Markov decision model employing a societal perspective. Patients : Four hypothetical cohorts of American adults 60 years of age at progressively greater risk for sudden cardiac death (SCD): 1) all adults (annual probability of SCD 0.4%); 2) adults with multiple SCD risk factors (probability 2%); 3) adults with previous myocardial infarction (probability 4%); and 4) adults with ischemic cardiomyopathy unable to receive an implantable defibrillator (probability 6%). Intervention : Strategy 1: individuals suffering an in-home cardiac arrest were treated with emergency medical services equipped with AEDs (EMS-D). Strategy 2: individuals suffering an in-home cardiac arrest received initial treatment with an in-home AED, followed by EMS. Results : Assuming cardiac arrest survival rates of 15% with EMS-D and 30% with AEDs, the cost per quality-adjusted life-year gained (QALY) of providing in-home AEDs to all adults 60 years of age is $216,000. Costs of providing in-home AEDs to adults with multiple risk factors (2$132,000, $104,000, and$88,000, respectively. Conclusions : The cost-effectiveness of in-home AEDs is intimately linked to individuals' risk of SCD. However, providing in-home AEDs to all adults over age 60 appears relatively expensive.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72168/1/j.1525-1497.2005.40247.x.pd

Cost-effectiveness analysis of guidelines for antihypertensive care in Finland

<p>Abstract</p> <p>Background</p> <p>Hypertension is one of the major causes of disease burden affecting the Finnish population. Over the last decade, evidence-based care has emerged to complement other approaches to antihypertensive care, often without health economic assessment of its costs and effects. This study looks at the extent to which changes proposed by the 2002 Finnish evidence-based Current Care Guidelines concerning the prevention, diagnosis, and treatment of hypertension (the ACCG scenario) can be considered cost-effective when compared to modelled prior clinical practice (the PCP scenario).</p> <p>Methods</p> <p>A decision analytic model compares the ACCG and PCP scenarios using information synthesised from a set of national registers covering prescription drug reimbursements, morbidity, and mortality with data from two national surveys concerning health and functional capacity. Statistical methods are used to estimate model parameters from Finnish data. We model the potential impact of the different treatment strategies under the ACCG and PCP scenarios, such as lifestyle counselling and drug therapy, for subgroups stratified by age, gender, and blood pressure. The model provides estimates of the differences in major health-related outcomes in the form of life-years and costs as calculated from a 'public health care system' perspective. Cost-effectiveness analysis results are presented for subgroups and for the target population as a whole.</p> <p>Results</p> <p>The impact of the use of the ACCG scenario in subgroups (aged 40–80) without concomitant cardiovascular and related diseases is mainly positive. Generally, costs and life-years decrease in unison in the lowest blood pressure group, while in the highest blood pressure group costs and life-years increase together and in the other groups the ACCG scenario is less expensive and produces more life-years. When the costs and effects for subgroups are combined using standard decision analytic aggregation methods, the ACCG scenario is cost-saving and more effective.</p> <p>Conclusion</p> <p>The ACCG scenario is likely to reduce costs and increase life-years compared to the PCP scenario in many subgroups. If the estimated trade-offs between the subgroups in terms of outcomes and costs are acceptable to decision-makers, then widespread implementation of the ACCG scenario is expected to reduce overall costs and be accompanied by positive outcomes overall.</p

Spermatogenesis-Specific Features of the Meiotic Program in Caenorhabditis elegans

In most sexually reproducing organisms, the fundamental process of meiosis is implemented concurrently with two differentiation programs that occur at different rates and generate distinct cell types, sperm and oocytes. However, little is known about how the meiotic program is influenced by such contrasting developmental programs. Here we present a detailed timeline of late meiotic prophase during spermatogenesis in Caenorhabditis elegans using cytological and molecular landmarks to interrelate changes in chromosome dynamics with germ cell cellularization, spindle formation, and cell cycle transitions. This analysis expands our understanding C. elegans spermatogenesis, as it identifies multiple spermatogenesis-specific features of the meiotic program and provides a framework for comparative studies. Post-pachytene chromatin of spermatocytes is distinct from that of oocytes in both composition and morphology. Strikingly, C. elegans spermatogenesis includes a previously undescribed karyosome stage, a common but poorly understood feature of meiosis in many organisms. We find that karyosome formation, in which chromosomes form a constricted mass within an intact nuclear envelope, follows desynapsis, involves a global down-regulation of transcription, and may support the sequential activation of multiple kinases that prepare spermatocytes for meiotic divisions. In spermatocytes, the presence of centrioles alters both the relative timing of meiotic spindle assembly and its ultimate structure. These microtubule differences are accompanied by differences in kinetochores, which connect microtubules to chromosomes. The sperm-specific features of meiosis revealed here illuminate how the underlying molecular machinery required for meiosis is differentially regulated in each sex