Enhancing Automated Test Selection in Probabilistic Networks

In diagnostic decision-support systems, test selection amounts to selecting, in a sequential manner, a test that is expected to yield the largest decrease in the uncertainty about a patient’s diagnosis. For capturing this uncertainty, often an information measure is used. In this paper, we study the Shannon entropy, the Gini index, and the misclassification error for this purpose. We argue that the Gini index can be regarded as an approximation of the Shannon entropy and that the misclassification error can be looked upon as an approximation of the Gini index. We further argue that the differences between the first derivatives of the three functions can explain different test sequences in practice. Experimental results from using the measures with a real-life probabilistic network in oncology support our observations

Punctual Hilbert Schemes and Certified Approximate Singularities

In this paper we provide a new method to certify that a nearby polynomial system has a singular isolated root with a prescribed multiplicity structure. More precisely, given a polynomial system f $=(f\_1, \ldots, f\_N)\in C[x\_1, \ldots, x\_n]^N$, we present a Newton iteration on an extended deflated system that locally converges, under regularity conditions, to a small deformation of $f$ such that this deformed system has an exact singular root. The iteration simultaneously converges to the coordinates of the singular root and the coefficients of the so called inverse system that describes the multiplicity structure at the root. We use $$\alpha$$-theory test to certify the quadratic convergence, and togive bounds on the size of the deformation and on the approximation error. The approach relies on an analysis of the punctual Hilbert scheme, for which we provide a new description. We show in particular that some of its strata can be rationally parametrized and exploit these parametrizations in the certification. We show in numerical experimentation how the approximate inverse system can be computed as a starting point of the Newton iterations and the fast numerical convergence to the singular root with its multiplicity structure, certified by our criteria.Comment: International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata, Franc

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

Standard monomial theory for wonderful varieties

A general setting for a standard monomial theory on a multiset is introduced and applied to the Cox ring of a wonderful variety. This gives a degeneration result of the Cox ring to a multicone over a partial flag variety. Further, we deduce that the Cox ring has rational singularities.Comment: v3: 20 pages, final version to appear on Algebras and Representation Theory. The final publication is available at Springer via http://dx.doi.org/10.1007/s10468-015-9586-z. v2: 20 pages, examples added in Section 3 and in Section

Issues in Cost Effectiveness in Health Care

Cost-effectiveness analysis (CEA) is becoming increasingly popular as society moves toward rationalizing health costs. This review describes the applications and limitations of the technique. Conceptually simple though frequently complicated in application, CEA compares the cost of a procedure with its effectiveness, thus helping an administrator to judge whether the procedure is worth its cost. CEA also permits comparison of various interventions that result in a similar health outcome. A major benefit of CEA is that it forces decision makers to confront the tradeoffs implicit in all decisions regarding alternative approaches. Limitations of the CEA philosophy and technique also have to be understood if it is to be employed effectively; it is not an assessment of cost savings, nor is it a decision-making technique because it does not incorporate value judgments. A number of potential applications to dentistry are described.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65700/1/j.1752-7325.1989.tb02085.x.pd

Single-dose versus multiple-dose antibiotic prophylaxis for the surgical treatment of closed fractures: A cost-effectiveness analysis

Background and purpose Recent meta-analyses have suggested similar wound infection rates when using single- or multiple-dose antibiotic prophylaxis in the operative management of closed long bone fractures. In order to assist clinicians in choosing the optimal prophylaxis strategy, we performed a cost-effectiveness analysis comparing single- and multiple-dose prophylaxis

A nearly continuous measure of birth weight for gestational age using a United States national reference

BACKGROUND: Fully understanding the determinants and sequelae of fetal growth requires a continuous measure of birth weight adjusted for gestational age. Published United States reference data, however, provide estimates only of the median and lowest and highest 5(th )and 10(th )percentiles for birth weight at each gestational age. The purpose of our analysis was to create more continuous reference measures of birth weight for gestational age for use in epidemiologic analyses. METHODS: We used data from the most recent nationwide United States Natality datasets to generate multiple reference percentiles of birth weight at each completed week of gestation from 22 through 44 weeks. Gestational age was determined from last menstrual period. We analyzed data from 6,690,717 singleton infants with recorded birth weight and sex born to United States resident mothers in 1999 and 2000. RESULTS: Birth weight rose with greater gestational age, with increasing slopes during the third trimester and a leveling off beyond 40 weeks. Boys had higher birth weights than girls, later born children higher weights than firstborns, and infants born to non-Hispanic white mothers higher birth weights than those born to non-Hispanic black mothers. These results correspond well with previously published estimates reporting limited percentiles. CONCLUSIONS: Our method provides comprehensive reference values of birth weight at 22 through 44 completed weeks of gestation, derived from broadly based nationwide data. Other approaches require assumptions of normality or of a functional relationship between gestational age and birth weight, which may not be appropriate. These data should prove useful for researchers investigating the predictors and outcomes of altered fetal growth

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

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