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

Multi-level Trainable Segmentation for Measuring Gestational and Yolk Sacs from Ultrasound Images

As a non-hazardous and non-invasive approach to medical diagnostic imaging, ultrasound serves as an ideal candidate for tracking and monitoring pregnancy development. One critical assessment during the first trimester of the pregnancy is the size measurements of the Gestation Sac (GS) and the Yolk Sac (YS) from ultrasound images. Such measurements tend to give a strong indication on the viability of the pregnancy. This paper proposes a novel multi-level trainable segmentation method to achieve three objectives in the following order: (1) segmenting and measuring the GS, (2) automatically identifying the stage of pregnancy, and (3) segmenting and measuring the YS. The first level segmentation employs a trainable segmentation technique based on the histogram of oriented gradients to segment the GS and estimate its size. This is then followed by an automatic identification of the pregnancy stage based on histogram analysis of the content of the segmented GS. The second level segmentation is used after that to detect the YS and extract its relevant size measurements. A trained neural network classifier is employed to perform the segmentation at both levels. The effectiveness of the proposed solution has been evaluated by comparing the automatic size measurements of the GS and YS against the ones obtained gynaecologist. Experimental results on 199 ultrasound images demonstrate the effectiveness of the proposal in producing accurate measurements as well as identifying the correct stage of pregnancy

Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals

We prove a theorem unifying three results from combinatorial homological and commutative algebra, characterizing the Koszul property for incidence algebras of posets and affine semigroup rings, and characterizing linear resolutions of squarefree monomial ideals. The characterization in the graded setting is via the Cohen-Macaulay property of certain posets or simplicial complexes, and in the more general nongraded setting, via the sequential Cohen-Macaulay property.Comment: 31 pages, 1 figure. Minor changes from previous version. To appear in Advances in Mathematic

Quantum field theory meets Hopf algebra

This paper provides a primer in quantum field theory (QFT) based on Hopf algebra and describes new Hopf algebraic constructions inspired by QFT concepts. The following QFT concepts are introduced: chronological products, S-matrix, Feynman diagrams, connected diagrams, Green functions, renormalization. The use of Hopf algebra for their definition allows for simple recursive derivations and lead to a correspondence between Feynman diagrams and semi-standard Young tableaux. Reciprocally, these concepts are used as models to derive Hopf algebraic constructions such as a connected coregular action or a group structure on the linear maps from S(V) to V. In most cases, noncommutative analogues are derived.Comment: 27 pages, 4 figures. Slightly edited version of the published pape

Cost-effectiveness analysis of introducing RDTs for malaria diagnosis as compared to microscopy and presumptive diagnosis in central and peripheral public health facilities in Ghana.

Cost-effectiveness information on where malaria rapid diagnostic tests (RDTs) should be introduced is limited. We developed incremental cost-effectiveness analyses with data from rural health facilities in Ghana with and without microscopy. In the latter, where diagnosis had been presumptive, the introduction of RDTs increased the proportion of patients who were correctly treated in relation to treatment with antimalarials, from 42% to 65% at an incremental societal cost of Ghana cedis (GHS)12.2 (US$8.3) per additional correctly treated patients. In the "microscopy setting" there was no advantage to replacing microscopy by RDT as the cost and proportion of correctly treated patients were similar. Results were sensitive to a decrease in the cost of RDTs, which cost GHS1.72 (US$1.17) per test at the time of the study and to improvements in adherence to negative tests that was just above 50% for both RDTs and microscopy

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

Studies in partitions and permutations.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1973.Vita.Bibliography: leaves 132-136.Ph.D

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

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