Modeling hospital infrastructure by optimizing quality, accessibility and efficiency via a mixed integer programming model

BACKGROUND: The majority of curative health care is organized in hospitals. As in most other countries, the current 94 hospital locations in the Netherlands offer almost all treatments, ranging from rather basic to very complex care. Recent studies show that concentration of care can lead to substantial quality improvements for complex conditions and that dispersion of care for chronic conditions may increase quality of care. In previous studies on allocation of hospital infrastructure, the allocation is usually only based on accessibility and/or efficiency of hospital care. In this paper, we explore the possibilities to include a quality function in the objective function, to give global directions to how the ‘optimal’ hospital infrastructure would be in the Dutch context. METHODS: To create optimal societal value we have used a mathematical mixed integer programming (MIP) model that balances quality, efficiency and accessibility of care for 30 ICD-9 diagnosis groups. Typical aspects that are taken into account are the volume-outcome relationship, the maximum accepted travel times for diagnosis groups that may need emergency treatment and the minimum use of facilities. RESULTS: The optimal number of hospital locations per diagnosis group varies from 12-14 locations for diagnosis groups which have a strong volume-outcome relationship, such as neoplasms, to 150 locations for chronic diagnosis groups such as diabetes and chronic obstructive pulmonary disease (COPD). CONCLUSIONS: In conclusion, our study shows a new approach for allocating hospital infrastructure over a country or certain region that includes quality of care in relation to volume per provider that can be used in various countries or regions. In addition, our model shows that within the Dutch context chronic care may be too concentrated and complex and/or acute care may be too dispersed. Our approach can relatively easily be adopted towards other countries or regions and is very suitable to perform a ‘what-if’ analysis

Differential Calculi on Commutative Algebras

A differential calculus on an associative algebra A is an algebraic analogue of the calculus of differential forms on a smooth manifold. It supplies A with a structure on which dynamics and field theory can be formulated to some extent in very much the same way we are used to from the geometrical arena underlying classical physical theories and models. In previous work, certain differential calculi on a commutative algebra exhibited relations with lattice structures, stochastics, and parametrized quantum theories. This motivated the present systematic investigation of differential calculi on commutative and associative algebras. Various results about their structure are obtained. In particular, it is shown that there is a correspondence between first order differential calculi on such an algebra and commutative and associative products in the space of 1-forms. An example of such a product is provided by the Ito calculus of stochastic differentials. For the case where the algebra A is freely generated by `coordinates' x^i, i=1,...,n, we study calculi for which the differentials dx^i constitute a basis of the space of 1-forms (as a left A-module). These may be regarded as `deformations' of the ordinary differential calculus on R^n. For n < 4 a classification of all (orbits under the general linear group of) such calculi with `constant structure functions' is presented. We analyse whether these calculi are reducible (i.e., a skew tensor product of lower-dimensional calculi) or whether they are the extension (as defined in this article) of a one dimension lower calculus. Furthermore, generalizations to arbitrary n are obtained for all these calculi.Comment: 33 pages, LaTeX. Revision: A remark about a quasilattice and Penrose tiling was incorrect in the first version of the paper (p. 14

Clinical longevity of intracoronal restorations made of gold, lithium disilicate, leucite, and indirect resin composite:a systematic review and meta-analysis

OBJECTIVES: The aim of this systematic review and meta-analysis is to assess the comparative clinical success and survival of intracoronal indirect restorations using gold, lithium disilicate, leucite, and indirect composite materials.MATERIAL AND METHODS: This systematic review and meta-analysis were conducted following the Cochrane Handbook for Systematic Reviews of Interventions and PRISMA guidelines. The protocol for this study was registered in PROSPERO (registration number: CRD42021233185). A comprehensive literature search was conducted across various databases and sources, including PubMed/Medline, Embase, Cochrane Library, Web of Science, ClinicalTrials.gov, and gray literature. A total of 7826 articles were screened on title and abstract. Articles were not excluded based on the vitality of teeth, the language of the study, or the observation period. The risk difference was utilized for the analyses, and a random-effects model was applied. All analyses were conducted with a 95% confidence interval (95% CI). The calculated risk differences were derived from the combined data on restoration survival and failures obtained from each individual article. The presence of heterogeneity was assessed using the I2 statistic, and if present, the heterogeneity of the data in the articles was evaluated using the non-parametric chi-squared statistic (p &lt; 0.05).RESULTS: A total of 12 eligible studies were selected, which included 946 restorations evaluated over a minimum observation period of 1 year and a maximum observation period of 7 years. Results of the meta-analysis indicated that intracoronal indirect resin composite restorations have an 18% higher rate of failure when compared to intracoronal gold restorations over 5-7 years of clinical service (risk difference =  - 0.18 [95% CI: - 0.27, - 0.09]; p = .0002; I2 = 0%). The meta-analysis examining the disparity in survival rates between intracoronal gold and leucite restorations could not be carried out due to methodological differences in the studies.CONCLUSIONS: According to the currently available evidence, medium-quality data indicates that lithium disilicate and indirect composite materials demonstrate comparable survival rates in short-term follow-up. Furthermore, intracoronal gold restorations showed significantly higher survival rates, making them a preferred option over intracoronal indirect resin-composite restorations. Besides that, the analysis revealed no statistically significant difference in survival rates between leucite and indirect composite restorations. The short observation period, limited number of eligible articles, and low sample size of the included studies were significant limitations.CLINICAL SIGNIFICANCE: Bearing in mind the limitations of the reviewed literature, this systematic review and meta-analysis help clinicians make evidence-based decisions on how to restore biomechanically compromised posterior teeth.</p

Noncommutative Geometry of Finite Groups

A finite set can be supplied with a group structure which can then be used to select (classes of) differential calculi on it via the notions of left-, right- and bicovariance. A corresponding framework has been developed by Woronowicz, more generally for Hopf algebras including quantum groups. A differential calculus is regarded as the most basic structure needed for the introduction of further geometric notions like linear connections and, moreover, for the formulation of field theories and dynamics on finite sets. Associated with each bicovariant first order differential calculus on a finite group is a braid operator which plays an important role for the construction of distinguished geometric structures. For a covariant calculus, there are notions of invariance for linear connections and tensors. All these concepts are explored for finite groups and illustrated with examples. Some results are formulated more generally for arbitrary associative (Hopf) algebras. In particular, the problem of extension of a connection on a bimodule (over an associative algebra) to tensor products is investigated, leading to the class of `extensible connections'. It is shown that invariance properties of an extensible connection on a bimodule over a Hopf algebra are carried over to the extension. Furthermore, an invariance property of a connection is also shared by a `dual connection' which exists on the dual bimodule (as defined in this work).Comment: 34 pages, Late

Towards Spinfoam Cosmology

We compute the transition amplitude between coherent quantum-states of geometry peaked on homogeneous isotropic metrics. We use the holomorphic representations of loop quantum gravity and the Kaminski-Kisielowski-Lewandowski generalization of the new vertex, and work at first order in the vertex expansion, second order in the graph (multipole) expansion, and first order in 1/volume. We show that the resulting amplitude is in the kernel of a differential operator whose classical limit is the canonical hamiltonian of a Friedmann-Robertson-Walker cosmology. This result is an indication that the dynamics of loop quantum gravity defined by the new vertex yields the Friedmann equation in the appropriate limit.Comment: 8 page

Differential Geometry of Group Lattices

In a series of publications we developed "differential geometry" on discrete sets based on concepts of noncommutative geometry. In particular, it turned out that first order differential calculi (over the algebra of functions) on a discrete set are in bijective correspondence with digraph structures where the vertices are given by the elements of the set. A particular class of digraphs are Cayley graphs, also known as group lattices. They are determined by a discrete group G and a finite subset S. There is a distinguished subclass of "bicovariant" Cayley graphs with the property that ad(S)S is contained in S. We explore the properties of differential calculi which arise from Cayley graphs via the above correspondence. The first order calculi extend to higher orders and then allow to introduce further differential geometric structures. Furthermore, we explore the properties of "discrete" vector fields which describe deterministic flows on group lattices. A Lie derivative with respect to a discrete vector field and an inner product with forms is defined. The Lie-Cartan identity then holds on all forms for a certain subclass of discrete vector fields. We develop elements of gauge theory and construct an analogue of the lattice gauge theory (Yang-Mills) action on an arbitrary group lattice. Also linear connections are considered and a simple geometric interpretation of the torsion is established. By taking a quotient with respect to some subgroup of the discrete group, generalized differential calculi associated with so-called Schreier diagrams are obtained.Comment: 51 pages, 11 figure

Women with anorexia nervosa and bulimia nervosa : Individual and family characteristics, with particular emphasis on perfectionism

This study investigated socio-cultural, family and individual factors associated with anorexia and bulimia nervosa, with particular emphasis on dysfunctional perfectionism, and adopting a general social learning perspective. Theories of the development of eating disorders were interwoven with theories of the development of perfectionism. A model was proposed for the development of anorexia and bulimia nervosa via a dysfunctional perfectionism pathway. The 135 participants, aged 18 to 40 years, were women with anorexia nervosa (N=25), bulimia nervosa (N=32), Type 1 diabetes (N= 53, a North Canterbury population-based sample), and healthy women students (N=25). The women with eating disorders were recruited from various treatment centres throughout New Zealand. Participants completed a battery of seven self-report psychometric tests, namely, the Eating Disorder Inventory-2 (EDI-2), Beck Depression Inventory (BDI), Multidimensional Perfectionism Scale (MPS), Setting Conditions for Anorexia Nervosa Scale (SCANS), Tridimensional Personality Questionnaire (TPQ), Parental Bonding Instrument (PBI), and Family Environment Scale (FES). Analysis of Covariance, using the BDI as a covariate, revealed that, in addition to measures concerned with weight, shape and dieting, both anorexia and bulimia nervosa group means were significantly higher than both healthy and diabetes group means for EDI-2 Interpersonal Distrust and Social Insecurity; MPS Concern over Mistakes, Personal Standards, and Parental Criticism; and TPQ Harm A voidance, and significantly different from the healthy group mean for MPS Parental Expectations; SCANS Perfectionism; and PBI Maternal Protection, Maternal Care, and Paternal Care. Correlational analyses confirmed hypothesized moderate or strong associations between some perfectionism measures and other characteristics of women with eating disorders, such as a harm-avoidant temperament, and perceptions of maternal overprotection. Discriminant function analysis revealed seven variables, in combination, that maximally discriminated between eating disordered and non-eating disordered groups: three EDI-2 variables of Drive for Thinness, Ineffectiveness, and Social Insecurity, three MPS subscales of Concern over Mistakes, Personal Standards, and Doubts about Actions, and the BDI. Of the three instruments measuring perfectionism, in this study, only the MPS effectively discriminated between eating disordered and non-eating disordered groups. Findings indicated the importance of controlling for depression when comparing eating disordered groups with other groups, and that dysfunctional perfectionism is largely independent of the mood of the respondent. Findings suggest that the PBI may be limited by cultural sensitivity. Findings led to questioning of the applicability of the EDI-SC to diabetes groups and of the validity of the Novelty Seeking and Reward Dependence Dimensions of the TPQ. In concluding that dysfunctional perfectionism is a key personality characteristic of women with anorexia and bulimia nervosa, it is argued that multidimensional measures of perfectionism provide more insight than unidimensional measures into the dysfunctional facets of perfectionism, and that perfectionism per se is not necessarily problematic. Dysfunctional perfectionism may distinguish psychopathology associated with anorexia and bulimia nervosa from numerous other forms of psychopathology, including depression. Although aetiological factors were not assessed in this study, the MPS and PBI, considered in conjunction with the theoretical literature, may provide insight into the development of dysfunctional perfectionism. This has implications for the treatment and prevention of eating disorders