Sobrification and bicompletion of totally bounded quasi-uniform spaces

We observe that if is a compatible totally bounded quasi-uniformity on a T0-space (X,), then the bicompletion of (X, ) is a strongly sober, locally quasicompact space. It follows that the b-closure S of (X, ) in is homeomorphic to the sobrification of the space (X, ). We prove that S is equal to if and only if (X, ) is a core-compact space in which every ultrafilter has an irreducible convergence set and is the coarsest quasi-uniformity compatible with . If is the Pervin quasi-uniformity on X, then S is equal to if and only if X is hereditarily quasicompact, or equivalently, is the Pervin quasi-uniformity o

CVaR minimization by the SRA algorithm

Using the risk measure CV aR in �nancial analysis has become more and more popular recently. In this paper we apply CV aR for portfolio optimization. The problem is formulated as a two-stage stochastic programming model, and the SRA algorithm, a recently developed heuristic algorithm, is applied for minimizing CV aR

Patients' motives for choosing a physician: comparison between conventional and complementary medicine in Swiss primary care

<p>Abstract</p> <p>Background</p> <p>The study is part of a nationwide evaluation of complementary and alternative medicine (CAM) in primary care in Switzerland. The Objective was to identify patients' expectations and reasons governing the choice of complementary medicine compared with conventional primary care (CONV).</p> <p>Methods</p> <p>The data were derived from the PEK study (Programm Evaluation Komplementärmedizin), which was conducted in 2002–2003 with 7879 adult patients and parents of 1291 underage patients, seeking either complementary (CAM) or conventional (CONV) primary care. The study was performed as a cross-sectional survey. The respondents were asked to document their (or their children's) self-perceived health status, reasons governing their choice, and treatment expectations. Physicians were practicing conventional medicine and/or complementary methods (homeopathy, anthroposophic medicine, neural therapy, and traditional Chinese medicine). Reasons governing the choice of physician were evaluated on the basis of a three-part classification (physician-related, procedure-related, and pragmatic/other reasons)</p> <p>Results and Discussion</p> <p>Patients seeing CAM physicians tend to be younger and more often female. CAM patients referred to procedure-related reasons more frequently, whereas pragmatic reasons dominated among CONV patients. CAM respondents expected fewer adverse side effects compared to conventional care patients.</p> <p>Conclusion</p> <p>The majority of alternative medicine users appear to have chosen CAM mainly because they wish to undergo a certain procedure; additional reasons include desire for more comprehensive treatment, and expectation of fewer side-effects.</p

Processing second-order stochastic dominance models using cutting-plane representations

This is the post-print version of the Article. The official published version can be accessed from the links below. Copyright @ 2011 Springer-VerlagSecond-order stochastic dominance (SSD) is widely recognised as an important decision criterion in portfolio selection. Unfortunately, stochastic dominance models are known to be very demanding from a computational point of view. In this paper we consider two classes of models which use SSD as a choice criterion. The first, proposed by Dentcheva and Ruszczyński (J Bank Finance 30:433–451, 2006), uses a SSD constraint, which can be expressed as integrated chance constraints (ICCs). The second, proposed by Roman et al. (Math Program, Ser B 108:541–569, 2006) uses SSD through a multi-objective formulation with CVaR objectives. Cutting plane representations and algorithms were proposed by Klein Haneveld and Van der Vlerk (Comput Manage Sci 3:245–269, 2006) for ICCs, and by Künzi-Bay and Mayer (Comput Manage Sci 3:3–27, 2006) for CVaR minimization. These concepts are taken into consideration to propose representations and solution methods for the above class of SSD based models. We describe a cutting plane based solution algorithm and outline implementation details. A computational study is presented, which demonstrates the effectiveness and the scale-up properties of the solution algorithm, as applied to the SSD model of Roman et al. (Math Program, Ser B 108:541–569, 2006).This study was funded by OTKA, Hungarian National Fund for Scientific Research, project 47340; by Mobile Innovation Centre, Budapest University of Technology, project 2.2; Optirisk Systems, Uxbridge, UK and by BRIEF (Brunel University Research Innovation and Enterprise Fund)

Patient satisfaction and side effects in primary care: An observational study comparing homeopathy and conventional medicine

<p>Abstract</p> <p>Background</p> <p>This study is part of a nationwide evaluation of complementary medicine in Switzerland (Programme Evaluation of Complementary Medicine PEK) and was funded by the Swiss Federal Office of Public Health. The main objective of this study is to investigate patient satisfaction and perception of side effects in homeopathy compared with conventional care in a primary care setting.</p> <p>Methods</p> <p>We examined data from two cross-sectional studies conducted in 2002–2003. The first study was a physician questionnaire assessing structural characteristics of practices. The second study was conducted on four given days during a 12-month period in 2002/2003 using a physician and patient questionnaire at consultation and a patient questionnaire mailed to the patient one month later (including Europep questionnaire).</p> <p>The participating physicians were all trained and licensed in conventional medicine. An additional qualification was required for medical doctors providing homeopathy (membership in the Swiss association of homeopathic physicians SVHA).</p> <p>Results</p> <p>A total of 6778 adult patients received the questionnaire and 3126 responded (46.1%). Statistically significant differences were found with respect to health status (higher percentage of chronic and severe conditions in the homeopathic group), perception of side effects (higher percentage of reported side effects in the conventional group) and patient satisfaction (higher percentage of satisfied patients in the homeopathic group).</p> <p>Conclusion</p> <p>Overall patient satisfaction was significantly higher in homeopathic than in conventional care. Homeopathic treatments were perceived as a low-risk therapy with two to three times fewer side effects than conventional care</p

Dual Space of a Lattice as the Completion of a Pervin Space

16th International Conference, RAMiCS 2017, Lyon, France, May 15-18, 2017, ProceedingsInternational audienceThis survey paper presents well-known results from a new angle. A Pervin space is a set X equipped with a set of subsets,called the blocks of the Pervin space. Blocks are closed under finite intersections and finite unions and hence form a lattice of subsets of X. Pervin spaces are thus easier to define than topological spaces or (quasi)-uniform spaces. As a consequence, most of the standard topological notions, like convergence and cluster points, specialisation order, filtersand Cauchy filters, complete spaces and completion are much easier to define for Pervin spaces. In particular, the completion of a Pervin space turns out to be the dual space (in the sense of Stone) of the original lattice.We show that any lattice of subsets can be described by a set of inequations of the form u ≤ v, where u and v are elements of its dual space. Applications to formal languages and complexity classes are given.Cet article de synthèse présente des résultats bien connus sous un nouvel angle. Un espace de Pervin est unensemble X équipé d'un ensemble de parties, appelé les blocs de l'espace de Pervin. Les blocs sont fermés par intersection finie et union finie et forment ainsi un treillis de parties de X. Les espaces de Pervin sont doncplus faciles à définir que les espaces topologiques ou les espaces (quasi-)uniformes. Par conséquent, la plupart des notions topologiques, comme la convergence et les points d'adhérence, l'ordre de spécialisation, les filtres de Cauchy, les espaces complets et la complétion sont beaucoup plus faciles à définir pour les espaces Pervin. En particulier, la complétion d'un espace Pervin s'avère être l'espace dual (au sens de Stone) du treillis de départ.Nous montrons que tout treillis de parties peut être décrit par un ensemble d'inéquations de la forme u ≤ v, où u et v sont des éléments de son espace dual. On donne des applications aux langages formels et aux classes de complexité

A characterization of Smyth complete quasi-metric spaces via Caristi's fixed point theorem

We obtain a quasi-metric generalization of Caristi's fixed point theorem for a kind of complete quasi-metric spaces. With the help of a suitable modification of its proof, we deduce a characterization of Smyth complete quasi-metric spaces which provides a quasi-metric generalization of the well-known characterization of metric completeness due to Kirk. Some illustrative examples are also given. As an application, we deduce a procedure which allows to easily show the existence of solution for the recurrence equation of certain algorithms.The authors are grateful to the reviewers for several suggestions which have allowed to improve the first version of the paper. This research is supported by the Ministry of Economy and Competitiveness of Spain, Grant MTM2012-37894-C02-01.Romaguera Bonilla, S.; Tirado Peláez, P. (2015). A characterization of Smyth complete quasi-metric spaces via Caristi's fixed point theorem. Fixed Point Theory and Applications. 2015:183. https://doi.org/10.1186/s13663-015-0431-1S2015:183Cobzaş, S: Functional Analysis in Asymmetric Normed Spaces. Springer, Basel (2013)Künzi, HPA: Nonsymmetric distances and their associated topologies: about the origins of basic ideas in the area of asymmetric topology. In: Aull, CE, Lowen, R (eds.) Handbook of the History of General Topology, vol. 3, pp. 853-968. Kluwer Academic, Dordrecht (2001)Reilly, IL, Subrhamanyam, PV, Vamanamurthy, MK: Cauchy sequences in quasi-pseudo-metric spaces. Monatshefte Math. 93, 127-140 (1982)Künzi, HPA, Schellekens, MP: On the Yoneda completion of a quasi-metric spaces. Theor. Comput. Sci. 278, 159-194 (2002)Romaguera, S, Valero, O: Domain theoretic characterisations of quasi-metric completeness in terms of formal balls. Math. Struct. Comput. Sci. 20, 453-472 (2010)Künzi, HPA: Nonsymmetric topology. In: Proc. Szekszárd Conf. Bolyai Society of Math. Studies, vol. 4, pp. 303-338 (1993)García-Raffi, LM, Romaguera, S, Schellekens, MP: Applications of the complexity space to the general probabilistic divide and conquer algorithms. J. Math. Anal. Appl. 348, 346-355 (2008)Stoltenberg, RA: Some properties of quasi-uniform spaces. Proc. Lond. Math. Soc. 17, 226-240 (1967)Caristi, J: Fixed point theorems for mappings satisfying inwardness conditions. Trans. Am. Math. Soc. 215, 241-251 (1976)Kirk, WA: Caristi’s fixed point theorem and metric convexity. Colloq. Math. 36, 81-86 (1976)Abdeljawad, T, Karapınar, E: Quasi-cone metric spaces and generalizations of Caristi Kirk’s theorem. Fixed Point Theory Appl. 2009, Article ID 574387 (2009)Acar, O, Altun, I: Some generalizations of Caristi type fixed point theorem on partial metric spaces. Filomat 26(4), 833-837 (2012)Acar, O, Altun, I, Romaguera, S: Caristi’s type mappings on complete partial metric spaces. Fixed Point Theory 14, 3-10 (2013)Aydi, H, Karapınar, E, Kumam, P: A note on ‘Modified proof of Caristi’s fixed point theorem on partial metric spaces, Journal of Inequalities and Applications 2013, 2013:210’. J. Inequal. Appl. 2013, 355 (2013)Cobzaş, S: Completeness in quasi-metric spaces and Ekeland variational principle. Topol. Appl. 158, 1073-1084 (2011)Hadžić, O, Pap, E: Fixed Point Theory in Probabilistic Metric Spaces. Kluwer Academic, Dordrecht (2001)Karapınar, E: Generalizations of Caristi Kirk’s theorem on partial metric spaces. Fixed Point Theory Appl. 2011, 4 (2011)Romaguera, S: A Kirk type characterization of completeness for partial metric spaces. Fixed Point Theory Appl. 2010, Article ID 493298 (2010)Park, S: On generalizations of the Ekeland-type variational principles. Nonlinear Anal. TMA 39, 881-889 (2000)Du, W-S, Karapınar, E: A note on Caristi type cyclic maps: related results and applications. Fixed Point Theory Appl. 2013, 344 (2013)Ali-Akbari, M, Honari, B, Pourmahdian, M, Rezaii, MM: The space of formal balls and models of quasi-metric spaces. Math. Struct. Comput. Sci. 19, 337-355 (2009)Romaguera, S, Schellekens, M: Quasi-metric properties of complexity spaces. Topol. Appl. 98, 311-322 (1999)Brøndsted, A: On a lemma of Bishop and Phelps. Pac. J. Math. 55, 335-341 (1974)Brøndsted, A: Fixed points and partial order. Proc. Am. Math. Soc. 60, 365-366 (1976)Smyth, MB: Quasi-uniformities: reconciling domains with metric spaces. In: Main, M, Melton, A, Mislove, M, Schmidt, D (eds.) Mathematical Foundations of Programming Language Semantics, 3rd Workshop, Tulane, 1987. Lecture Notes in Computer Science, vol. 298, pp. 236-253. Springer, Berlin (1988)Cull, P, Flahive, M, Robson, R: Difference Equations: From Rabbits to Chaos. Springer, New York (2005)Schellekens, M: The Smyth completion: a common foundation for denotational semantics and complexity analysis. Electron. Notes Theor. Comput. Sci. 1, 535-556 (1995)García-Raffi, LM, Romaguera, S, Sánchez-Pérez, EA: Sequence spaces and asymmetric norms in the theory of computational complexity. Math. Comput. Model. 49, 1852-1868 (2009)Rodríguez-López, J, Schellekens, MP, Valero, O: An extension of the dual complexity space and an application to computer science. Topol. Appl. 156, 3052-3061 (2009)Romaguera, S, Schellekens, MP, Valero, O: The complexity space of partial functions: a connection between complexity analysis and denotational semantics. Int. J. Comput. Math. 88, 1819-1829 (2011

Extent and structure of health insurance expenditures for complementary and alternative medicine in Swiss primary care

BACKGROUND: The study is part of a nationwide evaluation of complementary and alternative medicine (CAM) in primary care in Switzerland. The goal was to evaluate the extent and structure of basic health insurance expenditures for complementary and alternative medicine in Swiss primary care. METHODS: The study was designed as a cross-sectional evaluation of Swiss primary care providers and included 262 certified CAM physicians, 151 noncertified CAM physicians and 172 conventional physicians. The study was based on data from a mailed questionnaire and on reimbursement information obtained from health insurers. It was therefore purely observational, without interference into diagnostic and therapeutic procedures applied or prescribed by physicians. Main outcome measures included average reimbursed costs per patient, structured into consultation- and medication-related costs, and referred costs. RESULTS: Total average reimbursed cost per patient did not differ between CAM physicians and conventional practitioners, but considerable differences were observed in cost structure. The proportions of reimbursed costs for consultation time were 56% for certified CAM, 41% for noncertified CAM physicians and 40% for conventional physicians; medication costs – including expenditures for prescriptions and directly dispensed drugs – respectively accounted for 35%, 18%, and 51% of costs. CONCLUSION: The results indicate no significant difference for overall treatment cost per patient between CAM and COM primary care in Switzerland. However, CAM physicians treat lower numbers of patients and a more cost-favourable patient population than conventional physicians. Differences in cost structure reflect more patient-centred and individualized treatment modalities of CAM physicians

Quantitative Concept Analysis

Formal Concept Analysis (FCA) begins from a context, given as a binary relation between some objects and some attributes, and derives a lattice of concepts, where each concept is given as a set of objects and a set of attributes, such that the first set consists of all objects that satisfy all attributes in the second, and vice versa. Many applications, though, provide contexts with quantitative information, telling not just whether an object satisfies an attribute, but also quantifying this satisfaction. Contexts in this form arise as rating matrices in recommender systems, as occurrence matrices in text analysis, as pixel intensity matrices in digital image processing, etc. Such applications have attracted a lot of attention, and several numeric extensions of FCA have been proposed. We propose the framework of proximity sets (proxets), which subsume partially ordered sets (posets) as well as metric spaces. One feature of this approach is that it extracts from quantified contexts quantified concepts, and thus allows full use of the available information. Another feature is that the categorical approach allows analyzing any universal properties that the classical FCA and the new versions may have, and thus provides structural guidance for aligning and combining the approaches.Comment: 16 pages, 3 figures, ICFCA 201