Integral formulae for a Riemannian manifold with a distribution

We obtain a new series of integral formulae for symmetric functions of curvature of a distribution of arbitrary codimension (an its orthogonal complement) given on a compact Riemannian manifold, which start from known formula by P.Walczak (1990) and generalize ones for foliations by several authors: Asimov (1978), Brito, Langevin and Rosenberg (1981), Brito and Naveira (2000), Andrzejewski and Walczak (2010), etc. Our integral formulae involve the co-nullity tensor, certain component of the curvature tensor and their products. The formulae also deal with a number of arbitrary functions depending on the scalar invariants of the co-nullity tensor. For foliated manifolds of constant curvature the obtained formulae give us the classical type formulae. For a special choice of functions our formulae reduce to ones with Newton transformations of the co-nullity tensor.

Profile, cost and pattern of prescriptions for polymedicated patients in Catalonia (Spain).

OBJECTIVES: Polypharmacy is one of the main management issues in public health policies because of its financial impact and the increasing number of people involved. The polymedicated population according to their demographic and therapeutic profile and the cost for the public healthcare system were characterised. DESIGN: Cross-sectional study. SETTING: Primary healthcare in Barcelona Health Region, Catalonia, Spain (5 105 551 inhabitants registered). PARTICIPANTS: All insured polymedicated patients. Polymedicated patients were those with a consumption of ≥16 drugs/month. MAIN OUTCOMES MEASURES: The study variables were related to age, gender and medication intake obtained from the 2008 census and records of prescriptions dispensed in pharmacies and charged to the public health system. RESULTS: There were 36 880 polymedicated patients (women: 64.2%; average age: 74.5±10.9 years). The total number of prescriptions billed in 2008 was 2 266 830 (2 272 920 total package units). The most polymedicated group (up to 40% of the total prescriptions) was patients between 75 and 84 years old. The average number of prescriptions billed monthly per patient was 32±2, with an average cost of 452.7±27.5. The total cost of those prescriptions corresponded to 2% of the drug expenditure in Catalonia. The groups N, C, A, R and M represented 71.4% of the total number of drug package units dispensed to polymedicated patients. Great variability was found between the medication profiles of men and women, and between age groups; greater discrepancies were found in paediatric patients (5-14 years) and the elderly (≥65 years). CONCLUSIONS: This study provides essential information to take steps towards rational drug use and a structured approach in the polymedicated population in primary healthcare.

Generalization of Vélu’s formulae for isogenies between elliptic curves

Given an elliptic curve E and a finite subgroup G, V ́lu’s formulae concern to a separable isogeny IG : E → E ′ with kernel G. In particular, for a point P ∈ E these formulae express the first elementary symmetric polynomial on the abscissas of the points in the set P + G as the difference between the abscissa of IG (P ) and the first elementary symmetric polynomial on the abscissas of the nontrivial points of the kernel G. On the other hand, they express Weierstraß coefficients of E ′ as polynomials in the coefficients of E and two additional parameters: w0 = t and w1 = w. We generalize this by defining parameters wn for all n ≥ 0 and giving analogous formulae for all the elementary symmetric polynomials and the power sums on the abscissas of the points in P +G. Simultaneously, we obtain an efficient way of performing computations concerning the isogeny when G is a rational group.

A Collation of Recently published Western European Formulae for Age Estimation of Subadult Skeletal Remains: Recommendations For Forensic Anthropology and Osteoarchaeology

The aim of this study is to provide an effective and quick reference guide based on the most useful European formulae recently published for subadult age estimation. All of these formulae derive from studies on postnatal growth of the scapula, innominate, femur, and tibia, based on modern skeletal data (173 ♂, 173 ♀) from five documented collections from Spain, Portugal, and Britain. The formulae were calculated from Inverse Regression. For this reason, these formulae are especially useful for modern samples from Western Europe and in particular on 20th century human remains from the Iberian Peninsula. Eleven formulae were selected as the most useful because they can be applied to individuals from within a wide age range and in individuals of unknown sex. Due to their high reliability and because they derive from documented European skeletal samples, we recommend these formulae be used on individuals of Caucasoid ancestry from Western Europe.

Profile, cost and pattern of prescriptions for polymedicated patients in Catalonia, Spain

OBJECTIVES: Polypharmacy is one of the main management issues in public health policies because of its financial impact and the increasing number of people involved. The polymedicated population according to their demographic and therapeutic profile and the cost for the public healthcare system were characterised. DESIGN: Cross-sectional study. SETTING: Primary healthcare in Barcelona Health Region, Catalonia, Spain (5 105 551 inhabitants registered). PARTICIPANTS: All insured polymedicated patients. Polymedicated patients were those with a consumption of ≥16 drugs/month. MAIN OUTCOMES MEASURES: The study variables were related to age, gender and medication intake obtained from the 2008 census and records of prescriptions dispensed in pharmacies and charged to the public health system. RESULTS: There were 36 880 polymedicated patients (women: 64.2%; average age: 74.5±10.9 years). The total number of prescriptions billed in 2008 was 2 266 830 (2 272 920 total package units). The most polymedicated group (up to 40% of the total prescriptions) was patients between 75 and 84 years old. The average number of prescriptions billed monthly per patient was 32±2, with an average cost of 452.7±27.5. The total cost of those prescriptions corresponded to 2% of the drug expenditure in Catalonia. The groups N, C, A, R and M represented 71.4% of the total number of drug package units dispensed to polymedicated patients. Great variability was found between the medication profiles of men and women, and between age groups; greater discrepancies were found in paediatric patients (5-14 years) and the elderly (≥65 years). CONCLUSIONS: This study provides essential information to take steps towards rational drug use and a structured approach in the polymedicated population in primary healthcare.

Una Aproximació a la construcció significativa del coneixement matemàtic a l'ESO

This study displays and analyzes the contents of the Mathematics subject in ESO’s second cycle from a constructivist perspective. This analysis has been carried out by contrasting two groups of participants (control group and experimental group). These groups were formed by a sample of 240 students between the ages of 14 and 16 from four different educational centres of the Osona area. Research – Action methodology has been employed, combining quantitative techniques (statistical study with the SPSS package) with qualitative analysis (transcriptions of interviews and discussion group). This study has been carried out after years of classroom observation, reflection and action. The theoretical framework employed is a cognitive one, based on Ausubel’s Significative Learning Theory. Quantitative analysis shows how the researcher’s design improves, on the one hand, the students’ academic motivation and, on the other hand, their comprehensive memory, enabling them to achieve a more significant learning of the subjects’ contents. Furthermore, our analysis shows that the proposed method is more comprehensive than those employed by teachers collaborating with control groups. The main aim of the qualitative analysis is that of identifying the elements which configure the programme and contribute to an improvement of the aspects mentioned above. The key elements here are: co-operation as the basis of group dynamics; the employment, in some cases, of easily handled materials; the type of interaction between teacher and students, where, through open discussion, students are lead by teaching staff towards the course objectives; induction, that is, deducing formulae by initially using examples which are close to the students’ knowledge and experience or taken from everyday life (what we could call “down-top” mathematics). We should add here that the qualitative analysis does not only corroborate the results obtained by quantitative techniques, but also displays an increase of motivation in teaching staff. Teachers did show a positive attitude and welcomed the use and development of these materials in the next academic year. Finally, we discuss possible directions for further research.

Generic drugs in Spain: price competition vs. moral hazard

This paper examines competition between generic and brand-name drugs in the regulated Spanish pharmaceutical market. A nested logit demand model is specified for the three most consumed therapeutic subgroups in Spain: statins (anticholesterol), selective serotonin reuptake inhibitors (antidepressants) and proton pump inhibitors (antiulcers). The model is estimated with instrumental variables from a panel of monthly prescription data from 1999 to 2005. The dataset distinguishes between three different levels of patients’ copayments within the prescriptions and the results show that the greater the level of insurance that the patient has (and therefore the lower the patient’s copayment), the lower the proportion of generic prescriptions made by physicians. It seems that the low level of copayment has delayed the penetration of generics into the Spanish market. Additionally, the estimation of the demand model suggests that the substitution rules and promotional efforts associated with the reference pricing system have increased generic market share, and that being among the first generic entrants has an additional positive effect.

Symbolic meaning of local identity – A case study on Barcelona place brand representation

The core objective of this research process was to design an operational tool for place brand analysis. By modelling the emotional significance and the deeper-lying symbols associated to a specific place identity I expected to create a semiotic tool that could be applied, mutatis mutandis, on other similar place brands. As a field case study to develop the instrument, my choice of the research arena was Barcelona city, the capital of Catalonia Autonomous Community, Spain. Barcelona brand identity was approached in the line of the Chicago Urban Anthropology School. The research methods were designed according to the prescriptions of the urban anthropology, namely qualitative methods: in-depth interviews and discourse analysis. The final research outcome was a model summarizing a range of specific emotional values that support a place brand to position in the collective mindset and to assume a positively valued status and identity in the world order.

Financial Repression in a Natural Experiment: Loan Allocation and the Change in the Usury Laws in 1714

If financial deepening aids economic growth, then financial repression should be harmful. We use a natural experiment – the change in the English usury laws in 1714 – to analyze the effects of interest rate restrictions. We use a sample of individual loan transactions to demonstrate how the reduction of the legal maximum rate of interest affected the supply and demand for credit. Average loan size and minimum loan size increased strongly, and access to credit worsened for those with little ‘social capital.’ While we have no direct evidence that loans were misallocated, the discontinuity in loan receipts makes this highly likely. We conclude that financial repression can undermine the positive effects of financial deepening.

Drug Utilization Studies and Data Registries in Primary Care.

This article reviews the methodology of the studies on drug utilization with particular emphasis on primary care. Population based studies of drug inappropriateness can be done with microdata from Health Electronic Records and e-prescriptions. Multilevel models estimate the influence of factors affecting the appropriateness of drug prescription at different hierarchical levels: patient, doctor, health care organization and regulatory environment. Work by the GIUMAP suggest that patient characteristics are the most important factor in the appropriateness of prescriptions with significant effects at the general practicioner level.

What other sciences look like

In order to have references for discussing mathematical menus in political science, Ireview the most common types of mathematical formulae used in physics andchemistry, as well as some mathematical advances in economics. Several issues appearrelevant: variables should be well defined and measurable; the relationships betweenvariables may be non-linear; the direction of causality should be clearly identified andnot assumed on a priori grounds. On these bases, theoretically-driven equations onpolitical matters can be validated by empirical tests and can predict observablephenomena.

Quality safeguards and regulation of online pharmacies

Using econometric evidence, this article confirms that distribution ofmedicines online is split into two market segments of very diversequality, and identifies the factors that drive quality and qualityassurance in this activity. Unlike fraudulent, rogue, websites, whichoffer scant guarantees and usually sell just a few medicines withoutprescription, online pharmacies offering insurance coverage and linkedto conventional pharmacies typically sell a wholerange of drugs, require third-party medical prescriptions and provideabundant information to patients. It is shown that, where onlinepharmacies are allowed to act legally, market forces enhance quality,as private insurers require professional standards, and specialized thirdparties make a business of certifying them. Furthermore, older onlinepharmacies and those running conventional operations offer higherquality, probably because of reputational investments. Overall, this evidence supports licensing online pharmacies, especiallyconsidering that prohibiting them is ineffective against fraudulent sites.

Population based resource allocation: The use of hybrid risk adjustment

The emphasis on integrated care implies new incentives that promote coordinationbetween levels of care. Considering a population as a whole, the resource allocation systemhas to adapt to this environment. This research is aimed to design a model that allows formorbidity related prospective and concurrent capitation payment. The model can be applied inpublicly funded health systems and managed competition settings.Methods: We analyze the application of hybrid risk adjustment versus either prospective orconcurrent risk adjustment formulae in the context of funding total health expenditures for thepopulation of an integrated healthcare delivery organization in Catalonia during years 2004 and2005.Results: The hybrid model reimburses integrated care organizations avoiding excessive risktransfer and maximizing incentives for efficiency in the provision. At the same time, it eliminatesincentives for risk selection for a specific set of high risk individuals through the use ofconcurrent reimbursement in order to assure a proper classification of patients.Conclusion: Prospective Risk Adjustment is used to transfer the financial risk to the healthprovider and therefore provide incentives for efficiency. Within the context of a National HealthSystem, such transfer of financial risk is illusory, and the government has to cover the deficits.Hybrid risk adjustment is useful to provide the right combination of incentive for efficiency andappropriate level of risk transfer for integrated care organizations.

Sovereign risk and secondary markets

Conventional wisdom views the problem of sovereign risk as one of insufficient penalties.Foreign creditors can only be repaid if the government enforces foreign debts. And this will onlyhappen if foreign creditors can effectively use the threat of imposing penalties to the country.Guided by this assessment of the problem, policy prescriptions to reduce sovereign risk havefocused on providing incentives for governments to enforce foreign debts. For instance, countriesmight want to favor increased trade ties and other forms of foreign dependence that make themvulnerable to foreign retaliation thereby increasing the costs of default penalties.

Drug utilization studies and data registries in primary care

This article reviews the methodology of the studies on drug utilization with particular emphasis on primary care. Population based studies of drug inappropriateness can be done with microdata from Health Electronic Records and e-prescriptions. Multilevel models estimate the influence of factors affecting the appropriateness of drug prescription at different hierarchical levels: patient, doctor, health care organization and regulatory environment.Work by the GIUMAP suggest that patient characteristics are the most important factor in the appropriateness of prescriptions with significant effects at the general practicioner level.