Mathematical Explanations and Mathematical Applications

One of the key questions in the philosophy of mathematics is the role and status of mathematical applications in the natural sciences. The importance of mathematics for science is indisputable, but philosophers have disagreed on what the relation between mathematical theories and scientific theories are. This chapter presents these topics through a distinction between mathematical applications and mathematical explanations. Particularly important is the question whether mathematical applications are ever indispensable. If so, it has often been argued, such applications should count as proper mathematical explanations. Following Quine, many philosophers have also contended that if there are indispensable mathematical applications in the natural sciences, then the mathematical objects posited in those applications have an independent existence like the scientific objects. Thus the question of mathematical explanations and applications has an important relevance for the ontology of mathematics.Peer reviewe

On the Mathematical Constitution and Explanation of Physical Facts

The mathematical nature of modern physics suggests that mathematics is bound to play some role in explaining physical reality. Yet, there is an ongoing controversy about the prospects of mathematical explanations of physical facts and their nature. A common view has it that mathematics provides a rich and indispensable language for representing physical reality but that, ontologically, physical facts are not mathematical and, accordingly, mathematical facts cannot really explain physical facts. In what follows, I challenge this common view. I argue that, in addition to its representational role, in modern physics mathematics is constitutive of the physical. Granted the mathematical constitution of the physical, I propose an account of explanation in which mathematical frameworks, structures, and facts explain physical facts. In this account, mathematical explanations of physical facts are either species of physical explanations of physical facts in which the mathematical constitution of some physical facts in the explanans are highlighted, or simply explanations in which the mathematical constitution of physical facts are highlighted. In highlighting the mathematical constitution of physical facts, mathematical explanations of physical facts deepen and increase the scope of the understanding of the explained physical facts. I argue that, unlike other accounts of mathematical explanations of physical facts, the proposed account is not subject to the objection that mathematics only represents the physical facts that actually do the explanation. I conclude by briefly considering the implications that the mathematical constitution of the physical has for the question of the unreasonable effectiveness of the use of mathematics in physics

Disparities in Healthcare Utilisation Rates for Aboriginal and Non-Aboriginal Albertan Residents, 1997-2006: A Population Database Study

Background: It is widely recognised that significant discrepancies exist between the health of indigenous and nonindigenous populations. Whilst the reasons are incompletely defined, one potential cause is that indigenous communities do not access healthcare to the same extent. We investigated healthcare utilisation rates in the Canadian Aboriginal population to elucidate the contribution of this fundamental social determinant for health to such disparities. Methods: Healthcare utilisation data over a nine-year period were analysed for a cohort of nearly two million individuals to determine the rates at which Aboriginal and non-Aboriginal populations utilised two specialties (Cardiology and Ophthalmology) in Alberta, Canada. Unadjusted and adjusted healthcare utilisation rates obtained by mixed linear and Poisson regressions, respectively, were compared amongst three population groups - federally registered Aboriginals, individuals receiving welfare, and other Albertans. Results: Healthcare utilisation rates for Aboriginals were substantially lower than those of non-Aboriginals and welfare recipients at each time point and subspecialty studied [e.g. During 2005/06, unadjusted Cardiology utilisation rates were 0.28% (Aboriginal, n = 97,080), 0.93% (non-Aboriginal, n = 1,720,041) and 1.37% (Welfare, n = 52,514), p = ,0.001]. The age distribution of the Aboriginal population was markedly different [2.7%$65 years of age, non-Aboriginal 10.7%], and comparable utilisation rates were obtained after adjustment for fiscal year and estimated life expectancy [Cardiology: Incidence Rate Ratio 0.66, Ophthalmology: IRR 0.85]. Discussion: The analysis revealed that Aboriginal people utilised subspecialty healthcare at a consistently lower rate than either comparatively economically disadvantaged groups or the general population. Notably, the differences were relatively invariant between the major provincial centres and over a nine year period. Addressing the causes of these discrepancies is essential for reducing marked health disparities, and so improving the health of Aboriginal people

Application of Acoustic Telemetry to Assess Residency and Movements of Rockfish and Lingcod at Created and Natural Habitats in Prince William Sound

Loss and/or degradation of nearshore habitats have led to increased efforts to restore or enhance many of these habitats, particularly those that are deemed essential for marine fishes. Copper rockfish (Sebastes caurinus) and lingcod (Ophiodon enlongatus) are dominant members of the typical reef fish community that inhabit rocky and high-relief substrates along the Pacific Northwest. We used acoustic telemetry to document their residency and movements in the nearshore waters of Prince William Sound, Alaska in order to assess use of created reef habitat in an individual-based manner. A total of 57 fish were surgically implanted with acoustic transmitters. Forty-five fish were captured and monitored in three habitats: artificial reef, low-relief natural reef, and patchy high-relief natural reef. Within each habitat, both rockfish and lingcod exhibited long periods of residency with limited movements. Twelve rockfish were captured at the natural reefs and displaced a distance of 4.0 km to the artificial reef. Five of the 12 rockfish returned within 10 d of their release to their initial capture site. Another five of the 12 displaced fish established residency at the artificial reef through the duration of our study. Our results suggest the potential for artificial reefs to provide rockfish habitat in the event of disturbances to natural habitat

Estimating the Resources Needed and Savings Anticipated from Roll-Out of Adult Male Circumcision in Sub-Saharan Africa

Background: Trials in Africa indicate that medical adult male circumcision (MAMC) reduces the risk of HIV by 60%. MAMC may avert 2 to 8 million HIV infections over 20 years in sub-Saharan Africa and cost less than treating those who would have been infected. This paper estimates the financial and human resources required to roll out MAMC and the net savings due to reduced infections. Methods: We developed a model which included costing, demography and HIV epidemiology. We used it to investigate 14 countries in sub-Saharan Africa where the prevalence of male circumcision was lower than 80% and HIV prevalence among adults was higher than 5%, in addition to Uganda and the Nyanza province in Kenya. We assumed that the roll-out would take 5 years and lead to an MC prevalence among adult males of 85%. We also assumed that surgery would be done as it was in the trials. We calculated public program cost, number of full-time circumcisers and net costs or savings when adjusting for averted HIV treatments. Costs were in USD, discounted to 2007. 95% percentile intervals (95% PI) were estimated by Monte Carlo simulations. Results: In the first 5 years the number of circumcisers needed was 2 282 (95% PI: 2 018 to 2 959), or 0.24 (95% PI: 0.21 to 0.31) per 10 000 adults. In years 6-10, the number of circumcisers needed fell to 513 (95% PI: 452 to 664). The estimated 5-year cost of rolling out MAMC in the public sector was $919 million (95$672 million (95% PI: 437 to 1 021) and over 20 years there were net savings of $2.3 billion (95% PI: 1.4 to 3.4). Conclusion: A rapid roll-out of MAMC in sub-Saharan Africa requires substantial funding and a high number of circumcisers for the first five years. These investments are justified by MAMC's substantial health benefits and the savings accrued by averting future HIV infections. Lower ongoing costs and continued care savings suggest long-term sustainability

Voluntary Medical Male Circumcision: Strategies for Meeting the Human Resource Needs of Scale-Up in Southern and Eastern Africa

Kelly Curran and colleagues conducted a program review to identify human resource approaches that are being used to improve voluntary medical male circumcision volume and efficiency, identifying several innovative responses to human resource challenges

Alcohol use as a risk factor for tuberculosis – a systematic review

<p>Abstract</p> <p>Background</p> <p>It has long been evident that there is an association between alcohol use and risk of tuberculosis. It has not been established to what extent this association is confounded by social and other factors related to alcohol use. Nor has the strength of the association been established. The objective of this study was to systematically review the available evidence on the association between alcohol use and the risk of tuberculosis.</p> <p>Methods</p> <p>Based on a systematic literature review, we identified 3 cohort and 18 case control studies. These were further categorized according to definition of exposure, type of tuberculosis used as study outcome, and confounders controlled for. Pooled effect sizes were obtained for each sub-category of studies.</p> <p>Results</p> <p>The pooled relative risk across all studies that used an exposure cut-off level set at 40 g alcohol per day or above, or defined exposure as a clinical diagnosis of an alcohol use disorder, was 3.50 (95% CI: 2.01–5.93). After exclusion of small studies, because of suspected publication bias, the pooled relative risk was 2.94 (95% CI: 1.89–4.59). Subgroup analyses of studies that had controlled for various sets of confounders did not give significantly different results and did not explain the significant heterogeneity that was found across the studies.</p> <p>Conclusion</p> <p>The risk of active tuberculosis is substantially elevated in people who drink more than 40 g alcohol per day, and/or have an alcohol use disorder. This may be due to both increased risk of infection related to specific social mixing patterns associated with alcohol use, as well as influence on the immune system of alcohol itself and of alcohol related conditions.</p

Determinants of circumcision and willingness to be circumcised by Rwandan men, 2010

<p>Abstract</p> <p>Background</p> <p>Male Circumcision (MC) has been recommended as one of the preventive measures against sexual HIV transmission by the World Health Organization (WHO). Rwanda has adopted MC as recommended but the country is a non-traditionally circumcising society. The objective was to explore knowledge and perception of Rwandan men on Male Circumcision (MC) and to determine the factors associated with the willingness to be circumcised and to circumcise their sons.</p> <p>Methods</p> <p>This cross sectional study was conducted in 29 districts of Rwanda between January and March 2010. Data were collected using a structured questionnaire among men aged 15-59 years. The rate of MC was measured and its perception from respondents, and then the factors associated with the willingness to go for MC were analysed using multiple logistic regressions.</p> <p>Results</p> <p>A total of 1098 men were interviewed. Among respondents 17% (95% CI 14-19%) reported being circumcised. About three-quarter (72%) could define MC, but 37% of adolescent could not. Half of the participants were willing to get circumcised and 79% of men would accept circumcision for their sons. The main motivators for MC were its benefits in HIV/STI prevention (69%) and improving hygiene (49%). Being too old was the main reason (32%) reported by men reluctant to undergo MC and younger men were afraid of pain in particular those less than 19 years old (42%). The willingness to circumcise was significantly associated with younger age, living in the Eastern Province, marital status, and the knowledge of the preventive role of circumcision.</p> <p>Conclusions</p> <p>Adolescents and young adults were more willing to be circumcised. It is critical to ensure the availability of pain free services in order to satisfy the increasing demand for the scale up of MC in Rwanda.</p