Mathematics Is Physics

In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for this view is to explain how mathematical theories can become increasingly abstract and develop their own internal structure, whilst still maintaining an appropriate empirical tether that can explain their later use in physics. In order to address this, I offer a theory of mathematical theory-building based on the idea that human knowledge has the structure of a scale-free network and that abstract mathematical theories arise from a repeated process of replacing strong analogies with new hubs in this network. This allows mathematics to be seen as the study of regularities, within regularities, within ..., within regularities of the natural world. Since mathematical theories are derived from the natural world, albeit at a much higher level of abstraction than most other scientific theories, it should come as no surprise that they so often show up in physics. This version of the essay contains an addendum responding to Slyvia Wenmackers' essay and comments that were made on the FQXi website.Comment: 15 pages, LaTeX. Second prize winner in 2015 FQXi Essay Contest (see http://fqxi.org/community/forum/topic/2364

A comparison of cervical smear adequacy using either the cytobrush or the Ayre spatula: a practice audit

Background: To obtain an adequate cervical (Papanicolaou) smear, the transformation zone, including the squamo-columnar junction, should be sampled as carcinoma develops preferentially in this transformation zone. The Ayre spatula has been widely used but is not very effective. Other sampling devices have been developed to improve efficiency, including the cytobrush. The purpose of this study was to compare the adequacy of cervical smears taken with the Ayre spatula as opposed to the cytobrush. Methods: This was a retrospective analytical study. One sampler, an experienced general practitioner, took the smears in the period 1990 to 2004. Initially, the Ayre spatula was used to consecutively sample the cervix and thereafter, a cytobrush alone was used. Two groups were thus formed for comparison. The presence of endocervical cells was accepted as an indicator of an adequate smear. A Cusco speculum was used to visualize the cervix. The sample was smeared onto a slide and fixated with an alcohol aerosol spray. Results: A total of 4561 smears were taken and 247 had no endocervical cells. A further 34 smears were classified as unsatisfactory due to the presence of degeneration (19), insufficient squamous cells (7), inflammatory exudate (4), excess blood (3) and/or a thick slide (1).The cytobrush group was similar demographically to the Ayre spatula group: 1981 (99%) and 2490 (98%) respectively were non pregnant; 67 (3%) and 110 (4%) were nulliparous, 1008 (50%) and 1370 (54%) were para 1 – 5, and 931 (46%) and 1075 (42%) were para 6 or more; 0 (0%) and 2 (0.1%) were aged between 10 – 19 years, 1496 (75%) and 2012 (78%) between 20 – 49, and 510 (25%) and 541 (21%) were aged 50 years or more. Of 2006 smears taken with a cytobrush, 1955 (97.5%) contained endocervical cells compared with 2325 (91%) of 2555 smears taken with an Ayre spatula. The difference was significant with an Odds Ratio of 4.56 (95% Confidence Interval 3.42-6.42). Conclusion: The cytobrush is significantly more efficacious than the Ayre spatula in obtaining adequate cervical smears. Use of the cytobrush will ensure less repeat smears with a consequent reduction in workload for samplers and laboratories. Although very few smears lacked sufficient squamous cells (an indicator of adequate ectocervical sampling), current best practice is that the cytobrush be used together with a wooden spatula to ensure adequate sampling of both the endocervical and ectocervical components of the transformation zone. For full text, click here: South African Family Practice2006;48(9): 15-15

Formalising the Continuous/Discrete Modeling Step

Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete domains. The difference between the two is quantified using generic results from ODE theory, and these estimates can be compared with the exact solutions. Such results do not fit well into a conventional model based refinement framework; however they can be accommodated into a model based retrenchment. The retrenchment is described, and the way it can interface to refinement development on both the continuous and discrete sides is outlined. The approach is compared to what can be achieved using hybrid systems techniques.Comment: In Proceedings Refine 2011, arXiv:1106.348

Supersymmetric Biorthogonal Quantum Systems

We discuss supersymmetric biorthogonal systems, with emphasis given to the periodic solutions that occur at spectral singularities of PT symmetric models. For these periodic solutions, the dual functions are associated polynomials that obey inhomogeneous equations. We construct in detail some explicit examples for the supersymmetric pairs of potentials V_{+/-}(z) = -U(z)^2 +/- z(d/(dz))U(z) where U(z) = \sum_{k>0}u_{k}z^{k}. In particular, we consider the cases generated by U(z) = z and z/(1-z). We also briefly consider the effects of magnetic vector potentials on the partition functions of these systems.Comment: Changes are made to conform to the published version. In particular, some errors are corrected on pp 12-1

Crispr gene editing in lipid disorders and atherosclerosis: Mechanisms and opportunities

Elevated circulating concentrations of low-density lipoprotein cholesterol (LDL-C) have been conclusively demonstrated in epidemiological and intervention studies to be causally associated with the development of atherosclerotic cardiovascular disease. Enormous advances in LDL-C reduction have been achieved through the use of statins, and in recent years, through drugs targeting proprotein convertase subtilisin/kexin type 9 (PCSK9), a key regulator of the hepatic LDL-receptor. Existing approaches to PCSK9 targeting have used monoclonal antibodies or RNA interference. Although these approaches do not require daily dosing, as statins do, repeated subcutaneous injections are nevertheless necessary to maintain effectiveness over time. Recent experimental studies suggest that clustered regularly interspaced short palindromic repeats (CRISPR) gene-editing targeted at PCSK9 may represent a promising tool to achieve the elusive goal of a ‘fire and forget’ lifelong approach to LDL-C reduction. This paper will provide an overview of CRISPR technology, with a particular focus on recent studies with relevance to its potential use in atherosclerotic cardiovascular disease

The major molecular mechanisms mediating the renoprotective effects of SGLT2 inhibitors: An update

Abstract The incidence of diabetes mellitus, as well as its complications, is rapidly growing. Diabetic nephropathy is one of the most prevalent disorders induced by chronic uncontrolled hyperglycemia and is accompanied by a reduction in renal sufficiency with microstructural tissue damage in the kidneys. Many therapeutic protocols have been designed to address the treatment and prevention of diabetic nephropathy. Sodium-glucose co-transporter 2 inhibitors (SGLT2i) are a newly introduced class of glucose-lowering agents that reduce blood glucose by inhibition of urinary glucose reabsorption in renal proximal tubules and so induce glycosuria. Also, these hypoglycemic agents may provide protective effects in different tissues such as cardiovascular, brain, and kidneys. In recent years, accumulating evidence has indicated that SGLT2i possess potent renal protective properties in the setting of diabetes. In the current study, we present the latest findings regarding the renoprotective effects of SGLT2 inhibition and discuss the molecular mechanisms involved

Nutraceuticals for the Control of Dyslipidaemias in Clinical Practice

Dyslipidaemias result in the deposition of cholesterol and lipids in the walls of blood vessels, chronic inflammation and the formation of atherosclerotic plaques, which impede blood flow and (when they rupture) result in acute ischaemic episodes. Whilst recent years have seen enormous success in the reduction of cardiovascular risk using conventional pharmaceuticals, there is increasing interest amongst patients and practitioners in the use of nutraceuticals to combat dyslipidaemias and inflammation in cardiovascular disease. Nutraceutical is a portmanteau term: ‘ceutical’ indicate pharmaceutical-grade preparations, and ‘nutra’ indicates that the products contain nutrients from food. Until relatively recently, little high-quality evidence relating to the safety and efficacy of nutraceuticals has been available to prescribers and policymakers. However, as a result of recent randomised-controlled trials, cohort studies and meta-analyses, this situation is changing, and nutraceuticals are now recommended in several mainstream guidelines relating to dyslipidaemias and atherosclerosis. This article will summarise recent clinical-practice guidance relating to the use of nutraceuticals in this context and the evidence which underlies them. Particular attention is given to position papers and recommendations from the International Lipid Expert Panel (ILEP), which has produced several practical and helpful recommendations in this field

Established and potential echocardiographic markers of embolism and their therapeutic implications in patients with ischemic stroke

Cardiogenic strokes comprised 11% of all strokes and 25% of ischemic strokes. An accurate identificationof the cause of stroke is necessary in order to prepare an adequate preventive strategy. In this reviewthe confirmed and potential causes of embolic strokes are presented, which can be detected in echocardiography in the context of present treatment guidelines and gaps in evidence. There remains a need for further studies assessing the meaning of potential cardiac sources of embolism and establishment of rules for optimal medical prevention (antiplatelet therapy [APT] vs. oral anticoagulation [OAC]) andinterventional procedures to reduce the incidence of ischemic strokes. Currently available data does not provide definitive evidence on the comparative benefits of OAC vs. APT in patients with cryptogenic stroke or embolic stroke of undetermined source. There is a lack of antithrombotic treatment scheme in the time between stroke and the completed diagnosis of potential sources of thromboembolism

RNA Silencing in the Management of Dyslipidemias

PURPOSE OF REVIEW: Remarkable reductions in cardiovascular morbidity and mortality have been achieved in recent decades through the widespread use of ‘small-molecule’ hypolipidaemic drugs such as statins and ezetimibe. An alternative approach is to perturb the production of proteins through ribonucleic acid (RNA) silencing, leading to long-lasting knock-down of specific biological molecules. This review describes the scientific basis of RNA silencing, and critically evaluates the evidence relating to inclisiran, a small interfering RNA against proprotein convertase subtilisin kexin 9 (PCSK9). RECENT FINDINGS: Pooled analysis of three recent ORION trials has demonstrated that twice-yearly administration of inclisiran reduces LDL-C by 50% in a range of patient groups, with only mild adverse effects. SUMMARY: Inclisiran provides safe, effective and long-lasting reductions in PCSK9 and LDL-C. The results of the phase-3 ORION-4 outcomes study are eagerly awaited. Further promising RNA silencing technologies have the potential to improve the management of dyslipidaemia