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 case of granulomatous rosacea

A 49-year-old housewife had complained of an itchy facial rash for four years. She denied using steroid creams and skin lighteners. On examination, dark grey papules were found on her face, with some coalescing into plaques (see Figures 1 and 2). A skin biopsy revealed many perifollicular non-caseating granulomas (see Figure 3). Periodic Acid-Schiff stains for fungi, Ziehl-Neelson stains for M tuberculosis, and Fite-Ferraco stains for M leprae were negative

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

On aspects of self-consistency in the Dyson-Schwinger approach to QED and \lambda (\phi^\star \phi)^2 theories

We investigate some aspects of the self-consistency in the Dyson-Schwinger approach to both the QED and the self-interacting scalar field theories. We prove that the set of the Dyson-Schwinger equations, together with the Green-Ward-Takahashi identity, is equivalent to the analogous set of integral equations studied in condensed matter, namely many-body perturbation theory, where it is solved self-consistently and iteratively. In this framework, we compute the non-perturbative solution of the gap equation for the self-interacting scalar field theory.Comment: 9 pages, to appear on Phys. Rev.

A case of vulval schistosomiasis

While schistosomiasis is endemic in South Africa, cutaneous manifestations are relatively uncommon. This case report describes the clinical findings in a patient with vulval schistosomiasis. Schistosomiasis should be considered in the differential diagnosis of genital lesions in residents in endemic areas or visitors to these areas.South African Family Practice Vol. 49 (9) 2007: pp. 42-4

Quantum Complex Scalar Field in the Two-Dimensional Spacetime with Closed Timelike Curves and a Time-Machine Problem

It is considered the quantum complex scalar field which obeys the authomorphic condition in the two-dimensional spacetime with closed timelike curves and the chronology horizon. The renormalized stress-energy tensor is obtained. It is shown that the value of the stress-energy tensor is regular at the chronology horizon for specific authomorphic parameters. Thus the particular example of field configuration is given for which the Hawking's chronology protection conjecture is violated.Comment: 21(Latex)Postscript file of the figure may be received from author, CQG-94-100

Towards a method for rigorous development of generic requirements patterns

We present work in progress on a method for the engineering, validation and verification of generic requirements using domain engineering and formal methods. The need to develop a generic requirement set for subsequent system instantiation is complicated by the addition of the high levels of verification demanded by safety-critical domains such as avionics. Our chosen application domain is the failure detection and management function for engine control systems: here generic requirements drive a software product line of target systems. A pilot formal specification and design exercise is undertaken on a small (twosensor) system element. This exercise has a number of aims: to support the domain analysis, to gain a view of appropriate design abstractions, for a B novice to gain experience in the B method and tools, and to evaluate the usability and utility of that method.We also present a prototype method for the production and verification of a generic requirement set in our UML-based formal notation, UML-B, and tooling developed in support. The formal verification both of the structural generic requirement set, and of a particular application, is achieved via translation to the formal specification language, B, using our U2B and ProB tools

Sound and Relaxed Behavioural Inheritance

Object-oriented (OO) inheritance establishes taxonomies of OO classes. Behavioural inheritance (BI), a strong version, emphasises substitutability: objects of child classes replace objects of their ascendant classes without any observable effect difference on the system. BI is related to data refinement, but refinement's constrictions rule out many useful OO subclassings. This paper revisits BI at the light of Z and the theory of data refinement. It studies existing solutions to this problem, criticises them, and proposes improved relaxations. The results are applicable to any OO language that supports design-by-contract (DbC). The paper's contributions include three novel BI relaxations supported by a mathematical model with proofs carried out in the Isabelle proof assistant, and an examination of BI in the DbC languages Eiffel, JML and Spec#

Bioresorbable scaffold - A magic bullet for the treatment of coronary artery disease?

Today, drug-eluting metal stents are considered the gold standard for interventional treatment of coronary artery disease. While providing inhibition of neointimal hyperplasia, drug-eluting metal stents have many limitations such as the risk of late and very late stent thrombosis, restriction of vascular vasomotion and chronic local inflammatory reaction due to permanent implantation of a 'metallic cage', recognized as a foreign body. Bioresorbable scaffold stents (BRS) are a new solution, which is trying to overcome the limitation of the 'metallic cage'. This structure provides short-term scaffolding of the vessel and then disappears, leaving nothing behind. The purpose of this review is to present the theoretical rationale for the use of BRS and to outline the clinical outcomes associated with their use in terms of data obtained from RCTs, clinical trials, registries and real life use. We have also tried to answer all questions on this intervention based on available data, with a focus on ABSORB BVS (Abbott Vascular, Santa Clara, USA). We consider that this new technology can be the "magic bullet" to treat coronary artery disease

Emergency Department Super-utilizer Program Involvement: Pilot Data and Methods Challenges

Super-utilizers are patients who use extreme amounts of medical services, often due to comorbid medical, social, and mental health issues. The MyLink Evaluation Project (MEP) studies MyLink, a program that connects super-utilizers with community support workers (CSWs) to improve the patient experience and reduce costs. The MEP-eligible population is ≥18 years old with at least 5 Emergency Department (ED) visits within 12 months and no other exclusions (e.g., language barriers, living out-of-region). During MEP’s pilot, among 58 eligible patients, 28 consented to being referred to MyLink and followed up. Of these, 7 could not be located for follow-up, 8 refused enrollment, and the remaining 13 enrolled and “engaged” (had at least 3 face-to-face contacts and developed an initial plan). All 13 enrollees were followed at 6 months vs. 4 of the 8 not enrolled. Consequently, we expect about 50% of eligible patients to consent to the main randomized study, with the vast majority of the MyLink-assigned group becoming engaged and completing follow-up. Achieving this requires identifying patients in real-time at the ED, frequent communications between researchers and CSWs, cultivating rapport during patient referral, enrollment, and follow-up, coordinating with other care management programs serving our patients, and adhering to MEP protocols that are rapidly evolving to address and overcome barriers. Challenges include: increasingly heavy CSW case-loads that decrease “warm” handoffs during the ED visit; problematic patient contact information; and incomplete program and follow-up assessments due to patient withdrawal, relocation, or death. These challenges lead to missing quality-of-life and healthcare utilization data needed for program evaluation. To reduce incomplete assessments, we lengthened time windows and expanded outreach methods (e.g., in-person upon ED revisit, web and medical record searches for updated contact information). We hypothesize that MyLink will improve patient quality-of-life and reduce ED utilization and total costs of care for super-utilizers