The Identity Correspondence Problem and its Applications

In this paper we study several closely related fundamental problems for words and matrices. First, we introduce the Identity Correspondence Problem (ICP): whether a finite set of pairs of words (over a group alphabet) can generate an identity pair by a sequence of concatenations. We prove that ICP is undecidable by a reduction of Post's Correspondence Problem via several new encoding techniques. In the second part of the paper we use ICP to answer a long standing open problem concerning matrix semigroups: "Is it decidable for a finitely generated semigroup S of square integral matrices whether or not the identity matrix belongs to S?". We show that the problem is undecidable starting from dimension four even when the number of matrices in the generator is 48. From this fact, we can immediately derive that the fundamental problem of whether a finite set of matrices generates a group is also undecidable. We also answer several question for matrices over different number fields. Apart from the application to matrix problems, we believe that the Identity Correspondence Problem will also be useful in identifying new areas of undecidable problems in abstract algebra, computational questions in logic and combinatorics on words.Comment: We have made some proofs clearer and fixed an important typo from the published journal version of this article, see footnote 3 on page 1

Applications of three-dimensional printing in ophthalmology

Three-dimensional (3D) printing is increasingly used to produce customised objects and is a promising alternative to traditional manufacturing methods in diverse fields, such as dentistry and orthopaedics. Already in use in other medical specialities, adoption in ophthalmology has been limited to date. This review aims to provide an overview of 3D printing technology with respect to current and potential applications in ophthalmic practice. Medline, Embase and internet search were performed with "3D printing", "ophthalmology", "dentistry", "orthopaedics" and their synonyms used as main search terms. In addition, search terms related to clinical applications such as "surgery" and "implant" were employed. 3D printing has multiple applications in ophthalmology, including in diagnosis, surgery, prosthetics, medications and medical education. Within the past decade, researchers have produced 3D printed models of objects such as implants, prostheses, anatomical models and surgical simulators. Further development is necessary to generate optimal biomaterials for various applications, and the quality and long-term performance of 3D models needs to be validated

The impact of the dark matter-gas interaction on the collapse behaviour of spherical symmetric systems

If the gas in the evolving cosmic halos is dissipating energy (cooling) then due to the variation of the gravitational potential the dark matter halo also undergoes a compactification. This is well-known as Adiabatic contraction (AC). Complementary to the AC we investigate the resulting dynamical behaviour of the whole system if the backreaction of the AC of DM onto the gas is taken into account. In order to achieve sufficient high resolution also within the central halo region, we use a crude fluid approximation for the DM obeying the adiabatic contraction behaviour. Further, we restrict ourself to spherical symmetry and vanishing angular momentum of the studied matter configurations. The computations are done using a first-order Godunov type scheme. Our results show that the dynamical interaction between gas and DM may lead to significant shorter collapse times. If the gas cools the dynamical behaviour of the whole system depends strongly on the shape of the initial density profile. Our findings indicate that for a certain mass range of halo configurations the dynamical interaction between gas and DM might be important for the halo evolution and must be taken into account.Comment: 9 pages, 13 figures, accepted for publication in A&A, added reference

Acute coronary syndrome-associated depression: Getting to the heart of the data

Objectives: We sought to identify and consider methodological issues that may have limited or confounded investigations into links between depression and acute coronary syndrome (ACS) events. Methods: We reviewed salient research studies to identify such issues. Results: Against previous conclusions, we found that lifetime depression is unlikely to have any primary ACS impact, while we clarify that ‘incident depression’ (depression commencing at variable periods around the time of the ACS event) appears to confer a greater risk than non-incident depression. As the time periods of incident depressions are likely to have quite differing causes, evaluating any consolidated risk period appears unwise. It remains unclear whether it is ‘depression’ that provides the risk for ACS events or a higher order factor. Variable use of depression measures and failure to evaluate depressive sub-types have further limited clarification. The response by ACS patients to antidepressant medication appears limited, and it remains to be determined whether exposure to an antidepressant might be a contributing factor. Finally, studies may have focused on an excessively refined association, and neglected to recognise that depression is associated with a wide range of vascular events, suggesting that a broader conceptual model may be required. Limitations: The authors have considered only a limited set of studies in preparing this review, with the critique relying at times on subjective interpretation. Conclusions: After decades of research pursuing links between depression and ACS events explanatory links remain obscure, presumably reflecting a range of methodological issues that we have discussed in this paper

Global axisymmetric stability analysis for a composite system of two gravitationally coupled scale-free discs

In a composite system of gravitationally coupled stellar and gaseous discs, we perform linear stability analysis for axisymmetric coplanar perturbations using the two-fluid formalism. The background stellar and gaseous discs are taken to be scale-free with all physical variables varying as powers of cylindrical radius $r$ with compatible exponents. The unstable modes set in as neutral modes or stationary perturbation configurations with angular frequency $\omega=0$.Comment: 7 pages using AAS styl

A Dose-Escalation Study of Recombinant Human Interleukin-18 Using Two Different Schedules of Administration in Patients with Cancer

Purpose: Interleukin-18 (IL-18) is an immunostimulatory cytokine with antitumor activity in preclinical models. A phase I study of recombinant human IL-18 (rhIL-18) was done to determine the toxicity, pharmacokinetics, and biological activities of rhIL-18 administered at different doses in two different schedules to patients with advanced cancer. Experimental design: Cohorts of three to four patients were given escalating doses of rhIL-18 as a 2-h i.v. infusion either on 5 consecutive days repeated every 28 days (group A) or once a week (group B) for up to 6 months. Toxicities were graded using standard criteria. Blood samples were obtained for safety, pharmacokinetic, and pharmacodynamic measurements. Results: Nineteen patients (10 melanoma and 9 renal cell cancer) were given rhIL-18 in doses of 100, 500, or 1,000 microg/kg (group A) or 100, 1,000, or 2,000 microg/kg (group B). Common side effects included chills, fever, headache, fatigue, and nausea. Common laboratory abnormalities included transient, asymptomatic grade 1 to 3 lymphopenia, grade 1 to 4 hyperglycemia, grade 1 to 2 anemia, neutropenia, hypoalbuminemia, liver enzyme elevations, and serum creatinine elevations. No dose-limiting toxicities were observed. Biological effects of rhIL-18 included transient lymphopenia and increased expression of activation antigens on lymphocytes. Increases in serum concentrations of IFN-gamma, granulocyte macrophage colony-stimulating factor, and IL-18-binding protein were observed following dosing. Conclusions: rhIL-18 can be given in biologically active doses by either weekly infusions or daily infusions for 5 days repeated every 28 days to patients with advanced cancer. Toxicity was generally mild to moderate, and a maximum tolerated dose of rhIL-18 by either schedule was not determined

Standard set of health outcome measures for older persons

Background: The International Consortium for Health Outcomes Measurement (ICHOM) was founded in 2012 to propose consensus-based measurement tools and documentation for different conditions and populations.This article describes how the ICHOM Older Person Working Group followed a consensus-driven modified Delphi technique to develop multiple global outcome measures in older persons. The standard set of outcome measures developed by this group will support the ability of healthcare systems to improve their care pathways and quality of care. An additional benefit will be the opportunity to compare variations in outcomes which encourages and supports learning between different health care systems that drives quality improvement. These outcome measures were not developed for use in research. They are aimed at non researchers in healthcare provision and those who pay for these services. Methods: A modified Delphi technique utilising a value based healthcare framework was applied by an international panel to arrive at consensus decisions.To inform the panel meetings, information was sought from literature reviews, longitudinal ageing surveys and a focus group. Results: The outcome measures developed and recommended were participation in decision making, autonomy and control, mood and emotional health, loneliness and isolation, pain, activities of daily living, frailty, time spent in hospital, overall survival, carer burden, polypharmacy, falls and place of death mapped to a three tier value based healthcare framework. Conclusions: The first global health standard set of outcome measures in older persons has been developed to enable health care systems improve the quality of care provided to older persons

Applying psychological learning theory to helping students overcome learned difficulties in mathematics: An alternative approach to intervention

The appearance of systematic errors in computation suggests relatively unlinked computational knowledge to conceptual knowledge, and hence difficulties with forward learning of mathematics. The provision of programs of good teaching, where concrete materials are used to exemplify and thus legitimize algorithmic processes, frequently are not effective for use with upper primary students: systematic errors often resurface. A novel and quite alternate approach to intervention is the Old Way/New Way (O/N) strategy (Lyndon, 1989) based on psychological principles of memory, forgetting and interference. In this article, issues associated with intervention, systematic errors and upper primary students are addressed through a discussion of results of previous research into seventh graders' subtraction knowledge development by overcoming error patterns in subtraction computation. By comparing re-teaching strategies and O/N, it is proposed that both good teaching and effective intervention strategies should be integral to the craft of teaching, particularly in the middle school

Weekly variation in health-care quality by day and time of admission: a nationwide, registry-based, prospective cohort study of acute stroke care.

Studies in many health systems have shown evidence of poorer quality health care for patients admitted on weekends or overnight than for those admitted during the week (the so-called weekend effect). We postulated that variation in quality was dependent on not only day, but also time, of admission, and aimed to describe the pattern and magnitude of variation in the quality of acute stroke care across the entire week.Accepted manuscript (12 month embargo