Non-Schlesinger Deformations of Ordinary Differential Equations with Rational Coefficients

We consider deformations of $2\times2$ and $3\times3$ matrix linear ODEs with rational coefficients with respect to singular points of Fuchsian type which don't satisfy the well-known system of Schlesinger equations (or its natural generalization). Some general statements concerning reducibility of such deformations for $2\times2$ ODEs are proved. An explicit example of the general non-Schlesinger deformation of $2\times2$-matrix ODE of the Fuchsian type with 4 singular points is constructed and application of such deformations to the construction of special solutions of the corresponding Schlesinger systems is discussed. Some examples of isomonodromy and non-isomonodromy deformations of $3\times3$ matrix ODEs are considered. The latter arise as the compatibility conditions with linear ODEs with non-singlevalued coefficients.Comment: 15 pages, to appear in J. Phys.

Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2+1 dimensions

Hamiltonian systems of hydrodynamic type occur in a wide range of applications including fluid dynamics, the Whitham averaging procedure and the theory of Frobenius manifolds. In 1+1 dimensions, the requirement of the integrability of such systems by the generalised hodograph transform implies that integrable Hamiltonians depend on a certain number of arbitrary functions of two variables. On the contrary, in 2+1 dimensions the requirement of the integrability by the method of hydrodynamic reductions, which is a natural analogue of the generalised hodograph transform in higher dimensions, leads to finite-dimensional moduli spaces of integrable Hamiltonians. In this paper we classify integrable two-component Hamiltonian systems of hydrodynamic type for all existing classes of differential-geometric Poisson brackets in 2D, establishing a parametrisation of integrable Hamiltonians via elliptic/hypergeometric functions. Our approach is based on the Godunov-type representation of Hamiltonian systems, and utilises a novel construction of Godunov's systems in terms of generalised hypergeometric functions.Comment: Latex, 34 page

Mathematical structure of unit systems

We investigate the mathematical structure of unit systems and the relations between them. Looking over the entire set of unit systems, we can find a mathematical structure that is called preorder (or quasi-order). For some pair of unit systems, there exists a relation of preorder such that one unit system is transferable to the other unit system. The transfer (or conversion) is possible only when all of the quantities distinguishable in the latter system are always distinguishable in the former system. By utilizing this structure, we can systematically compare the representations in different unit systems. Especially, the equivalence class of unit systems (EUS) plays an important role because the representations of physical quantities and equations are of the same form in unit systems belonging to an EUS. The dimension of quantities is uniquely defined in each EUS. The EUS's form a partially ordered set. Using these mathematical structures, unit systems and EUS's are systematically classified and organized as a hierarchical tree.Comment: 27 pages, 3 figure

A Values-Based Learning Model to Impact Maturational Change: The College Fraternity as Developmental Crucible

The period of late adolescence and early adulthood is a critical time during which individual identity is developed. One fraternity recently implemented a developmental process that facilitated identity maturation within its members by emphasizing self-awareness and reflection. Utilizing a learning model as the core component of all aspects of its programming, the fraternity conducted research to determine the impact of its learning model on the development of self-awareness. This article provides data from three years of implementation that documents significant increases in this critical developmental competency

Productivity Gaps Between European and United States Agriculture

A set of purchasing power parities was constructed for the inputs and the outputs of the agricultural sector in 10 European countries and the United States. This made it possible to deflate both spatially and in time the nominal agricultural accounts. Real values of inputs and outputs made it possible to construct spatial indexes of productivity. These indexes measure the productivity gaps between countries for a given year. Extrapolation between 1973 and 1989 measures how these gaps have changed over time. The results show that the productivity of the United States has been 20 percent higher than the average productivity of European agriculture. This gap has persisted over time. However, large discrepancies exist in Europe and a few countries such as The Netherlands obtain a higher productivity than the United States

A Values-Based Learning Model to Impact Maturational Change: The College Fraternity as Developmental Crucible

The period of late adolescence and early adulthood is a critical time during which individual identity is developed. One fraternity recently implemented a developmental process that facilitated identity maturation within its members by emphasizing self-awareness and reflection. Utilizing a learning model as the core component of all aspects of its programming, the fraternity conducted research to determine the impact of its learning model on the development of self-awareness. This article provides data from three years of implementation that documents significant increases in this critical developmental competency

MITE-Hunter: a program for discovering miniature inverted-repeat transposable elements from genomic sequences

Miniature inverted-repeat transposable elements (MITEs) are a special type of Class 2 non-autonomous transposable element (TE) that are abundant in the non-coding regions of the genes of many plant and animal species. The accurate identification of MITEs has been a challenge for existing programs because they lack coding sequences and, as such, evolve very rapidly. Because of their importance to gene and genome evolution, we developed MITE-Hunter, a program pipeline that can identify MITEs as well as other small Class 2 non-autonomous TEs from genomic DNA data sets. The output of MITE-Hunter is composed of consensus TE sequences grouped into families that can be used as a library file for homology-based TE detection programs such as RepeatMasker. MITE-Hunter was evaluated by searching the rice genomic database and comparing the output with known rice TEs. It discovered most of the previously reported rice MITEs (97.6%), and found sixteen new elements. MITE-Hunter was also compared with two other MITE discovery programs, FINDMITE and MUST. Unlike MITE-Hunter, neither of these programs can search large genomic data sets including whole genome sequences. More importantly, MITE-Hunter is significantly more accurate than either FINDMITE or MUST as the vast majority of their outputs are false-positives

Mortality after admission for acute myocardial infarction in Aboriginal and non-Aboriginal people in New South Wales, Australia: a multilevel data linkage study

Background - Heart disease is a leading cause of the gap in burden of disease between Aboriginal and non-Aboriginal Australians. Our study investigated short- and long-term mortality after admission for Aboriginal and non-Aboriginal people admitted with acute myocardial infarction (AMI) to public hospitals in New South Wales, Australia, and examined the impact of the hospital of admission on outcomes. Methods - Admission records were linked to mortality records for 60047 patients aged 25–84 years admitted with a diagnosis of AMI between July 2001 and December 2008. Multilevel logistic regression was used to estimate adjusted odds ratios (AOR) for 30- and 365-day all-cause mortality. Results - Aboriginal patients admitted with an AMI were younger than non-Aboriginal patients, and more likely to be admitted to lower volume, remote hospitals without on-site angiography. Adjusting for age, sex, year and hospital, Aboriginal patients had a similar 30-day mortality risk to non-Aboriginal patients (AOR: 1.07; 95% CI 0.83-1.37) but a higher risk of dying within 365 days (AOR: 1.34; 95% CI 1.10-1.63). The latter difference did not persist after adjustment for comorbid conditions (AOR: 1.12; 95% CI 0.91-1.38). Patients admitted to more remote hospitals, those with lower patient volume and those without on-site angiography had increased risk of short and long-term mortality regardless of Aboriginal status. Conclusions - Improving access to larger hospitals and those with specialist cardiac facilities could improve outcomes following AMI for all patients. However, major efforts to boost primary and secondary prevention of AMI are required to reduce the mortality gap between Aboriginal and non-Aboriginal people