Learning and using mathematics software the natural way

AbstractWe motivate the need for more standard while natural ways of accessing the growing number of internet applications of mathematics software. We then identify a subset of natural language appropriate for this task, and describe an efficient logic programming transformation from this subset of language into the desired commands. We use substructural logic for dealing with different kinds of mathematical anaphora. We exemplify our ideas in the context of Maple, an advanced mathematics software for symbolic computing

Intrinsic Spin Hall Effect in the presence of Extrinsic Spin-Orbit Scattering

Intrinsic and extrinsic spin Hall effects are considered together on an equal theoretical footing for the Rashba spin-orbit coupling in two-dimensional (2D) electron and hole systems, using the diagrammatic method for calculating the spin Hall conductivity. Our analytic theory for the 2D holes shows the expected lowest-order additive result for the spin Hall conductivity. But, the 2D electrons manifest a very surprising result, exhibiting a non-analyticity in the Rashba coupling strength $\alpha$ where the strictly extrinsic spin Hall conductivity (for $\alpha = 0$) cannot be recovered from the $\alpha \to 0$ limit of the combined theory. The theoretical results are discussed in the context of existing experimental results.Comment: 5 pages, 2 figure

Anti-arrhythmic effects of hypercalcemia in hyperkalemic, Langendorff-perfused mouse hearts

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Probability weighting, stop-loss and the disposition effect

In this paper we study a continuous-time, optimal stopping model of an asset sale with prospect theory preferences under pre-commitment. We show for a wide range of value and probability weighting functions, including those of Tversky and Kahneman (1992), that the optimal prospect takes the form of a stop-loss threshold and a distribution over gains. It is skewed with a long right tail. This is consistent with both the widespread use of stop-loss strategies in financial markets, and recent experimental evidence. Moreover, our model with probability weighting in tandem with the S-shaped value function makes predictions for the disposition effect which match in magnitude that calculated by Odean (1998)

One read per cell per gene is optimal for single-cell RNA-Seq

An underlying question for virtually all single-cell RNA sequencing experiments is how to allocate the limited sequencing budget: deep sequencing of a few cells or shallow sequencing of many cells? A mathematical framework reveals that, for estimating many important gene properties, the optimal allocation is to sequence at the depth of one read per cell per gene. Interestingly, the corresponding optimal estimator is not the widely-used plug-in estimator but one developed via empirical Bayes

Isolated heart models for studying cardiac electrophysiology: a historical perspective and recent advances

Experimental models used in cardiovascular research range from cellular to whole heart preparations. Isolated whole hearts show higher levels of structural and functional integration than lower level models such as tissues or cellular fragments. Cardiovascular diseases are multi-factorial problems that are dependent on highly organized structures rather than on molecular or cellular components alone. This article first provides a general introduction on the animal models of cardiovascular diseases. It is followed by a detailed overview and a historical perspective of the different isolated heart systems with a particular focus on the Langendorff perfusion method for the study of cardiac arrhythmias. The choice of species, perfusion method, and perfusate composition are discussed in further detail with particular considerations of the theoretical and practical aspects of experimental settings

Atypical case of post-partum cardiomyopathy: an overlap syndrome with arrhythmogenic right ventricular cardiomyopathy?

A middle-aged female patient presented with increasing dyspnoea following delivery of her second child. Echocardiography showed left ventricular (LV) dilatation and severe global impairment of systolic function (ejection fraction < 10%) but normal right ventricular (RV) dimensions. Plasma B-type natriuretic peptide level was elevated. Post-partum cardiomyopathy (PPCM) was considered and after initiating appropriate heart failure pharmacotherapy, her symptoms improved significantly. Cardiovascular MR showed RV free wall dyskinesia and aneurysms at the LV apex, RV free wall and RV outflow tract. Genetic analysis showed a C11842T substitution in the titin gene (TTN). This is the first case to propose an overlap syndrome of PPCM and arrhythmogenic RV cardiomyopathy.published_or_final_versio

Determination of action potential wavelength restitution in Scn5a+/− mouse hearts modelling human Brugada syndrome

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Glass-Like Heat Conduction in High-Mobility Crystalline Semiconductors

The thermal conductivity of polycrystalline semiconductors with type-I clathrate hydrate crystal structure is reported. Ge clathrates (doped with Sr and/or Eu) exhibit lattice thermal conductivities typical of amorphous materials. Remarkably, this behavior occurs in spite of the well-defined crystalline structure and relatively high electron mobility ($\sim 100 cm^2/Vs$). The dynamics of dopant ions and their interaction with the polyhedral cages of the structure are a likely source of the strong phonon scattering.Comment: 4 pages, 3 postscript figures, to be published, Phys. Rev. Let

Winter Counts as Transformative Inquiry: The Role of Creative Imagery as an Expression of Adaptive Change

Pre-service teachers face a complex educational context and Transformative Inquiry is a useful approach for negotiating this terrain. We interpret the movement of students via the adaptive cycle put forth in panarchy theory as they engage in the inquiry process through ‘winter counts’, a Plains First Nation tradition, as expressions of their understanding. These image-based expressions demonstrate the emotional, mental, spiritual and physical movement students have made within their inquiry. Panarchy theory moves beyond interpreting systems using simplistic equilibrium models and acknowledging the more complex and dynamic set of equilibria that describes transformation in ecological, social, and economic systems and considers the multiple complexities of systems thinking while providing insight into how change occurs as a constantly adaptive cycle process. Used sparingly within social sciences until recently, we argue it as particularly relevant for seeing Transformative Inquiry through Indigenist and interconnected lenses