Locations and patterns of functional brain activity in humans are difficult to compare across subjects because of differences in cortical folding and functional foci are often buried within cortical ...sulci. Unfolding a cortical surface via flat mapping has become a key method for facilitating the recognition of new structural and functional relationships. Mathematical and other issues involved in flat mapping are the subject of this paper. It is mathematically
impossible to flatten curved surfaces without metric and area distortion. Nevertheless, “metric” flattening has flourished based on a variety of computational methods that minimize distortion. However, it is mathematically possible to flatten without any
angular distortion — a fact known for 150 years. Computational methods for this “conformal” flattening have only recently emerged. Conformal maps are particularly versatile and are backed by a uniquely rich mathematical theory. This paper presents a tutorial level introduction to the mathematics of conformal mapping and provides both conceptual and practical arguments for its use. Discrete conformal mapping computed via circle packing is a method that has provided the first practical realization of the Riemann Mapping Theorem (RMT). Maps can be displayed in three geometries, manipulated with Möbius transformations to zoom and focus on particular regions of interest, they respect canonical coordinates useful for intersubject registration and are locally Euclidean. The versatility and practical advantages of the circle packing approach are shown by producing conformal flat maps using MRI data of a human cerebral cortex, cerebellum and a specific region of interest (ROI).
In this concise and engaging analysis of rock music, music theorist Ken Stephenson explores the features that make this internationally popular music distinct from earlier music styles. The author ...offers a guided tour of rock music from the 1950s to the present, emphasizing the theoretical underpinnings of the style and, for the first time, systematically focusing not on rock music's history or sociology, but on the structural aspects of the music itself.What structures normally happen in rock music? What theoretical systems or models might best explain them? The book addresses these questions and more in chapters devoted to phrase rhythm, scales, key determination, cadences, harmonic palette and succession, and form. Each chapter provides richly detailed analyses of individual rock pieces from groups including Chicago; the Beatles; Emerson, Lake, and Palmer; Kansas; and others. Stephenson shows how rock music is stylistically unique, and he demonstrates how the features that make it distinct have tended to remain constant throughout the past half-century and within most substyles. For music students at the college level and for practicing rock musicians who desire a deeper understanding of their music, this book is an essential resource.
Maintaining a sharp lateral dose falloff in pencil beam scanning (PBS) proton therapy is crucial for sparing organs at risk (OARs), especially when they are in close proximity to the target volume. ...The most common approach to improve lateral dose falloff is through the use of physical beam shaping devices, such as brass apertures or collimator based systems. A recently proposed approach focuses on proton beam spot placements, moving away from traditional grid-based placements to concentric-contours based schemes. This improves lateral dose falloff in two ways: (1) by better conforming all spots to the tumor boundary and (2) allowing for 'edge enhancement', where boundary spots deliver higher fluence than more central spots, thereby creating a steeper lateral dose falloff. However, these benefits come at the expense of maintaining uniformity of spot distribution inside the target volume. In this work we have developed a new optimized spot placement scheme that provides robust spot distributions inside the target. This approach achieves the boundary conformity of a concentric-contours based approach and uses a fast-iterative method to distribute the interior spots in a highly uniform fashion in an attempt to improve both the lateral dose falloff and uniformity. Furthermore, we quantified the impact of this new approach through direct comparison with grid, contour, and hybrid spot placements schemes, showing improvements for this new approach. The results were validated in homogeneous medium for two different target shapes having concave and convex geometry.
The significant contribution made by Chief Justice Bayda to Canadian tort law exemplified the theme of "judicial activism," the topic which the learned justice selected and presented for the 2006 ...'Saskatchewan Law Review' Lecture, delivered one month after his retirement from twenty-four years as Chief Justice and some thirty-four years on the Bench. The Bayda style of legal reasoning was "open-textured" and included a "justice factor" which draws on the decision-maker's understanding of what moral, social, economic, and political norms should be respected and implemented as binding rules of law. Such an approach permits the judge not only to reflect prevailing extra-legal norms, but also to actually advance them. It is "activist" in Chief Justice Bayda's own definition because it is "the exercise by a judge of his or her discretion in interpreting a law in such a way that the beholder of the law-the ponderer of the law-regards it as having been changed".
Cortical flattening algorithms are becoming more widely used to assist in visualizing the convoluted cortical gray matter sheet of the brain. Metric-based approaches are the most common but suffer ...from high distortions. Conformal, or angle-based algorithms, are supported by a comprehensive mathematical theory. The conformal approach that uses circle packings is versatile in the manipulation and display of results. In addition, it offers some new and interesting metrics that may be useful in neuroscientific analysis and are not available through numerical partial differential equation conformal methods.
In this paper, we begin with a brief description of cortical “flat” mapping, from data acquisition to map displays, including a brief review of past flat mapping approaches. We then describe the mathematics of conformal geometry and key elements of conformal mapping. We introduce the mechanics of circle packing and discuss its connections with conformal geometry. Using a triangulated surface representing a cortical hemisphere, we illustrate several manipulations available using circle packing methods and describe the associated “ensemble conformal features” (ECFs). We conclude by discussing current and potential uses of conformal methods in neuroscience and computational anatomy.
Mark Noll has nothing to say about music theory in The Scandal of the Evangelical Mind; neither does George Marsden in either The Soul of the American University or The Outrageous Idea of Christian ...Scholarship, and neither does J. P. Moreland in Love Your God with All Your Mind.1 A perusal of the contents of the present journal over the last few years uncovers articles on anthropology, biology, cultural criticism, ecology, economics, education, film criticism, geography, history, journalism, literature, philosophy, physics, political science, psychology, sociology, and theology, but no articles on music theory. While most readers could no doubt lend a somewhat informed voice to a discussion on the topic of special creation vs. "blind-watchmaker" evolution or the status of truth as either absolute or relative, and while the names Aristotle and Kant, Newton and Einstein, Dewey and Piaget, Gibbon and Toynbee, Derrida and Foucault, and Lewis, Plantinga, Noll, Marsden, and Moreland are familiar to this readership, the ideas and even the names of the greatest music theorists of history-for instance, Guido of Arezzo, Gioseffo Zarlino, Jean Rameau, Heinrich Schenker, and Allen Forte-are less known, much less the nature of the debate between Christian and secular music theory. With so much zealous commitment in the world of Christian scholars to the notion that all academic disciplines must themselves be brought under the liberating discipline of faith and Scripture, it would seem that Christian scholars in music theory would join the cause. Ken Stephenson offers five proposals for developing distinctly Christian work in this field: (1) analysis of works by Christian composers, (2) analysis of the ethics of musical actions, (3) revival of the field of speculative music theory, (4) emphasis on ways in which music, as part of an integrated creation, reveals God's glory, and (5) analysis of music by Christians and non-Christians alike as pointing to God.
Reflecting on the past 70 years Cooper-Stephenson, Ken; Newman, Dwight G; Singer, Barry M
Saskatchewan law review,
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Journal Article
To improve health care outcomes with cost-effective treatments and prevention initiatives, basic health research must be translated into clinical application and studied during implementation, a ...process commonly referred to as translational research. It is estimated that only 14% of health-related scientific discoveries enter into medical practice and that it takes an average of 17 years for them to do so. The transition from basic research to clinical knowledge and from clinical knowledge to practice or implementation is so fraught with obstacles that these transitions are often referred to as "valleys of death". The Rick Hansen Institute has developed a unique praxis model for translational research in the field of spinal cord injury (SCI). The praxis model involves three components. The first is a coordinated program strategy of cure, care, consumer engagement, and commercialization. The second is a knowledge cycle that consists of four phases, ie, environmental scanning, knowledge generation and synthesis, knowledge validation, and implementation. The third is the provision of relevant resources and infrastructure to overcome obstacles in the "valleys of death", ie, funding, clinical research operations, informatics, clinical research and best practice implementation, consumer engagement, collaborative networks, and strategic partnerships. This model, which is to be independently evaluated in 2018 to determine its strengths and limitations, has been used to advance treatments for pressure ulcers in SCI. The Rick Hansen Institute has developed an innovative solution to move knowledge into action by bridging the "valleys of death" in the research continuum, with the intention of improving health outcomes for people with SCI and decreasing the financial impact on the health care system. This model may be generalizable to other health conditions and the lessons learned in developing the praxis model may assist other organizations dealing with similar translational research challenges. Keywords: spinal cord injuries, clinical outcomes, translational research, implementation, knowledge mobilization, praxis model
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