Ducci iterates and similar ordering of visible points in convex regions

Hardy et al. first introduced the notion of similar ordering of pairs of rationals, and Mayer proved that pairs of Farey fractions in [Formula: see text] are similarly ordered when [Formula: see text] is large enough. We generalize Mayer’s result to Ducci iterates of Farey sequence and visible points in certain regions in the plane. We also study the distribution of values of generalized indices of these sequences.

Functional Somatic Symptoms and Somatization: Person-centered Approach to Understanding their Relationships

Background: Despite the visible points of overlapping between the psychopathologic concepts of "somatization" and "somatoform disorders" with those of "functional symptoms" and "somatic syndromes" of general medicine, there is little literature which clarifies their relationships, making it difficult to formulate common grounds for work between psychiatry and the rest of medicine. Objectives: The purpose of this article is to review and critically analyze current knowledge on the subject, in search for conceptual links between different paradigms involving the underlying phenomena, proposing present and future lines of work according to the basic concepts of the Person Centered Medicine. Methodology: A wide ranging review and critical analysis of the literature on these subjects was conducted, trying to explore the relationship and integration of different paradigms according to the MCP framework and an outline of the author´s current research. Results: A need was found to establish transdisciplinary concepts which leave aside the particular visions of each paradigm, in search for links which may integrate different insights, considering the person as a whole. Therefore, it is essential to analyze carefully the phenomenon from various points of view to elucidate wider conceptualizations so as to reformulate this spectrum of phenomena from an integrative perspective. The possibility of the existence of a “general factor”, both present in the so-called “functional” disorder of general medicine, and in those that in psychopathology are grouped as somatization, is suggested. This general factor could be represented by certain personality dimensions and psychic representations encompassed by complex context variables. Conclusions: It would be valuable to continue with research of this phenomena structure as well as to look for strategies to benefit from the theoretical findings in the health care field, according to the proposals of Person Centered Medicine.

Seeing the invisible: Theorising connections between informal and formal musical knowledge

This article explores the perceived disconnect between informal and formal musical knowledge, through a focused case study which aligned students’ informal knowledge with aspects of the formal curriculum. The upper high school or senior secondary student participants had a background in the creation and performance of popular and contemporary music, and already possessed well-developed informal and aural-based learning skills. Using a latter phase of Green’s (2008) informal learning research as a starting point, the students completed two written tasks: a scoring or transcription exercise, and an analysis report using the music “elements” or “concepts” framework of the syllabus. Legitimation Code Theory (LCT), was utilised in the theoretical appraisal of themes emerging from the study. Employing one LCT dimension known as Semantics, which explores the context-dependence and complexity of knowledge, a range of knowledge types were observed. These made visible points of connection and disconnection between the students’ informal knowledge and the formal knowledge required to complete the tasks. The study highlights the limitations of informal knowledge as a sole basis for formal knowledge construction, but equally unveils points of connection between the two, important in informing teacher facilitation, and, much needed in curriculum reform.

Basel to Boston: An Itinerary for Modernist Typography in America

Starting in the 1960s, the Massachusetts Institute of Technology (MIT) became one of the most visible points of entry in America for the so-called “Swiss-style,” a distinctive, modernist approach to graphic design. Three women were largely responsible for its success: Therese Moll, Jacqueline Casey, and Muriel Cooper. While Casey and Cooper have begun to get their due, Moll—a visiting designer from Basel—remains almost unknown. This article examines why MIT provided such fertile ground for this style, before it became the lingua franca of corporate modernism, and how, by the 1980s, it traveled from print to screens.

VISIBLE POINTS ON EXPONENTIAL CURVES

We provide two new bounds on the number of visible points on exponential curves modulo a prime for all choices of primes. We also provide one new bound on the number of visible points on exponential curves modulo a prime for almost all primes.

A Point-Based Virtual Reality System for Supporting Product Development

In this paper, we discuss methods to efficiently render stereoscopic scenes of large-scale point-clouds on inexpensive VR systems. Recently, terrestrial laser scanners are significantly improved, and they can easily capture tens of millions points in a short time from large fields, such as engineering plants. If 3D stereoscopic scenes of large-scale point-clouds could be easily rendered using inexpensive devices, they might be involved in casual product development phases. However, it is difficult to render a huge number of points using common PCs, because VR systems require high frame rates to avoid VR sickness. To solve this problem, we introduce an efficient culling method for large-scale point-clouds. In our method, we project all points onto angle-space panoramic images, whose axes are the azimuth and elevation angles of head directions. Then we eliminate occluded and redundant points according to the resolutions of devices. Once visible points are selected, they can be rendered in high frame rates. Visible points are updated when the user stays at a certain position to observe target objects. Since points are processed on image space in our method, preprocessing is very fast. In our experiments, our method could render stereoscopic views of large-scale point-clouds in high frame rates.

Reid's response to Hume's perceptual relativity argument

Reid declared Hume's appeal to variation in the magnitude of a table with distance to be the best argument that had ever been offered for the ‘ideal hypothesis’ that we experience nothing but our own mental states. Reid's principal objection to this argument fails to apply to minimally visible points. He did establish that we have reason to take our perceptions to be caused by external objects. But his case that we directly perceive external objects is undermined by what Hume had to say about the role played by color in our perception of the primary qualities of bodies.