Walking Through Cantor's Paradise and Escher's Garden: Epistemological Reflections on the Mathematical Infinite (II)

Infinity is not an easy concept. A number of difficulties that people cope with when dealing with problems related to infinity include its abstract nature, understanding infinity as an ongoing, never ending process, understanding infinity as a set of an infinite number of elements and appreciating well-known paradoxes. Infinity can be understood in several ways with often incompatible meanings, and can involve value judgments or assumptions that are neither explicit nor desired. To usher in its definition, we distinguish several aspects, teleological, artistic (Escher); some definitive, some potential, and others actual. This article also deals with some still unresolved aspects of the concept of infinity.

Contributions from the New York Botanical Garden.

v.7 (1912-1915)

Old-fashioned garden flowers / by Donald Culross Peattie.

no.19(1936)

Bulletin of the New York Botanical Garden.

v.11 (1921)

Boston, Massachusetts -- Emerald Necklace parks, 1894 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Plan of portion of park system from Common to Franklin Park : including Charles River Basin, Charlesbank, Commonwealth Avenue, Back Bay Fens, Muddy River Improvement, Leverett Park, Jamaica Park, Arborway and Arnold Arboretum, [by] William Jackson, city engineer ; Olmsted, Olmsted & Eliot, landscape architects. It was published in Jan. 1894. Scale [ca. 1:9,000]. Covers Boston parks collectively known as the "Emerald Necklace." The image inside the map neatline is georeferenced to the surface of the earth and fit to the Massachusetts State Plane Coordinate System, Mainland Zone (in Feet) (Fipszone 2001). All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, or other information associated with the principal map. This map shows park features such as roads, paths, recreational buildings and facilities, ground cover, and drainage. Also includes features surrounding parks: city roads, railroads, drainage, some public buildings, and more. This layer is part of a selection of digitally scanned and georeferenced historic maps of Massachusetts from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of regions, originators, ground condition dates (1755-1922), scales, and purposes. The digitized selection includes maps of: the state, Massachusetts counties, town surveys, coastal features, real property, parks, cemeteries, railroads, roads, public works projects, etc.

Rawda al-Ushshaq (Garden of Lovers) of Arifi, with three paintings : manuscript, ca. 1560-1575

Artist unknown.

Developmental Paths and Activities of Successful Sport Coaches

The purpose of this research report is to present an overview of an ongoing, international project designed to chart the developmental paths and activities of sport coaches. This brief report includes three sections: (a) conceptual framework used to guide the project, (b) project design and methodology, and (c) results from pilot studies with a sample of 15 successful coaches working in different sport contexts in the United States Unlike the findings for athletic profiles, where several trends across coaching contexts were evident, only one trend was found in how these diverse groups of coaches invested their time in coach developmental activities. In relation to other coaching activities very little time was devoted to formal coach education on an annual basis. The results reinforce the need to consider the coaching context when examining coach development and when designing coach development initiatives.

Tracking evolutionary paths in colonizing events temporal changes in life-history traits, microsatellites and inversions in Drosophila subobscura

Tese de doutoramento, Biologia (Biologia Evolutiva), Universidade de Lisboa, Faculdade de Ciências, 2016

Syria and Lebanon: Diverging paths of state unsustainability. MEDPRO Technical Report No. 6/June 2011

Any analysis of the prospects for stability and sustainability in the states of Syria and Lebanon reveals the strong ties that exist between these two countries and the impact of external influences on their overall development. Their trajectories, while starkly divergent in terms of the challenges confronting them at present, converge on a path of long-term unsustainability. Lebanon is in the midst of yet another transition phase, triggered by the collapse of Hariri’s government in January 2011. The current situation might be described as one of deteriorating status quo; the state is performing poorly in terms of its delivery of fundamental public services and its institutional legitimacy is tenuous in the face of emerging para-state structures and latent (occasionally active) violence. In Syria, challenges to the sustainability of the state have evolved dramatically since the beginning of 2011, and are now nearing a tipping point. In view of the mounting unrest and violence in the country, the future prospects for its economic and political development are dim. More ominously, the risk of widespread conflict, with sectarian overtones, cannot be discounted.

On ANOVA Decompositions of Kernels and Gaussian Random Field Paths

The FANOVA (or “Sobol’-Hoeffding”) decomposition of multivariate functions has been used for high-dimensional model representation and global sensitivity analysis. When the objective function f has no simple analytic form and is costly to evaluate, computing FANOVA terms may be unaffordable due to numerical integration costs. Several approximate approaches relying on Gaussian random field (GRF) models have been proposed to alleviate these costs, where f is substituted by a (kriging) predictor or by conditional simulations. Here we focus on FANOVA decompositions of GRF sample paths, and we notably introduce an associated kernel decomposition into 4 d 4d terms called KANOVA. An interpretation in terms of tensor product projections is obtained, and it is shown that projected kernels control both the sparsity of GRF sample paths and the dependence structure between FANOVA effects. Applications on simulated data show the relevance of the approach for designing new classes of covariance kernels dedicated to high-dimensional kriging.

The Grange garden. A romance.

Mode of access: Internet.

The autmumn garden ...

Mode of access: Internet.