Local integrands for the five-point amplitude in planar N=4 SYM up to five loops

Integrands for colour ordered scattering amplitudes in planar N=4 SYM are dual to those of correlation functions of the energy-momentum multiplet of the theory. The construction can relate amplitudes with different numbers of legs. By graph theory methods the integrand of the four-point function of energy-momentum multiplets has been constructed up to six loops in previous work. In this article we extend this analysis to seven loops and use it to construct the full integrand of the five-point amplitude up to five loops, and in the parity even sector to six loops. All results, both parity even and parity odd, are obtained in a concise local form in dual momentum space and can be displayed efficiently through graphs. We have verified agreement with other local formulae both in terms of supertwistors and scalar momentum integrals as well as BCJ forms where those exist in the literature, i.e. up to three loops. Finally we note that the four-point correlation function can be extracted directly from the four-point amplitude and so this uncovers a direct link from four- to five-point amplitudes.Comment: 29 pages LaTeX, 8 figure

Persian Gardens: Meanings, Symbolism, and Design

Culture and identity in a society can be represented in the architecture and the meanings intertwined with it. In this sense, the architecture and design are the interface for transferring meaning and identity to the nation and future generations. Persian gardens have been evolved through the history of Persian Empire in regard to the culture and beliefs of the society. This paper aims to investigate the patterns of design and architecture in Persian gardens and the meanings intertwined with their patterns and significant elements such as water and trees. Persian gardens are not only about geometries and shapes; but also manifest different design elements, each representing a specific symbol and its significance among the society. This paper seeks to explore Persian gardens in terms of their geometric structure, irrigation system, network construction and pavilions alongside design qualities such as hierarchy, symmetry, centrality, rhythm and harmony. In the second stage, the paper investigates the fundamental symbols and their philosophy in the creation of Persian gardens and in relation to the architecture and design

The Castello Plan-Evidence of Horticulture in New Netherland or Cartographer\u27s Whimsy?

Few descriptions or depictions of horticulture in New Netherland have come down to us, although 17th-century observers\u27 accounts of gardens and orchards present lengthy lists of fruits, vegetables, \u27and fiowers transplanted from Europe, as well as those discovered in North America. Perhaps the most evocative source is the mid-century Castello Plan, a view of the settlement af New Amsterdam, which shows elaborate · parterres on most of the unoccupied lots. Are the gardens of the Castello Plan fact, or simply cartographer\u27s whimsy? Based on data from both the Netherlands and New Netherland-including artists~ depiction~, travelers\u27 accounts, and gardening texts-that illustrate the cultural attitudes, cultural materials, and enviro\u27n~ ment the colonists would have known in Europe, the images of gardens depicted on this early view of Manhattan are evaluated

Imagining early Melbourne

A broad stroke examination of the surveying of early Melbourne and the anxiety surrounding the development of slums in the city

Water as blessing: recovering the symbolism of the Garden of Eden through Ezekiel for Christian theology – a theological investigation

The Garden of Eden is one of the most pervasive and enduring images in the Abrahamic Tradition. Despite being the inspiration of many profound works of art, including painting, music, literature, architecture, and landscape design, theological meaning has tended to be subsidiary to wider anthropological, archaeological or art-historical concerns. Recent interest in nature imagery in the Bible, including the Garden of Eden, suggests this aspect of religious expression is becoming more visible. However, most attention has tended to focus on the socio-political and ecological implications of these images, and is primarily agrarian in focus. Given the canonical location of the Eden myth in Genesis 2:5 and 3, and Revelation 22:1-5, bookending, as it were, the Christian Bible, this emphasis seems misplaced. Indeed, an examination of the use of Edenic imagery, with its roots in the temple cult of pre-exilic Jerusalem, points instead to an alternative interpretation expressive of an eschatology that simultaneously symbolizes, manifests and energises the enduring hope that lies at the root of the Christian experience. The Eden imagery used in Ezekiel 47:1-12, as it is reprised in Revelation 22:1-5, and also in John 4:4-42, is central to this understanding, mediating the Wisdom of God and the Holy Spirit through the notion of water as blessing

Unity and Diversity in Geometric Gardens

There are different types of gardens; each one is influenced by time, place, and science. Gardens’ design was inspired by the scientific results of a particular age. It transforms the practical need of people into beautiful edifice and provides users with comfort and convenience. Gardens are characterized by the deep thinking of geometry and beauty, as in Andalusia, Istanbul, Iran, Afghanistan, and Italy. Besides simplicity, shapes in geometric gardens have unity and diversity. These foundations can achieve harmony. Geometric gardens have a type, embodied in many models and organized by this main type, leading to common characteristics. This chapter will discuss these characteristics and their diversity with a comparative analytical study between East and West gardens to find the bases of diversity and the elements’ unity. It will discuss many models of geometric gardens through the concept of type and model. The chapter focuses on many examples to test its response to specific designing elements of landscape and how it reflects its experience of designing the garden. The conclusion is based on the interactive vision type, model, diversity, and unity to find common and noncommon characteristics in geometric gardens of different places and ages

Beauties of Nature: Flower and Landscape Gardening in Europe, 1700-1850

"Beauties of Nature" traces changes in taste from valuing grandiose formality to emulating nature, and changes in the study of botany from simple observation to a modern science. But it also traces changes in who the people were who practiced flower gardening and landscaping, from soley upper class men to a much wider array of both men and women.http://deepblue.lib.umich.edu/bitstream/2027.42/120291/1/Beauties_of_Nature_11.pd