GLOBAL REGISTRATION OF MULTIPLE POINT CLOUDS USING SEMIDEFINITE PROGRAMMING

Consider N points in R-d and M local coordinate systems that are related through unknown rigid transforms. For each point, we are given (possibly noisy) measurements of its local coordinates in some of the coordinate systems. Alternatively, for each coordinate system, we observe the coordinates of a subset of the points. The problem of estimating the global coordinates of the N points (up to a rigid transform) from such measurements comes up in distributed approaches to molecular conformation and sensor network localization, and also in computer vision and graphics. The least-squares formulation of this problem, although nonconvex, has a well-known closed-form solution when M = 2 (based on the singular value decomposition (SVD)). However, no closed-form solution is known for M >= 3. In this paper, we demonstrate how the least-squares formulation can be relaxed into a convex program, namely, a semidefinite program (SDP). By setting up connections between the uniqueness of this SDP and results from rigidity theory, we prove conditions for exact and stable recovery for the SDP relaxation. In particular, we prove that the SDP relaxation can guarantee recovery under more adversarial conditions compared to earlier proposed spectral relaxations, and we derive error bounds for the registration error incurred by the SDP relaxation. We also present results of numerical experiments on simulated data to confirm the theoretical findings. We empirically demonstrate that (a) unlike the spectral relaxation, the relaxation gap is mostly zero for the SDP (i.e., we are able to solve the original nonconvex least-squares problem) up to a certain noise threshold, and (b) the SDP performs significantly better than spectral and manifold-optimization methods, particularly at large noise levels.

A general theory on media with randomly distributed inclusions .1. The average field behaviors

In this paper, a theory is developed to calculate the average strain field in the materials with randomly distributed inclusions. Many previous researches investigating the average field behaviors were based upon Mori and Tanaka's idea. Since they were restricted to studying those materials with uniform distributions of inclusions they did not need detailed statistical information of random microstructures, and could use the volume average to replace the ensemble average. To study more general materials with randomly distributed inclusions, the number density function is introduced in formulating the average field equation in this research. Both uniform and nonuniform distributions of inclusions are taken into account in detail.

Theory of high-power mode-locked lasers with a slow absorber

We develop an analytical theory of high-power passively mode-locked lasers with a slow absorber; the theory is valid at pulse energies well exceeding the saturation energy. We analyze the Haus modelocking master equation in the pulse-energy-domain representation, approximating the intensity profile function by a series in the vicinity of its peak value. We consider the high-power operation regime of subpicosecond blue-violet GaN mode-locked diode lasers, using the approach developed. © 2010 Springer Science+Business Media, Inc.

Theory of World Security

Booth, Ken, Theory of World Security (Cambridge: Cambridge University Press, 2008), pp.xviii+489 RAE2008

A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Latitudinal phytoplankton distribution and the neutral theory of biodiversity

Aim Recent studies have suggested that global diatom distributions are not limited by dispersal, in the case of both extant species and fossil species, but rather that environmental filtering explains their spatial patterns. Hubbell's neutral theory of biodiversity provides a framework in which to test these alternatives. Our aim is to test whether the structure of marine phytoplankton (diatoms, dinoflagellates and coccolithophores) assemblages across the Atlantic agrees with neutral theory predictions. We asked: (1) whether intersite variance in phytoplankton diversity is explained predominantly by dispersal limitation or by environmental conditions; and (2) whether species abundance distributions are consistent with those expected by the neutral model. Location Meridional transect of the Atlantic (50 degrees N50 degrees S). Methods We estimated the relative contributions of environmental factors and geographic distance to phytoplankton composition using similarity matrices, Mantel tests and variation partitioning of the species composition based upon canonical ordination methods. We compared the species abundance distribution of phytoplankton with the neutral model using Etienne's maximum-likelihood inference method. Results Phytoplankton communities are slightly more determined by niche segregation (24%), than by dispersal limitation and ecological drift (17%). In 60% of communities, the assumption of neutrality in species' abundance distributions could not be rejected. In tropical zones, where oceanic gyres enclose large stable water masses, most communities showed low species immigration rates; in contrast, we infer that communities in temperate areas, out of oligotrophic gyres, have higher rates of species immigration. Conclusions Phytoplankton community structure is consistent with partial niche assembly and partial dispersal and drift assembly (neutral processes). The role of dispersal limitation is almost as important as habitat filtering, a fact that has been largely overlooked in previous studies. Furthermore, the polewards increase in immigration rates of species that we have discovered is probably caused by water mixing conditions and productivity.

The Global Politics of Contemporary Travel Writing

To what extent do bestselling travel books, such as those by Paul
Theroux, Bill Bryson, Bruce Chatwin and Michael Palin, tell us as
much about world politics as newspaper articles, policy documents and
press releases? Debbie Lisle argues that the formulations of genre,
identity, geopolitics and history at work in contemporary travel writing
are increasingly at odds with a cosmopolitan and multicultural world in
which ‘everybody travels’. Despite the forces of globalisation, common
stereotypes about ‘foreignness’ continue to shape the experience of
modern travel. The Global Politics of Contemporary Travel Writing is
concerned with the way contemporary travelogues engage with, and try
to resolve, familiar struggles in global politics such as the protection of
human rights, the promotion of democracy, the management of
equality within multiculturalism and the reduction of inequality. This is
a thoroughly interdisciplinary book that draws from international
relations, literary theory, political theory, geography, anthropology and
history.

Germany and the New Global History of Secularism: Questioning the Postcolonial Genealogy

Secularism has emerged as a central category of twenty-first century political thought that in many ways has replaced the theory of secularization. According to postcolonial scholars, neither the theory nor the practice of secularization was politically neutral. They define secularism as the set of discourses, policies, and constitutional arrangements whereby modern states and liberal elites have sought to unify nations and divide colonial populations. This definition is quite different from the original meaning of secularism, as an immanent scientific worldview linked to anticlericalism. Anthropologist Talal Asad has connected nineteenth-century worldview secularism to twenty-first century political secularism through a genealogical account that stresses continuities of liberal hegemony. This essay challenges this account. It argues that liberal elites did not merely subsume worldview secularism in their drive for state secularization. Using the tools of conceptual history, the essay shows that one reason that “secularization” only achieved its contemporary meaning in Germany after 1945 was that radical freethinkers and other anticlerical secularists had previously resisted liberal hegemony. The essay concludes by offering an agenda for research into the discontinuous history of these two types of secularism.

From Beijing with love: The global dimension of Bertolucci’s The Last Emperor

Famous for being the first foreign feature film that obtained permission to shoot in the Forbidden City, The Last Emperor (1987) is also one of the most ambitious and expensive independent productions of its time, awarded four Golden Globes and nine Academy Awards, including Best Picture. In addition, The Last Emperor can be considered as one of the first attempts of cinematic collaboration between West and East, in a period of cultural and economic transformations witnessed by China. This article aims to offer an overview of the production history of The Last Emperor, focusing on the co-production collaborations and the outcomes of a western auteur’s gaze on Chinese history. Questions of Orientalism, travel narrative and critical reception are taken into account in order to engage with the transnational implications of Bertolucci’s film and the western fascination with China.

Modelling risk perception and trust in food safety information within the theory of planned behaviour

This study suggests a statistical strategy for explaining how food purchasing intentions are influenced by different levels of risk perception and trust in food safety information. The modelling process is based on Ajzen's Theory of Planned Behaviour and includes trust and risk perception as additional explanatory factors. Interaction and endogeneity across these determinants is explored through a system of simultaneous equations, while the SPARTA equation is estimated through an ordered probit model. Furthermore, parameters are allowed to vary as a function of socio-demographic variables. The application explores chicken purchasing intentions both in a standard situation and conditional to an hypothetical salmonella scare. Data were collected through a nationally representative UK wide survey of 533 UK respondents in face-to-face, in-home interviews. Empirical findings show that interactions exist among the determinants of planned behaviour and socio-demographic variables improve the model's performance. Attitudes emerge as the key determinant of intention to purchase chicken, while trust in food safety information provided by media reduces the likelihood to purchase. (C) 2006 Elsevier Ltd. All rights reserved.

Construction management strategies : a theory of construction management

The construction industry has become a truly global network of interconnected stakeholders making demands which require the involvement of skilled workforces from all over the world. Construction Management Strategies sets the foundations for understanding and managing construction’s inherent complexity and uniqueness. It establishes clear definitions of commonly accepted terms like built environment, construction, civil engineering, etc. which are often given confusing and conflicting interpretations. It cuts through the plethora of overlapping role titles currently used in the construction sector that make it difficult to establish how projects are actually managed.

The economic theory of international supply chains: a systems view

This paper offers an integrated analysis of out-sourcing, off-shoring and foreign direct investment within a systems view of international business. This view takes the supply chain rather than the firm as the basic unit of analysis. It argues that competition in the global economy selects supply chains that maximise the joint profit of all the firms in the chain. The systems view is compared with the firm-centred view commonly used in strategy literature. The paper shows that a firm’s strategy must be embedded within an efficient supply chain strategy, and that this strategy must be negotiated with, rather than imposed upon, other firms. The paper analyses the conditions under which various supply chain strategies - and by implication various firm-level strategies - are efficient. Only by adopting a systems view of supply chains is it possible to determine which firm-level strategies will succeed in a volatile global economy.