Optimality Conditions for D.C. Vector Optimization Problems under D.C. Constraints

2000 Mathematics Subject Classification: Primary 90C29; Secondary 49K30.

Mapping Hydrophobicity on the Protein Molecular Surface at Atom-Level Resolution

A precise representation of the spatial distribution of hydrophobicity, hydrophilicity and charges on the molecular surface of proteins is critical for the understanding of the interaction with small molecules and larger systems. The representation of hydrophobicity is rarely done at atom-level, as this property is generally assigned to residues. A new methodology for the derivation of atomic hydrophobicity from any amino acid-based hydrophobicity scale was used to derive 8 sets of atomic hydrophobicities, one of which was used to generate the molecular surfaces for 35 proteins with convex structures, 5 of which, i.e., lysozyme, ribonuclease, hemoglobin, albumin and IgG, have been analyzed in more detail. Sets of the molecular surfaces of the model proteins have been constructed using spherical probes with increasingly large radii, from 1.4 to 20 A˚, followed by the quantification of (i) the surface hydrophobicity; (ii) their respective molecular surface areas, i.e., total, hydrophilic and hydrophobic area; and (iii) their relative densities, i.e., divided by the total molecular area; or specific densities, i.e., divided by property-specific area. Compared with the amino acid-based formalism, the atom-level description reveals molecular surfaces which (i) present an approximately two times more hydrophilic areas; with (ii) less extended, but between 2 to 5 times more intense hydrophilic patches; and (iii) 3 to 20 times more extended hydrophobic areas. The hydrophobic areas are also approximately 2 times more hydrophobicity-intense. This, more pronounced "leopard skin"-like, design of the protein molecular surface has been confirmed by comparing the results for a restricted set of homologous proteins, i.e., hemoglobins diverging by only one residue (Trp37). These results suggest that the representation of hydrophobicity on the protein molecular surfaces at atom-level resolution, coupled with the probing of the molecular surface at different geometric resolutions, can capture processes that are otherwise obscured to the amino acid-based formalism.

Non-existence of polar factorisations and polar inclusion of a vector-valued mapping

R.J. DOUGLAS, Non-existence of polar factorisations and polar inclusion of a vector-valued mapping. Intern. Jour. Of Pure and Appl. Math., (IJPAM) 41, no. 3 (2007).

Uniqueness of the polar factorisation and projection of a vector-valued mapping

G.R. BURTON and R.J. DOUGLAS, Uniqueness of the polar factorisation and projection of a vector-valued mapping. Ann. I.H. Poincare ? A.N. 20 (2003), 405-418.

Integral completeness of locally convex spaces

A locally convex space X is said to be integrally complete if each continuous mapping f: [0, 1] --> X is Riemann integrable. A criterion for integral completeness is established. Readily verifiable sufficient conditions of integral completeness are proved.

Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group

In this paper we solve a problem raised by Gutiérrez and Montanari about comparison principles for H−convex functions on subdomains of Heisenberg groups. Our approach is based on the notion of the sub-Riemannian horizontal normal mapping and uses degree theory for set-valued maps. The statement of the comparison principle combined with a Harnack inequality is applied to prove the Aleksandrov-type maximum principle, describing the correct boundary behavior of continuous H−convex functions vanishing at the boundary of horizontally bounded subdomains of Heisenberg groups. This result answers a question by Garofalo and Tournier. The sharpness of our results are illustrated by examples.

Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is l ∞(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel–Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system’s data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of Cánovas et al. (SIAM J. Optim. 20, 1504–1526, 2009) developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system’s coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case.

On the stability of the Motzkin representation of closed convex sets

A set is called Motzkin decomposable when it can be expressed as the Minkowski sum of a compact convex set with a closed convex cone. This paper analyzes the continuity properties of the set-valued mapping associating to each couple (C,D) formed by a compact convex set C and a closed convex cone D its Minkowski sum C + D. The continuity properties of other related mappings are also analyzed.

Mapping of indoor environments by robots using low-cost vision sensors

For robots to operate in human environments they must be able to make their own maps because it is unrealistic to expect a user to enter a map into the robot’s memory; existing floorplans are often incorrect; and human environments tend to change. Traditionally robots have used sonar, infra-red or laser range finders to perform the mapping task. Digital cameras have become very cheap in recent years and they have opened up new possibilities as a sensor for robot perception. Any robot that must interact with humans can reasonably be expected to have a camera for tasks such as face recognition, so it makes sense to also use the camera for navigation. Cameras have advantages over other sensors such as colour information (not available with any other sensor), better immunity to noise (compared to sonar), and not being restricted to operating in a plane (like laser range finders). However, there are disadvantages too, with the principal one being the effect of perspective. This research investigated ways to use a single colour camera as a range sensor to guide an autonomous robot and allow it to build a map of its environment, a process referred to as Simultaneous Localization and Mapping (SLAM). An experimental system was built using a robot controlled via a wireless network connection. Using the on-board camera as the only sensor, the robot successfully explored and mapped indoor office environments. The quality of the resulting maps is comparable to those that have been reported in the literature for sonar or infra-red sensors. Although the maps are not as accurate as ones created with a laser range finder, the solution using a camera is significantly cheaper and is more appropriate for toys and early domestic robots.

A new educational technology for media and communication studies : mapping media in Australia and Sweden

This chapter reports on Australian and Swedish experiences in the iterative design, development, and ongoing use of interactive educational systems we call ‘Media Maps.’ Like maps in general, Media Maps are usefully understood as complex cultural technologies; that is, they are not only physical objects, tools and artefacts, but also information creation and distribution technologies, the use and development of which are embedded in systems of knowledge and social meaning. Drawing upon Australian and Swedish experiences with one Media Map technology, this paper illustrates this three-layered approach to the development of media mapping. It shows how media mapping is being used to create authentic learning experiences for students preparing for work in the rapidly evolving media and communication industries. We also contextualise media mapping as a response to various challenges for curriculum and learning design in Media and Communication Studies that arise from shifts in tertiary education policy in a global knowledge economy.

Mapping the regulatory environment : implications for construction firms

As regulators, governments are often criticised for over‐regulating industries. This research project seeks to examine the regulation affecting the construction industry in a federal system of government. It uses a case study of the Australian system of government to focus on the question of the implications of regulation in the construction industry. Having established the extent of the regulatory environment, the research project considers the costs associated with this environment. Consequently, ways in which the regulatory burden on industry can be reduced are evaluated. The Construction Industry Business Environment project is working with industry and government agencies to improve regulatory harmonisation in Australia, and thereby reduce the regulatory burden on industry. It is found that while taxation and compliance costs are not likely to be reduced in the short term, costs arising from having to adapt to variation between regulatory regimes in a federal system of government, seem the most promising way of reducing regulatory costs. Identifying and reducing adaptive costs across jurisdictional are argued to present a novel approach to regulatory reform.

Curriculum mapping of the Spatial Science Program, QUT : what was the cartography journey?

There are currently a number of issues of great importance affecting universities and the way in which their programs are now offered. Many issues are largely being driven top-down and impact both at a university-wide and at an individual discipline level. This paper provides a brief history of cartography and digital mapping education at the Queensland University of Technology (QUT). It also provides an overview of what is curriculum mapping and presents some interesting findings from the program review process. Further, this review process has triggered discussion and action for the review, mapping and embedding of graduate attributes within the spatial science major program. Some form of practical based learning is expected in vocationally oriented degrees that lead to professional accreditation and are generally regarded as a good learning exposure. With the restructure of academic programs across the Faculty of Built Environment and Engineering in 2006, spatial science and surveying students now undertake a formal work integrated learning unit. There is little doubt that students acquire the skills of their discipline (mapping science, spatial) by being immersed in the industry culture- learning how to process information and solve real-world problems within context. The broad theme of where geo-spatial mapping skills are embedded in this broad-based tertiary education course are examined with some focused discussion on the learning objectives, outcomes and examples of some student learning experiences

Mapping the Australian political blogosphere

Network crawling and visualisation tools and other datamining systems are now advanced enough to provide significant new impulses to the study of cultural activity on the Web. A growing range of studies focus on communicative processes in the blogosphere – including for example Adamic & Glance’s 2005 map of political allegiances during the 2004 U.S. presidential election and Kelly & Etling’s 2008 study of blogging practices in Iran. There remain a number of significant shortcomings in the application of such tools and methodologies to the study of blogging; these relate both to how the content of blogs is analysed, and to how the network maps resulting from such studies are understood. Our project highlights and addresses such shortcomings.