Voronoi cells via linear inequality systems

The theory and methods of linear algebra are a useful alternative to those of convex geometry in the framework of Voronoi cells and diagrams, which constitute basic tools of computational geometry. As shown by Voigt and Weis in 2010, the Voronoi cells of a given set of sites T, which provide a tesselation of the space called Voronoi diagram when T is finite, are solution sets of linear inequality systems indexed by T. This paper exploits systematically this fact in order to obtain geometrical information on Voronoi cells from sets associated with T (convex and conical hulls, tangent cones and the characteristic cones of their linear representations). The particular cases of T being a curve, a closed convex set and a discrete set are analyzed in detail. We also include conclusions on Voronoi diagrams of arbitrary sets.

A semi-analytical particle filter for identification of nonlinear oscillators

Particle filters find important applications in the problems of state and parameter estimations of dynamical systems of engineering interest. Since a typical filtering algorithm involves Monte Carlo simulations of the process equations, sample variance of the estimator is inversely proportional to the number of particles. The sample variance may be reduced if one uses a Rao-Blackwell marginalization of states and performs analytical computations as much as possible. In this work, we propose a semi-analytical particle filter, requiring no Rao-Blackwell marginalization, for state and parameter estimations of nonlinear dynamical systems with additively Gaussian process/observation noises. Through local linearizations of the nonlinear drift fields in the process/observation equations via explicit Ito-Taylor expansions, the given nonlinear system is transformed into an ensemble of locally linearized systems. Using the most recent observation, conditionally Gaussian posterior density functions of the linearized systems are analytically obtained through the Kalman filter. This information is further exploited within the particle filter algorithm for obtaining samples from the optimal posterior density of the states. The potential of the method in state/parameter estimations is demonstrated through numerical illustrations for a few nonlinear oscillators. The proposed filter is found to yield estimates with reduced sample variance and improved accuracy vis-a-vis results from a form of sequential importance sampling filter.

Chaotic synchronization in 2D lattice for scene segmentation

Synchronization and chaos play important roles in neural activities and have been applied in oscillatory correlation modeling for scene and data analysis. Although it is an extensively studied topic, there are still few results regarding synchrony in locally coupled systems. In this paper we give a rigorous proof to show that large numbers of coupled chaotic oscillators with parameter mismatch in a 2D lattice can be synchronized by providing a sufficiently large coupling strength. We demonstrate how the obtained result can be applied to construct an oscillatory network for scene segmentation. (C) 2007 Elsevier B.V. All rights reserved.

Turning conflict into coexistence: cross-cutting ties and institutions in the agro-pastoral borderlands of Lake Naivasha basin, Kenya

The Maasai/Kikuyu agro-pastoral borderlands of Maiella and Enoosupukia, located in the hinterlands of Lake Naivasha’s agro-industrial hub, are particularly notorious in the history of ethnicised violence in the Kenya’s Rift Valley. In October 1993, an organised assault perpetrated by hundreds of Maasai vigilantes, with the assistance of game wardens and administration police, killed more than 20 farmers of Kikuyu descent. Consequently, thousands of migrant farmers were violently evicted from Enoosupukia at the instigation of leading local politicians. Nowadays, however, intercommunity relations are surprisingly peaceful and the cooperative use of natural resources is the rule rather than the exception. There seems to be a form of reorganization. Violence seems to be contained and the local economy has since recovered. This does not mean that there is no conflict, but people seem to have the facility to solve them peacefully. How did formerly violent conflicts develop into peaceful relations? How did competition turn into cooperation, facilitating changing land use? This dissertation explores the value of cross-cutting ties and local institutions in peaceful relationships and the non-violent resolution of conflicts across previously violently contested community boundaries. It mainly relies on ethnographic data collected between 2014 and 2015. The discussion therefore builds on several theoretical approaches in anthropology and the social sciences – that is, violent conflicts, cross-cutting ties and conflicting loyalties, joking relationships, peace and nonviolence, and institutions, in order to understand shared spaces that are experiencing fairly rapid social and economic changes, and characterised by conflict and coexistence. In the researched communities, cross-cutting ties and the split allegiances associated with them result from intermarriages, land transactions, trade, and friendship. By institutions, I refer to local peace committees, an attempt to standardise an aspect of customary law, and Nyumba Kumi, a strategy of anchoring community policing at the household level. In 2010, the state “implanted” these grassroots-level institutions and conferred on them the rights to handle specific conflicts and to prevent crime. I argue that the studied groups utilise diverse networks of relationships as adaptive responses to landlessness, poverty, and socio-political dynamics at the local level. Material and non-material exchanges and transfers accompany these social and economic ties and networks. In addition to being instrumental in nurturing a cohesive social fabric, I argue that such alliances could be thought of as strategies of appropriation of resources in the frontiers – areas that are considered to have immense agricultural potential and to be conducive to economic enterprise. Consequently, these areas are continuously changed and shaped through immigration, population growth, and agricultural intensification. However, cross-cutting ties and intergroup alliances may not necessarily prevent the occurrence or escalation of conflicts. Nevertheless, disputes and conflicts, which form part of the social order in the studied area, create the opportunities for locally contextualised systems of peace and non-violence that inculcate the values of cooperation, coexistence, and restraint from violence. Although the neo-traditional institutions (local peace committees and Nyumba Kumi) face massive complexities and lack the capacity to handle serious conflicts, their application of informal constraints in dispute resolution provides room for some optimism. Notably, the formation of ties and alliances between the studied groups, and the use of local norms and values to resolve disputes, are not new phenomena – they are reminiscent of historical patterns. Their persistence, particularly in the context of Kenya, indicates a form of historical continuity, which remains rather “undisturbed” despite the prevalence of ethnicised political economies. Indeed, the formation of alliances, which are driven by mutual pursuit of commodities (livestock, rental land, and agricultural produce), markets, and diversification, tends to override other identities. While the major thrust of social science literature in East Africa has focused on the search for root causes of violence, very little has been said about the conditions and practices of cooperation and non-violent conflict resolution. In addition, situations where prior violence turned into peaceful interaction have attracted little attention, though the analysis of such transitional phases holds the promise of contributing to applicable knowledge on conflict resolution. This study is part of a larger multidisciplinary project, “Resilience in East African Landscapes” (REAL), which is a Marie Curie Actions Innovative Training Networks (ITN) project. The principal focus of this multidisciplinary project is to study past, present, and future thresholds and sustainable trajectories in human-landscape interactions in East Africa over the last millennia. While other individual projects focus on long-term ecosystem dynamics and societal interactions, my project examines human-landscape interactions in the present and the very recent past (i.e. the period in which events and processes were witnessed or can still be recalled by today’s population). The transition from conflict to coexistence and from competition to cooperative use of previously violently contested land resources is understood here as enhancing adaptation in the face of social-political, economic, environmental, and climatic changes. This dissertation is therefore a contribution to new modes of resilience in human-landscape interactions after a collapse situation.

Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces

According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.

Using locally available components and local knowledge to build sustainable stand-alone power systems

The aim of this paper is to point out benefits as well as disadvantages associated with the use of locally available, not necessarily standardized, components in stand-alone electrical power systems at rural locations. Advantages and challenges arising when the direct involvement in design, construction and maintenance of the power system is reserved to people based in the area of implementation are discussed. The presented research is centered around one particular PV-diesel hybrid system in Tanzania; a case study in which technical and social aspects related to the particular power system are studied.

A point interpolation method with locally smoothed strain field (PIM-LS2) for mechanics problems using triangular mesh

A point interpolation method with locally smoothed strain field (PIM-LS2) is developed for mechanics problems using a triangular background mesh. In the PIM-LS2, the strain within each sub-cell of a nodal domain is assumed to be the average strain over the adjacent sub-cells of the neighboring element sharing the same field node. We prove theoretically that the energy norm of the smoothed strain field in PIM-LS2 is equivalent to that of the compatible strain field, and then prove that the solution of the PIM- LS2 converges to the exact solution of the original strong form. Furthermore, the softening effects of PIM-LS2 to system and the effects of the number of sub-cells that participated in the smoothing operation on the convergence of PIM-LS2 are investigated. Intensive numerical studies verify the convergence, softening effects and bound properties of the PIM-LS2, and show that the very ‘‘tight’’ lower and upper bound solutions can be obtained using PIM-LS2.

Vision based control for fixed wing UAVs inspecting locally linear infrastructure using skid-to-turn maneuvers

The following paper proposes a novel application of Skid-to-Turn maneuvers for fixed wing Unmanned Aerial Vehicles (UAVs) inspecting locally linear infrastructure. Fixed wing UAVs, following the design of manned aircraft, commonly employ Bank-to-Turn ma- neuvers to change heading and thus direction of travel. Whilst effective, banking an aircraft during the inspection of ground based features hinders data collection, with body fixed sen- sors angled away from the direction of turn and a panning motion induced through roll rate that can reduce data quality. By adopting Skid-to-Turn maneuvers, the aircraft can change heading whilst maintaining wings level flight, thus allowing body fixed sensors to main- tain a downward facing orientation. An Image-Based Visual Servo controller is developed to directly control the position of features as captured by onboard inspection sensors. This improves on the indirect approach taken by other tracking controllers where a course over ground directly above the feature is assumed to capture it centered in the field of view. Performance of the proposed controller is compared against that of a Bank-to-Turn tracking controller driven by GPS derived cross track error in a simulation environment developed to replicate the field of view of a body fixed camera.

Geographical information systems : an effective planning and decision-making platform for community health coalitions in Australia

The development of locally-based healthcare initiatives, such as community health coalitions that focus on capacity building programs and multi-faceted responses to long-term health problems, have become an increasingly important part of the public health landscape. As a result of their complexity and the level of investment, it has become necessary to develop innovative ways to help manage these new healthcare approaches. Geographical Information Systems (GIS) have been suggested as one of the innovative approaches that will allow community health coalitions to better manage and plan their activities. The focus of this paper is to provide a commentary on the use of GIS as a tool for community coalitions and discuss some of the potential benefits and issues surrounding the development of these tools.

Adding a receding horizon to Locally Weighted Regression for learning robot control

There have been notable advances in learning to control complex robotic systems using methods such as Locally Weighted Regression (LWR). In this paper we explore some potential limits of LWR for robotic applications, particularly investigating its application to systems with a long horizon of temporal dependence. We define the horizon of temporal dependence as the delay from a control input to a desired change in output. LWR alone cannot be used in a temporally dependent system to find meaningful control values from only the current state variables and output, as the relationship between the input and the current state is under-constrained. By introducing a receding horizon of the future output states of the system, we show that sufficient constraint is applied to learn good solutions through LWR. The new method, Receding Horizon Locally Weighted Regression (RH-LWR), is demonstrated through one-shot learning on a real Series Elastic Actuator controlling a pendulum.

Vision based control for fixed wing UAVs inspecting locally linear infrastructure using skid-to-turn maneuvers

The following paper proposes a novel application of Skid-to-Turn maneuvers for fixed wing Unmanned Aerial Vehicles (UAVs) inspecting locally linear infrastructure. Fixed wing UAVs, following the design of manned aircraft, traditionally employ Bank-to-Turn maneuvers to change heading and thus direction of travel. Commonly overlooked is the effect these maneuvers have on downward facing body fixed sensors, which as a result of bank, point away from the feature during turns. By adopting Skid-to-Turn maneuvers, the aircraft is able change heading whilst maintaining wings level flight, thus allowing body fixed sensors to maintain a downward facing orientation. Eliminating roll also helps to improve data quality, as sensors are no longer subjected to the swinging motion induced as they pivot about an axis perpendicular to their line of sight. Traditional tracking controllers that apply an indirect approach of capturing ground based data by flying directly overhead can also see the feature off center due to steady state pitch and roll required to stay on course. An Image Based Visual Servo controller is developed to address this issue, allowing features to be directly tracked within the image plane. Performance of the proposed controller is tested against that of a Bank-to-Turn tracking controller driven by GPS derived cross track error in a simulation environment developed to simulate the field of view of a body fixed camera.

Learning multidimensional joint control of a robot using receding horizon locally weighted regression

In this paper we explore the ability of a recent model-based learning technique Receding Horizon Locally Weighted Regression (RH-LWR) useful for learning temporally dependent systems. In particular this paper investigates the application of RH-LWR to learn control of Multiple-input Multiple-output robot systems. RH-LWR is demonstrated through learning joint velocity and position control of a three Degree of Freedom (DoF) rigid body robot.

Locally weighted learning model predictivek control for elastic joint robots

This paper proposes an efficient and online learning control system that uses the successful Model Predictive Control (MPC) method in a model based locally weighted learning framework. The new approach named Locally Weighted Learning Model Predictive Control (LWL-MPC) has been proposed as a solution to learn to control complex and nonlinear Elastic Joint Robots (EJR). Elastic Joint Robots are generally difficult to learn to control due to their elastic properties preventing standard model learning techniques from being used, such as learning computed torque control. This paper demonstrates the capability of LWL-MPC to perform online and incremental learning while controlling the joint positions of a real three Degree of Freedom (DoF) EJR. An experiment on a real EJR is presented and LWL-MPC is shown to successfully learn to control the system to follow two different figure of eight trajectories.

Locally weighted learning model predictive control for nonlinear and time varying dynamics

This paper proposes an online learning control system that uses the strategy of Model Predictive Control (MPC) in a model based locally weighted learning framework. The new approach, named Locally Weighted Learning Model Predictive Control (LWL-MPC), is proposed as a solution to learn to control robotic systems with nonlinear and time varying dynamics. This paper demonstrates the capability of LWL-MPC to perform online learning while controlling the joint trajectories of a low cost, three degree of freedom elastic joint robot. The learning performance is investigated in both an initial learning phase, and when the system dynamics change due to a heavy object added to the tool point. The experiment on the real elastic joint robot is presented and LWL-MPC is shown to successfully learn to control the system with and without the object. The results highlight the capability of the learning control system to accommodate the lack of mechanical consistency and linearity in a low cost robot arm.

Can sustainable cotton production systems be developed for tropical northern Australia?

This article reviews research coordinated by the Australian Cotton Cooperative Research Centre (CRC) that investigated production issues for irrigated cotton at five targeted sites in tropical northern Australia, north of 21°S from Broome in Western Australia to the Burdekin in Queensland. The biotic and abiotic issues for cotton production were investigated with the aim of defining the potential limitations and, where appropriate, building a sustainable technical foundation for a future industry if it were to follow. Key lessons from the Cotton CRC research effort were: (1) limitations thought to be associated with cotton production in northern Australia can be overcome by developing a deep understanding of biotic and environmental constraints, then tailoring and validating production practices; and (2) transplanting of southern farming practices without consideration of local pest, soil and climatic factors is unlikely to succeed. Two grower guides were published which synthesised the research for new growers into a rational blueprint for sustainable cotton production in each region. In addition to crop production and environmental impact issues, the project identified the following as key elements needed to establish new cropping regions in tropical Australia: rigorous quantification of suitable land and sustainable water yields; support from governments; a long-term funding model for locally based research; the inclusion of traditional owners; and development of human capacity.