Number Of Possible Trajectories Research Articles

Closed FRW holography: a time-dependent ER=EPR realization

Abstract We extend a recent de Sitter holographic proposal and entanglement entropy prescription to generic closed FRW cosmologies in arbitrary dimensions, and propose that for large classes of bouncing and Big Bang/Big Crunch cosmologies, the full spacetime can be encoded holographically on two holographic screens, associated to two antipodal observers. In the expanding phase, the two screens lie at the apparent horizons. In the contracting phase, there is an infinite number of possible trajectories of the holographic screens, which can be grouped in equivalence classes. In each class the effective holographic theory can be derived from a pair of “parent” screens on the apparent horizons. A number of cases including moduli dominated cosmologies escape our discussion, and it is expected that two antipodal observers and their associated screens do not suffice to reconstruct these cosmologies. The leading contributions to the entanglement entropy between the screens arise from a minimal extremal trapped or anti-trapped surface lying in the region between them. This picture entails a time-dependent realization of the ER=EPR conjecture, where an effective geometrical bridge connecting the screens via the minimal extremal surface emerges from entanglement. For the Big Crunch contracting cases, the screens disentangle and the geometrical bridge closes off when the minimal extremal trapped sphere hits the Big Crunch singularity at a finite time before the collapse of the Universe. Semiclassical, thermal corrections are incorporated in the cases of radiation dominated cosmologies.

A 2-D Trajectory Design Algorithm for Multiple Asteroid Flyby Missions

Asteroid mining is one of the most promising private space ventures of the near future. Near-Earth Asteroids (NEAs), i.e. those with perihelion at less than 1.3 AU from the Sun, are among the best candidates for such venture. In preparation of mining expeditions, it is likely that prospector missions will be carried out well in advance so to assess the accessibility, potential for revenues and possible critical issues of target asteroids. This work is concerned with the problem of the feasibility of a single spacecraft prospector mission capable of visiting as many NEAs as possible in one shot, focusing on Apollo-class asteroids only. The search of possible trajectories is done assuming a chemically propelled spacecraft with realistic specific impulse and propellant mass ratio, so to allow for a credible mission design with a reasonable, cost-effective total duration. In order to restrict the number of possible trajectories, only those that lie in the plane of the ecliptic are examined; such trajectories can be reached from the Earth without expensive plane change maneuvers. The search for a maximum number of encounters is thus restricted to those occurring where the asteroid orbit crosses the ecliptic. A deterministic building blocks approach is adopted, dividing the optimization problem in two parts: a local optimization for possible target determination; and a global optimization for the choice of the overall trajectory. It is found that the combined approach leads to the identification of viable trajectories, able to perform a number of encounters that depends on the launch epoch; as an example, in one test case two different sets of 21 NEA’s each were identified that could be reached with a single launch, with a slightly different propellant expenditure. It is concluded that the method is well suited to perform feasibility studies of NEA missions with good accuracy and moderate computational cost.

Multifidelity Design of Low-Thrust Resonant Captures for Near-Earth Asteroids

The design of a space trajectory is strongly linked to the gravitational and non-gravitational environment and the dynamical frameworks required to model it. These dynamical models may range from low to high fidelity, with corresponding computational costs. This paper proposes a multifidelity approach for the computation of nearly resonant trajectories with the Earth. This framework is used to compute trajectories for the capture of near-Earth asteroids into libration point orbits of the Sun–Earth system. The transfer is first computed in a suitable low-fidelity model, the Keplerian map, and a multifidelity approach is subsequently used to refine the solution from an impulsive approximation into a low-thrust transfer in the circular restricted three-body problem. The entire trajectory follows a nearly resonant motion with the Earth, lasting less than two synodic periods; starting when the retrieval spacecraft attaches itself to the asteroid, they will encounter the Earth twice, being captured into the target orbit at the end of the second encounter. A velocity change maneuver is carried out at the beginning of the motion, so that the first encounter with the Earth provides a gravitational perturbation resulting on a reduction of overall propellant costs of the transfer. The developed framework is very flexible in terms of the desired accuracy and allows for the low computational cost exploration of a vast number of possible trajectories. The obtained low-thrust transfers yield, for six asteroids, a much higher retrievable mass in comparison with direct capture trajectories, which do not undertake Earth-resonant encounters.

Monte Carlo tree search -based non-coplanar trajectory design for station parameter optimized radiation therapy (SPORT)

An important yet challenging problem in LINAC-based rotational arc radiation therapy is the design of beam trajectory, which requires simultaneous consideration of delivery efficiency and final dose distribution. In this work, we propose a novel trajectory selection strategy by developing a Monte Carlo tree search (MCTS) algorithm during the beam trajectory selection process.To search through the vast number of possible trajectories, the MCTS algorithm was implemented. In this approach, a candidate trajectory is explored by starting from a leaf node and sequentially examining the next level of linked nodes with consideration of geometric and physical constraints. The maximum Upper Confidence Bounds for Trees, which is a function of average objective function value and the number of times the node under testing has been visited, was employed to intelligently select the trajectory. For each candidate trajectory, we run an inverse fluence map optimization with an infinity norm regularization. The ranking of the plan as measured by the corresponding objective function value was then fed back to update the statistics of the nodes on the trajectory. The method was evaluated with a chest wall and a brain case, and the results were compared with the coplanar and noncoplanar 4pi beam configurations.For both clinical cases, the MCTS method found effective and easy-to-deliver trajectories within an hour. As compared with the coplanar plans, it offers much better sparing of the OARs while maintaining the PTV coverage. The quality of the MCTS-generated plan is found to be comparable to the 4pi plans.Artificial intelligence based on MCTS is valuable to facilitate the design of beam trajectory and paves the way for future clinical use of non-coplanar treatment delivery.

Computationally Efficient Trajectory Generation for Fully Actuated Multirotor Vehicles

This paper presents a computationally efficient method of generating state-to-state trajectories for fully actuated multirotor vehicles. The approach consists of computing translational and rotational motion primitives that guide the vehicle from any initial state, defined by position, velocity, and attitude, to any end state in a given time, and subsequently verifying the motion primitives’ feasibility. Computationally lightweight motion primitives for which closed-form solutions exist are presented and an efficient method to test their feasibility is derived. The algorithm is shown to be able to generate trajectories and verify their feasibility within a few microseconds and can thus be used as an implicit feedback law or in high-level path planners that involve evaluating a large number of possible trajectories to achieve some high-level goal. The algorithm's performance is analyzed by comparing it with time-optimal trajectories. An experimental demonstration that requires the computation of trajectories for a large set of end states in real time is used to evaluate the approach.

Multiple‐model multiple‐hypothesis filter with Gaussian mixture reduction

SummaryWe address the problem of state estimation for Markov jump nonlinear systems and present a modified version of the multiple‐model and multiple‐hypothesis (M3H) algorithm to suboptimally solve it. In such systems, the exact filter must track an exponentially increasing number of possible trajectories. Therefore, practical solutions must approximate the exact filter trading off filter precision for computational speed. In this contribution, we employ Gaussian mixture reduction methods in the merging of hypotheses of the original M3H. Thus, information from both the analog and digital states is used to merge the hypotheses, whereas only information from the digital state is employed in the original method. In our numerical results, we show that the proposed method outperforms the original M3H when increased precision constraints are imposed to the filter.

Stability optimization in robotic milling through the control of functional redundancies

Abstract Productivity in robotic machining processes can be limited by the low rigidity of the overall structure and vibration instability (chatter). The robot's dynamic behavior, due to changes in its posture along a machining trajectory, varies within its workspace. Chatter in robotic machining therefore depends not only on the cutting parameters but also on the robot configuration. Moreover, the robot can follow a machining trajectory in the operational space with an infinite number of possible trajectories in its configuration space. It is due to the redundancies offered by its kinematic chain. This paper deals with the optimization of robotic machining stability by controlling the robot configurations and the functional redundancies of its kinematic chain. It is shown that stability in robotic machining along a given trajectory can be ensured through the optimization of the robot configurations, without changing the cutting parameters, in order to maintain productivity performance. A multi-body dynamic model of an ABB IRB6660 industrial robot is elaborated using beam elements which can easily be integrated into the machining trajectory planning. The beam element geometry, elasticity and damping parameters are adjusted on the basis of experimental modal identifications. The present study is focused on the dynamic model-based predictions of stable and unstable zones along a robotic machining trajectory with one degree of functional redundancy. Experimental machining tests confirm the stability predictions from the numerical model.

Trajectory Optimization for VMAT Treatment Aided by Artificial Intelligence

Artificial Intelligence (AI) recently beat the top GO players. With the help of AI, here we tried to tackle one of the most difficult optimization problems in radiation oncology: designing an efficient trajectory to deliver an isocentric VMAT treatment with an optimum dose distribution on a C-arm machine, where the gantry and couch move in coordination. The state of art trajectory optimization still requires human expert to design heuristic algorithms such as those based on BEV or BEVD. We discretize the 4pi space into 2701 nodes, where the gantry and couch rotations are separated by 5 degrees. To search through the vast number of possible trajectories, we implemented Monte Carlo Tree Search (MCTS), the same method used by the AI which mastered the game of GO. Each simulated trajectory picks the nodes one by one. The next selected node would firstly need to be physically reachable, constrained by the rotation speed of the gantry and couch, as well as collision. Secondly it would have the maximum Upper Confidence Bounds for Trees (UCT), which is a function of average objective function value, the number of time this node has been selected and the total number of simulations. After forming a full trajectory, we run an inverse fluence map optimization with an infinity norm regularization term and the alternating direction method of multipliers (ADMM), using all the nodes on the trajectory. The obtained objective function value is then fed back to update the statistic of the nodes on the trajectory. The infinity norm regularization forces a solution with uniform fluence maps, close to that of VMAT treatment. The MCTS continues until the solution does not improve anymore or a predetermined time is reached. We tested the MCTS method with two challenging patient cases, one chest wall, and one skull and compared the dosimetry with coplanar plans. Without loss of generality, we confine the couch rotate uniformly from -90° to 90° with a speed of 0.5 degree/second and put no constraint on the gantry movement. The dose calculations are performed on the fly with the aid of GPU. For both patient cases, the AI with MCTS found optimum trajectories within an hour after ∼360 simulations with superior dosimetric qualities for OARs and same PTV coverages compared with coplanar plans. For the skull case, the brain V30, V20, and V10 are reduced by 21%, 38%, and 27%, respectively. The mean dose of the temporal lobe is decreased by 10%. For the chest wall case, the heart mean dose is reduced from 15 Gy to 7 Gy and V30 from 7.5% to 1.7%. The left and right lung mean dose decreased from 16 Gy and 8 Gy to 11 Gy and 3 Gy. The left and right lungs V20 are reduced from 27% and 4.4% to 15% and 0.9%. The estimated delivery time is ∼ 6 min. AI with MCTS successfully designed trajectories that are efficient to deliver and dosimetric superior compared with coplanar VMAT. The method can also be easily generalized to include non-isocentric treatments.

Optimality of Upper-Arm Reaching Trajectories Based on the Expected Value of the Metabolic Energy Cost.

When we move our body to perform a movement task, our central nervous system selects a movement trajectory from an infinite number of possible trajectories under constraints that have been acquired through evolution and learning. Minimization of the energy cost has been suggested as a potential candidate for a constraint determining locomotor parameters, such as stride frequency and stride length; however, other constraints have been proposed for a human upper-arm reaching task. In this study, we examined whether the minimum metabolic energy cost model can also explain the characteristics of the upper-arm reaching trajectories. Our results show that the optimal trajectory that minimizes the expected value of energy cost under the effect of signal-dependent noise on motor commands expresses not only the characteristics of reaching movements of typical speed but also those of slower movements. These results suggest that minimization of the energy cost would be a basic constraint not only in locomotion but also in upper-arm reaching.

Finite-Time Mass Separation for Comparative Visualizations of Inertial Particles

The visual analysis of flows with inertial particle trajectories is a challenging problem because time-dependent particle trajectories additionally depend on mass, which gives rise to an infinite number of possible trajectories passing through every point in space-time. This paper presents an approach to a comparative visualization of the inertial particles’ separation behavior. For this, we define the Finite-Time Mass Separation (FTMS), a scalar field that measures at each point in the domain how quickly inertial particles separate that were released from the same location but with slightly different mass. Extracting and visualizing the mass that induces the largest separation provides a simplified view on the critical masses. By using complementary coordinated views, we additionally visualize corresponding inertial particle trajectories in space-time by integral curves and surfaces. For a quantitative analysis, we plot Euclidean and arc length-based distances to a reference particle over time, which allows to observe the temporal evolution of separation events. We demonstrate our approach on a number of analytic and one real-world unsteady 2D field.

Watersheds on weighted graphs

The watershed is an efficient and versatile segmentation tool, as it partitions the images into disjoint catchment basins. We study the watershed on node or edge weighted graphs. We do not aim at constructing a partition of the nodes but consider the catchment zones, i.e., the attraction zones of a drop of water. Often, such zones largely overlap. In a first part, we show how to derive from a node or edge weighted graph a flooding graph with the same trajectories of a drop of water, whether one considers its node weights alone or its edge weights alone. In a second part we show how to reduce the number of possible trajectories of a drop of water in order to generate watershed partitions.

Validation of a stochastic temperature generator focusing on extremes, and an example of use for climate change

CR Climate Research Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsSpecials CR 59:61-75 (2014) - DOI: https://doi.org/10.3354/cr01201 Validation of a stochastic temperature generator focusing on extremes, and an example of use for climate change S. Parey1,*, T. T. H. Hoang1, D. Dacunha-Castelle2 1EDF/R&D, 6 quai Watier, 78 401 Chatou Cedex, France 2Laboratoire de Mathématiques, Université Paris 11, Orsay, France *Corresponding author: sylvie.parey@edf.fr ABSTRACT: We present a stochastic seasonal functional heteroscedastic auto-regressive model developed to simulate daily (minimum, maximum, or mean) temperature time series coherent with observed time series and designed to reliably reproduce extreme values through a careful study of extremes and the fact that the tails of the distribution are bounded. The model was first validated using different daily minimum and maximum weather station time series over Eurasia and the US in different climatic regions. The model was able to produce coherent results both for the bulk of the distribution and for its extremes and was able to produce higher or lower extreme values than observed. A possible use in the climate change context was then tested. We fit the model over the first part of a long temperature time series and then used it to simulate a large number of possible trajectories for the second part when temperature increased. Two approaches were tested to do so, one based on a simple mean change in mean and variance and the other in considering the full seasonalities and trends estimated over the observed second part of the time series. Both approaches yielded good results, both for the bulk and for the extremes of the temperature distribution over the second part of the period. However, the second approach allowed us to take interannual variability changes into account, which leads to more realistic results when this occurs. Our results support the use of this tool for statistical downscaling, enabling the reliable reproduction of temperature extremes. KEY WORDS: Daily temperature · Stochastic modeling · Extremes Full text in pdf format PreviousNextCite this article as: Parey S, Hoang TTH, Dacunha-Castelle D (2014) Validation of a stochastic temperature generator focusing on extremes, and an example of use for climate change. Clim Res 59:61-75. https://doi.org/10.3354/cr01201 Export citation RSS - Facebook - Tweet - linkedIn Cited by Published in CR Vol. 59, No. 1. Online publication date: February 04, 2014 Print ISSN: 0936-577X; Online ISSN: 1616-1572 Copyright © 2014 Inter-Research.

Collaborative electronic infrastructures to accelerate taxonomic research

The discipline of taxonomy lives in a state of perpetual beta, constantly evolving as species hypotheses change to reflect the latest character evidence. Likewise, the electronic infrastructures that underpin taxonomic research are evolving to reflect the latest technical advances. This collection of articles illustrates how advances to research infrastructures are reciprocally changing the practice of taxonomy. The infrastructures have, in part, been developed through the EU funded ViBRANT project. This is the latest in a series of EU funded initiatives that aim to move taxonomy towards a more collaborative, electronic framework in an effort to accelerate the pace of biodiversity research. Through a platform of web-based informatics tools and services, ViBRANT project partners are building a framework that allows distributed groups of scientists to create their own virtual research communities that support biodiversity science. To mark the first year of the ViBRANT project we have brought together a set of reviews, essays and research articles that reflect some of the project highlights and illustrate a number of associated activities. Fittingly, many of the contributions are from researchers who have no direct support from the ViBRANT project, but have used or reviewed some aspect of the infrastructure. This marks an important transition from many EU funded infrastructure projects have typically focused on technical developments, and less on the communities that use these systems. A detailed review of data issues in the life sciences (Thessen and Patterson 2011) sets the tone for subsequent articles in this special issue, whose contributions broadly fall into three categories. The initial articles consider some of the major infrastructure platforms that support the production and management of biodiversity data. These include the EDIT Platform for Cybertaxonomy, Wiki-based approaches including BioWikiFarm and the Scratchpads Virtual Research Environment. Later articles provide deeper coverage of specialist areas of interest to taxonomic and biodiversity researchers. The topics covered include the mark-up (Penev et al. 2011) and management (King et al. 2011) of taxonomic literature, geospatial assessment of species distributions (Bachman et al. 2011) and licensing issues specific to life science data (Hagedorn et al. 2011). Finally, the special issue closes with a series of research and review papers that provide detailed use cases illustrating how these research infrastructures are being put into practice. These articles make up the majority of this special issue and are subdivided into the sociological analysis of how people are using these infrastructures, as well as the practical experience of biodiversity researchers developing taxonomic data with these systems. Highlights from this section include citizen science approaches to collecting species information by the COMBER Marine observation network (Arvanitidis et al. 2011) and the Australian Bush Blitz programme (Lambkin and Bartlett 2011); use of new tools for data publishing like the Global Biodiversity Information Facility (GBIF) Integrated Publishing Toolkit (IPT) and the DRYAD Data Repository; new forms of publication via “data papers” that allow checklists and identification keys to be formally published as structured datasets (e.g., Narwade et al. 2011); and finally new taxonomic revisions and species descriptions constructed from within the collaborative systems like XPER2 and Scratchpads. This diverse collection of articles illustrates how the paradigm of scholarly communication in taxonomy is being changed by new electronic infrastructures. These support new ways to collaborate and disseminate taxonomic information, facilitating greater reuse of the underlying data. The infrastructures described here are in many cases experimental, but illustrate a number of possible trajectories for how taxonomic data might be assembled and disseminated in the future. These infrastructures will continue to change and evolve, but it now seems certain that the future of taxonomy is increasingly digital, to the point that non-digital work is becoming invisible and perhaps irreverent to the next generation of scholars.

Christianity Encountering World Religions: The Practice of Mission in the Twenty-First Century (review)

Reviewed by: Christianity Encountering World Religions: The Practice of Mission in the Twenty-First Century Gavin D'Costa Christianity Encountering World Religions: The Practice of Mission in the Twenty-First Century. By Terry Muck and Frances S. Adeney. Grand Rapids, MI: Baker Academic, 2009. 448 pp. In an age when dialogue is emphasized in the meeting of religions, this book presents a refreshing and interesting alternative approach. Muck and Adeney, both professors of evangelism in the United States, argue that Christians have no alternative to the practice of mission in the twenty-first century. They argue that central to Christian revelation is the unmerited gift that Christians have received in Christ, and this theme of gift drives their argument, inelegantly named "giftive mission." The argument runs something like this. First, they develop their approach from the Bible, fully recognizing that there are a number of possible trajectories out of the Bible on this issue. One massively helpful feature of this book is an appendix of 239 biblical references dealing with Israel's and the Church's encounters with the "Other." Their theological presuppositions are that the biblical message about the redemptive triune God is "true" and that other religions teach many truths, but not about who God is; that the salvation of the non-Christian is ambiguous and should not be conflated with the question of truth; that Christians must fully cooperate with non-Christians; that both dialogue and evangelism are required from Christians; and that spiritual practices inculturated from other religions might be usefully employed, but only with great care. This amounts to a kind of open evangelical position: the world religions are finally human creations, with enormous wisdom and truth to be found, but, finally, Christianity is the only true disclosure of God's self revelation. So far, clear and predictable, given the stable out of which our writers come. But the originality of the book is yet to be unleashed. [End Page 235] The authors next lay out a strategy for mission, beyond competition and cooperation, emphasising the theme of mission as gift sharing. One might recall Aquinas, which they do not at this point of their argument, although they do later, who argued that the greatest gift we can give a friend is sharing that which we value most. For friendship requires that we desire the greatest good for the friend and this means that we would desire the truth of Jesus Christ for our friends. This does not displace an element of competition, if understood as the belief that we can partly argue for the truth and should always do so against rival claims. This does not displace cooperation either. Rather, it is to bring into focus an organizing principle, which is profoundly centered on the nature of revelation as gift. The best feature of this book now emerges as our authors carefully and sensitively tease out aspects of this gift through highlighting certain values as exemplified in the practice of great missionaries of the past. Each person takes up an entire chapter and each is finally contrasted with an antitype, which makes this an immensely helpful resource for students in terms of discussion and engaging stories. Furthermore, the authors provide discussion questions, summaries, and notes in sidebars, little gray boxes that break the text up. The heroes and heroines are Paul the Apostle (universal reaching out); Patrick, missionary to Ireland (fellowship, emphasising that belonging precedes believing); Cyril and Methodius (localization, through their serving the local needs of the Slavic church); Thomas Aquinas (commitment, holding ideas with conviction but not allowing ideas to be divisive); Bartolomé Las Casas (freedom, honoring the principle of religious choice); Matteo Ricci (effectiveness, allowing the context to determine the form of witness); William Carey (consistency, striving for consistency between methods and goals); Catherine Booth (founder of the Salvation Army—variety, communicating the gospel in many forms); Mother Teresa of Calcutta (charity, loving those to whom she witnessed); and Billy Graham (missional ecumenicity, practicing mission as a joint project of the church). Note the balance in denominational types and gender—which is a typical mark of the ecumenical orientation of our authors. Admittedly, they downplay in some of their characters the...

Une loi limite pour les marches aléatoires avec des applications physiques

We consider a standard random walk on Z , starting from the origin. We build a law of probability on Z , based upon the evaluation, for each N ⩾ 0 and k ∈ Z , of the squared number of possible trajectories, reaching level k after N or less transitions. We normalize this squared number by its sum, with respect to k, to obtain a probability law, depending upon N. Our main result establishes that this probability law converges to a normal distribution as N → ∞ . Our construction is inspired and motivated by the basic model used for the interpretation of quantum mechanics. To cite this article: R. Charreton, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

The formation of trajectories during goal‐oriented locomotion in humans. II. A maximum smoothness model

Despite the theoretically infinite number of possible trajectories a human may take to reach a distant doorway, we observed that locomotor trajectories corresponding to this task were actually stereotyped, both at the geometric and the kinematic levels. In this paper, we propose a computational model for the formation of human locomotor trajectories. Our model is adapted from smoothness maximization models that have been studied in the context of hand trajectory generation. The trajectories predicted by our model are very similar to the experimentally recorded ones. We discuss the theoretical implications of this result in the context of movement planning and control in humans. In particular, this result supports the hypothesis that common principles, such as smoothness maximization, may govern the generation of very different types of movements (in this case, hand movements and whole-body movements).

The effect of distance on reaction time in aiming movements

Target distance affects movement duration in aiming tasks but its effect on reaction time (RT) is poorly documented. RT is a function of both preparation and initiation. Experiment 1 pre-cued movement (allowing advanced preparation) and found no influence of distance on RT. Thus, target distance does not affect initiation time. Experiment 2 removed pre-cue information and found that preparing a movement of increased distance lengthens RT. Experiment 3 explored movements to targets of cued size at non-cued distances and found size altered peak speed and movement duration but RT was influenced by distance alone. Thus, amplitude influences preparation time (for reasons other than altered duration) but not initiation time. We hypothesise that the RT distance effect might be due to the increased number of possible trajectories associated with further targets: a hypothesis that can be tested in future experiments.

Simulation-based sequential Bayesian design

We consider simulation-based methods for exploration and maximization of expected utility in sequential decision problems. We consider problems which require backward induction with analytically intractable expected utility integrals at each stage. We propose to use forward simulation to approximate the integral expressions, and a reduction of the allowable action space to avoid problems related to an increasing number of possible trajectories in the backward induction. The artificially reduced action space allows strategies to depend on the full history of earlier observations and decisions only indirectly through a low dimensional summary statistic. The proposed rule provides a finite-dimensional approximation to the unrestricted infinite-dimensional optimal decision rule. We illustrate the proposed approach with an application to an optimal stopping problem in a clinical trial.

A direction dependent least-cost-path algorithm for roads and canals

In planning routes for roads and canals, topography is often a significant constraint. Among the infinite number of possible trajectories between two points, the selected path should be a good approximation to the one with the least cost, and should avoid extremes of slopes. In the case of a canal, the number of uphill reaches of the trajectory should be minimised. This paper presents a least-cost-path algorithm developed to find the best path given the topography, the start and end-points of the linear feature (canal or road) and a function relating slope, distance and cost. The algorithm is based on dynamic programming techniques adapted to solve problems on the grid, or raster structure usually used in Geographical Information Systems. The algorithm was programmed and used to solve hypothetical problems. Although real cost functions were not used, the results were coherent and showed the algorithm's capabilities.

Property Ownership, Tenure, and Displacement: In Search of the Process of Gentrification

Despite three decades of continuous research on gentrification, there are a number of areas where understanding of this process still remains quite rudimentary, especially with respect to the actual process of gentrification itself. The author seeks to focus attention upon this issue by examining how historic change to property ownership and tenure structure of housing induced by gentrification impacted upon the unfolding of this process in the inner Sydney suburb of Glebe from 1960 to 1986. By using an empirical analysis he reveals that a synchronisation existed between the market behaviour of small-scale property owners, working-class incumbent upgraders, and middle-class homebuyers and renters which had a significant bearing upon both the timing and the extent of gentrification activity in the case study. In addition, once a less orthodox method of measurement was employed, social replacement was found to operate alongside social displacement. The implications of these findings suggest that the process of gentrification is much more complex than has been previously inferred in the empirical literature and that this particular form of neighbourhood change can follow a number of possible trajectories, as has been more recently asserted in cross-cultural research.