93 resultados para Topological Bifurcation
Resumo:
Ratites are large, flightless birds and include the ostrich, rheas, kiwi, emu, and cassowaries, along with extinct members, such as moa and elephant birds. Previous phylogenetic analyses of complete mitochondrial genome sequences have reinforced the traditional belief that ratites are monophyletic and tinamous are their sister group. However, in these studies ratite monophyly was enforced in the analyses that modeled rate heterogeneity among variable sites. Relaxing this topological constraint results in strong support for the tinamous (which fly) nesting within ratites. Furthermore, upon reducing base compositional bias and partitioning models of sequence evolution among protein codon positions and RNA structures, the tinamou–moa clade grouped with kiwi, emu, and cassowaries to the exclusion of the successively more divergent rheas and ostrich. These relationships are consistent with recent results from a large nuclear data set, whereas our strongly supported finding of a tinamou–moa grouping further resolves palaeognath phylogeny. We infer flight to have been lost among ratites multiple times in temporally close association with the Cretaceous–Tertiary extinction event. This circumvents requirements for transient microcontinents and island chains to explain discordance between ratite phylogeny and patterns of continental breakup. Ostriches may have dispersed to Africa from Eurasia, putting in question the status of ratites as an iconic Gondwanan relict taxon. [Base composition; flightless; Gondwana; mitochondrial genome; Palaeognathae; phylogeny; ratites.]
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Appearance-based localization can provide loop closure detection at vast scales regardless of accumulated metric error. However, the computation time and memory requirements of current appearance-based methods scale not only with the size of the environment but also with the operation time of the platform. Additionally, repeated visits to locations will develop multiple competing representations, which will reduce recall performance over time. These properties impose severe restrictions on long-term autonomy for mobile robots, as loop closure performance will inevitably degrade with increased operation time. In this paper we present a graphical extension to CAT-SLAM, a particle filter-based algorithm for appearance-based localization and mapping, to provide constant computation and memory requirements over time and minimal degradation of recall performance during repeated visits to locations. We demonstrate loop closure detection in a large urban environment with capped computation time and memory requirements and performance exceeding previous appearance-based methods by a factor of 2. We discuss the limitations of the algorithm with respect to environment size, appearance change over time and applications in topological planning and navigation for long-term robot operation.
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The paper presents a detailed analysis on the collective dynamics and delayed state feedback control of a three-dimensional delayed small-world network. The trivial equilibrium of the model is first investigated, showing that the uncontrolled model exhibits complicated unbounded behavior. Then three control strategies, namely a position feedback control, a velocity feedback control, and a hybrid control combined velocity with acceleration feedback, are then introduced to stabilize this unstable system. It is shown in these three control schemes that only the hybrid control can easily stabilize the 3-D network system. And with properly chosen delay and gain in the delayed feedback path, the hybrid controlled model may have stable equilibrium, or periodic solutions resulting from the Hopf bifurcation, or complex stranger attractor from the period-doubling bifurcation. Moreover, the direction of Hopf bifurcation and stability of the bifurcation periodic solutions are analyzed. The results are further extended to any "d" dimensional network. It shows that to stabilize a "d" dimensional delayed small-world network, at least a "d – 1" order completed differential feedback is needed. This work provides a constructive suggestion for the high dimensional delayed systems.
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In this article, we analyze the three-component reaction-diffusion system originally developed by Schenk et al. (PRL 78:3781–3784, 1997). The system consists of bistable activator-inhibitor equations with an additional inhibitor that diffuses more rapidly than the standard inhibitor (or recovery variable). It has been used by several authors as a prototype three-component system that generates rich pulse dynamics and interactions, and this richness is the main motivation for the analysis we present. We demonstrate the existence of stationary one-pulse and two-pulse solutions, and travelling one-pulse solutions, on the real line, and we determine the parameter regimes in which they exist. Also, for one-pulse solutions, we analyze various bifurcations, including the saddle-node bifurcation in which they are created, as well as the bifurcation from a stationary to a travelling pulse, which we show can be either subcritical or supercritical. For two-pulse solutions, we show that the third component is essential, since the reduced bistable two-component system does not support them. We also analyze the saddle-node bifurcation in which two-pulse solutions are created. The analytical method used to construct all of these pulse solutions is geometric singular perturbation theory, which allows us to show that these solutions lie in the transverse intersections of invariant manifolds in the phase space of the associated six-dimensional travelling wave system. Finally, as we illustrate with numerical simulations, these solutions form the backbone of the rich pulse dynamics this system exhibits, including pulse replication, pulse annihilation, breathing pulses, and pulse scattering, among others.
Resumo:
The challenge of persistent appearance-based navigation and mapping is to develop an autonomous robotic vision system that can simultaneously localize, map and navigate over the lifetime of the robot. However, the computation time and memory requirements of current appearance-based methods typically scale not only with the size of the environment but also with the operation time of the platform; also, repeated revisits to locations will develop multiple competing representations which reduce recall performance. In this paper we present a solution to the persistent localization, mapping and global path planning problem in the context of a delivery robot in an office environment over a one-week period. Using a graphical appearance-based SLAM algorithm, CAT-Graph, we demonstrate constant time and memory loop closure detection with minimal degradation during repeated revisits to locations, along with topological path planning that improves over time without using a global metric representation. We compare the localization performance of CAT-Graph to openFABMAP, an appearance-only SLAM algorithm, and the path planning performance to occupancy-grid based metric SLAM. We discuss the limitations of the algorithm with regard to environment change over time and illustrate how the topological graph representation can be coupled with local movement behaviors for persistent autonomous robot navigation.
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The design and construction community has shown increasing interest in adopting building information models (BIMs). The richness of information provided by BIMs has the potential to streamline the design and construction processes by enabling enhanced communication, coordination, automation and analysis. However, there are many challenges in extracting construction-specific information out of BIMs. In most cases, construction practitioners have to manually identify the required information, which is inefficient and prone to error, particularly for complex, large-scale projects. This paper describes the process and methods we have formalized to partially automate the extraction and querying of construction-specific information from a BIM. We describe methods for analyzing a BIM to query for spatial information that is relevant for construction practitioners, and that is typically represented implicitly in a BIM. Our approach integrates ifcXML data and other spatial data to develop a richer model for construction users. We employ custom 2D topological XQuery predicates to answer a variety of spatial queries. The validation results demonstrate that this approach provides a richer representation of construction-specific information compared to existing BIM tools.
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Identifying the design features that impact construction is essential to developing cost effective and constructible designs. The similarity of building components is a critical design feature that affects method selection, productivity, and ultimately construction cost and schedule performance. However, there is limited understanding of what constitutes similarity in the design of building components and limited computer-based support to identify this feature in a building product model. This paper contributes a feature-based framework for representing and reasoning about component similarity that builds on ontological modelling, model-based reasoning and cluster analysis techniques. It describes the ontology we developed to characterize component similarity in terms of the component attributes, the direction, and the degree of variation. It also describes the generic reasoning process we formalized to identify component similarity in a standard product model based on practitioners' varied preferences. The generic reasoning process evaluates the geometric, topological, and symbolic similarities between components, creates groupings of similar components, and quantifies the degree of similarity. We implemented this reasoning process in a prototype cost estimating application, which creates and maintains cost estimates based on a building product model. Validation studies of the prototype system provide evidence that the framework is general and enables a more accurate and efficient cost estimating process.
Resumo:
In recent years, there has been a growing interest from the design and construction community to adopt Building Information Models (BIM). BIM provides semantically-rich information models that explicitly represent both 3D geometric information (e.g., component dimensions), along with non-geometric properties (e.g., material properties). While the richness of design information offered by BIM is evident, there are still tremendous challenges in getting construction-specific information out of BIM, limiting the usability of these models for construction. In this paper, we describe our approach for extracting construction-specific design conditions from a BIM model based on user-defined queries. This approach leverages an ontology of features we are developing to formalize the design conditions that affect construction. Our current implementation analyzes the component geometry and topological relationships between components in a BIM model represented using the Industry Foundation Classes (IFC) to identify construction features. We describe the reasoning process implemented to extract these construction features, and provide a critique of the IFC’s to support the querying process. We use examples from two case studies to illustrate the construction features, the querying process, and the challenges involved in deriving construction features from an IFC model.
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Australia has many isolated communities that require human services provided by qualified professionals. Maintaining a viable and equitable spread of such educational capital across space as a public good is a challenge. Reports investigating this problem repeatedly point to ‘family issues’ such as limited options for children’s education, and limited access to ongoing professional development, as deterrents for rural/remote employment despite lucrative incentive schemes. This paper draws on semi-structured interviews with 30 parents of school-aged children, who work as doctors, nurses, teachers and police in six rural/remote towns in Queensland. We asked them how their family units reconcile career opportunities with educational strategy for family members over time and space. This paper considers these issues as a sociology of education problem in a context of educational marketisation and spiralling credentialism. This paper offers the concept of ‘mobius markets’ to capture the cyclical and intergenerational process underway in middle class professional families of investing in educational capitals, maintaining or maximising their value and profiting from them. A mobius strip is the topological anomaly of a single loop with one twist in it, whereby the loop becomes one continuous surface, not the double-sided shape it appears to be. This project is interested in how the middle class professional family is similarly on a constant circuit, investing in educational capitals, upgrading their currency/value, and profiting from them. This elaborated sense of educational markets extends the more usual sociological focus on school choice.
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We perform an analytic and numerical study of an inviscid contracting bubble in a two-dimensional Hele-Shaw cell, where the effects of both surface tension and kinetic undercooling on the moving bubble boundary are not neglected. In contrast to expanding bubbles, in which both boundary effects regularise the ill-posedness arising from the viscous (Saffman-Taylor) instability, we show that in contracting bubbles the two boundary effects are in competition, with surface tension stabilising the boundary, and kinetic undercooling destabilising it. This competition leads to interesting bifurcation behaviour in the asymptotic shape of the bubble in the limit it approaches extinction. In this limit, the boundary may tend to become either circular, or approach a line or "slit" of zero thickness, depending on the initial condition and the value of a nondimensional surface tension parameter. We show that over a critical range of surface tension values, both these asymptotic shapes are stable. In this regime there exists a third, unstable branch of limiting self-similar bubble shapes, with an asymptotic aspect ratio (dependent on the surface tension) between zero and one. We support our asymptotic analysis with a numerical scheme that utilises the applicability of complex variable theory to Hele-Shaw flow.
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A major challenge for robot localization and mapping systems is maintaining reliable operation in a changing environment. Vision-based systems in particular are susceptible to changes in illumination and weather, and the same location at another time of day may appear radically different to a system using a feature-based visual localization system. One approach for mapping changing environments is to create and maintain maps that contain multiple representations of each physical location in a topological framework or manifold. However, this requires the system to be able to correctly link two or more appearance representations to the same spatial location, even though the representations may appear quite dissimilar. This paper proposes a method of linking visual representations from the same location without requiring a visual match, thereby allowing vision-based localization systems to create multiple appearance representations of physical locations. The most likely position on the robot path is determined using particle filter methods based on dead reckoning data and recent visual loop closures. In order to avoid erroneous loop closures, the odometry-based inferences are only accepted when the inferred path's end point is confirmed as correct by the visual matching system. Algorithm performance is demonstrated using an indoor robot dataset and a large outdoor camera dataset.
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In this article, we analyse bifurcations from stationary stable spots to travelling spots in a planar three-component FitzHugh-Nagumo system that was proposed previously as a phenomenological model of gas-discharge systems. By combining formal analyses, center-manifold reductions, and detailed numerical continuation studies, we show that, in the parameter regime under consideration, the stationary spot destabilizes either through its zeroth Fourier mode in a Hopf bifurcation or through its first Fourier mode in a pitchfork or drift bifurcation, whilst the remaining Fourier modes appear to create only secondary bifurcations. Pitchfork bifurcations result in travelling spots, and we derive criteria for the criticality of these bifurcations. Our main finding is that supercritical drift bifurcations, leading to stable travelling spots, arise in this model, which does not seem possible for its two-component version.
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Consistency and invariance in movements are traditionally viewed as essential features of skill acquisition and elite sports performance. This emphasis on the stabilization of action has resulted in important processes of adaptation in movement coordination during performance being overlooked in investigations of elite sport performance. Here we investigate whether differences exist between the movement kinematics displayed by five, elite springboard divers (age 17 ± 2.4 years) in the preparation phases of baulked and completed take-offs. The two-dimensional kinematic characteristics of the reverse somersault take-off phases (approach and hurdle) were recorded during normal training sessions and used for intra-individual analysis. All participants displayed observable differences in movement patterns at key events during the approach phase; however, the presence of similar global topological characteristics suggested that, overall, participants did not perform distinctly different movement patterns during completed and baulked dives. These findings provide a powerful rationale for coaches to consider assessing functional variability or adaptability of motor behaviour as a key criterion of successful performance in sports such as diving.
Resumo:
Parametric ship roll resonance is a phenomenon where a ship can rapidly develop high roll motion while sailing in longitudinal waves. This effect can be described mathematically by periodic changes of the parameters of the equations of motion, which lead to a bifurcation. In this paper, the control design of an active u-tank stabilizer is carried out using Lyapunov theory. A nonlinear backstepping controller is developed to provide global exponential stability of roll. An extension of commonly used u-tank models is presented to account for large roll angles, and the control design is tested via simulation on a high-fidelity model of a vessel under parametric roll resonance.
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With specific reference to the writing of Dan Graham and the experiences of creative practice, this paper will elaborate an account of studio practice as a topology - a theory drawn from mathematics in which space is understood not as a static field but in terms of properties of connectedness, movement and differentiation. This paper will trace a brief sequence of topological formulations to draw together the expression of topology as form and its structural dimension as a methodology in the specific context of the author’s studio practice. In so doing, this paper seeks to expand the notion of topology in art beyond its association with Conceptual Art of the 1960s and 70s to propose that topology provides a dynamic theoretical model for apprehending the generative ‘logic’ that gives direction and continuity to the art-making process.