Approximate Map Research Articles

Potential Distribution of the American Bullfrog (Lithobates Catesbeianus) in Ecuador

The American bullfrog (Lithobates catesbeianus) is a native species from eastern North America that was introduced to Ecuador in 1985. We built two models in Maxent, (1) one model with native records and, (2) one model with native and invasive records, to provide an approximate map of the potential geographical distribution for this species in Ecuador. Both models showed significant differences in the prediction of suitable areas, model 2 being the most consistent in relation to occurrence records. Here, we present the invasive potential of the American bullfrog to occupy a wide variety of environments such as Amazonia, if human activities lead to an accidental or induced introduction. Furthermore, this study is the first survey about the distribution of the American bullfrog in Ecuador, thus identifying some susceptible areas where conservation efforts should be focused to prevent new settlements and uncontrolled breeding of this species.

An Explicit Nonlinear Mapping for Manifold Learning

Manifold learning is a hot research topic in the held of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there are no explicit mappings from the input data manifold to the output embedding. This prohibits the application of manifold learning methods in many practical problems such as classification and target detection. Previously, in order to provide explicit mappings for manifold learning methods, many methods have been proposed to get an approximate explicit representation mapping with the assumption that there exists a linear projection between the high-dimensional data samples and their low-dimensional embedding. However, this linearity assumption may be too restrictive. In this paper, an explicit nonlinear mapping is proposed for manifold learning, based on the assumption that there exists a polynomial mapping between the high-dimensional data samples and their low-dimensional representations. As far as we know, this is the hrst time that an explicit nonlinear mapping for manifold learning is given. In particular, we apply this to the method of locally linear embedding and derive an explicit nonlinear manifold learning algorithm, which is named neighborhood preserving polynomial embedding. Experimental results on both synthetic and real-world data show that the proposed mapping is much more effective in preserving the local neighborhood information and the nonlinear geometry of the high-dimensional data samples than previous work.

Complex mixed-mode oscillations in a Bonhoeffer–van der Pol oscillator under weak periodic perturbation

In this paper, we elucidate the extremely complicated bifurcation structure of a weakly driven relaxation oscillator by focusing on chaos, and notably, on complex mixed-mode oscillations (MMOs) generated in a simple dynamical model. Our model uses the Bonhoeffer–van der Pol (BVP) oscillator subjected to a weak periodic perturbation near a subcritical Andronov–Hopf bifurcation (AHB). The mechanisms underlying the chaotic dynamics can be explained using an approximate one-dimensional map. The MMOs that appear in this forced dynamical model may be more sophisticated than those appearing in three-variable slow–fast autonomous dynamics because the approximate one-dimensional mapping of the dynamics used herein is a circle map, whereas the one-dimensional first-return map that is derived from the three-variable slow–fast autonomous dynamics is usually a unimodal map. In this study, we generate novel bifurcations such as an MMO-incrementing bifurcation (MMOIB) and intermittently chaotic MMOs. MMOIBs trigger an MMO sequence that, upon varying a parameter, is followed by another type of MMO sequence. By constructing a two-parameter bifurcation diagram, we confirmed that MMOIBs occur successively. According to our numerical results, MMOIBs are often observed between two neighboring MMOs. Numerically, MMOIBs may occur as many times as desired. We also derive the universal constant of the associated successive MMOIBs. The existence of the universal constant suggests that MMOIBs could occur infinitely many times. Furthermore, intermittently chaotic MMOs appear in this dynamical circuit. The intermittently chaotic MMOs relate to a type of intermittent chaos that resembles MMOs at first glance, but includes rare bursts over a long time interval. Complex intermittently chaotic MMOs of various types are observed, and we clarify that the intermittently chaotic MMOs are generated by crisis-induced intermittency.

LIPSCHITZ CONTINUITY OF AN APPROXIMATE SOLUTION MAPPING TO EQUILIBRIUM PROBLEMS

In this paper, with respect to Hausdorff metric, we establish the Lipschitz continuity of an approximate solution mapping for a parametric scalar equilibrium problem. Simultaneously, we give some applications to parametric optimization problems and parametric variational inequalities. Our main results are new and strengthen some results in the recent literature.

Imaging quasi-vertical geological faults with earthquake data

SUMMARY We present a method for imaging quasi-vertically dipping faults with surface records of reflected P waves from small earthquakes. Faults are boundaries between geological structures, such as tectonic plates, and are located in earthquake active regions such as Parkfield, California. The high degree of seismic activity enables the use of multiple seismic recordings in our fault identification algorithm. Major challenges occur because of the quasi-vertical orientation of the fault and the fact that the wave reflected by the fault and recorded by the surface receivers is not well modelled by the direct arrival of the propagating wave generated by the earthquake source. Our method uses the 2-D acoustic wave equation as the model for P-wave propagation. We assume that an approximate wave speed map on the reflection side of the fault is available and the source locations are known, for example, from traveltime tomography. We also assume that the source time function is known. The new features of our method arise because earthquake sources are located very close to the fault. This has two implications: (1) the direct arrival and the reflected wave arrive almost simultaneously, so that it is impossible to separate them on a seismogram using standard techniques, and (2) most of the reflections occur above the critical angle which introduces a distortion in the reflected wave. To overcome these difficulties we use a modelled incident wave to (1) remove the direct arrival from the data, and (2) remove the post-critical distortion from the reflected wave. We justify the distortion removal using the leading-order term of an asymptotic expansion, and an optimization procedure. To complete our algorithm we utilize some features of reverse time migration: (1) the use of full acoustic wave equation for modelling and backpropagation, and (2) zero-lag correlation of the backpropagated time reversed reflected and incident fields. We present numerical examples of fault reconstructions with synthetic data.

The self-oscillating system with compensated dissipation – the dynamics of the approximate discrete map

We study the van der Pol oscillator subject to an external forcing given by δ-pulses depending on the dynamical variable. In order to simplify the computations, an approximate map is derived by solving the equations between subsequent pulses. It is shown that the period-doubling cascade in this map with nonlinear dissipation converges to a critical point of Hamiltonian type with scaling properties which are known for conservative systems.

Multi-pose lipreading and audio-visual speech recognition

In this article, we study the adaptation of visual and audio-visual speech recognition systems to non-ideal visual conditions. We focus on overcoming the effects of a changing pose of the speaker, a problem encountered in natural situations where the speaker moves freely and does not keep a frontal pose with relation to the camera. To handle these situations, we introduce a pose normalization block in a standard system and generate virtual frontal views from non-frontal images. The proposed method is inspired by pose-invariant face recognition and relies on linear regression to find an approximate mapping between images from different poses. We integrate the proposed pose normalization block at different stages of the speech recognition system and quantify the loss of performance related to pose changes and pose normalization techniques. In audio-visual experiments we also analyze the integration of the audio and visual streams. We show that an audio-visual system should account for non-frontal poses and normalization techniques in terms of the weight assigned to the visual stream in the classifier.

The geometric structure of unit dual quaternion with application in kinematic control

In this paper, the geometric structure, especially the Lie-group related properties, of unit dual quaternion is investigated. The exponential form of unit dual quaternion and its approximate logarithmic mapping are derived. Correspondingly, Lie-group and Lie-algebra on unit dual quaternions and the approximate logarithms are explored, respectively. Afterwards, error and metric based on unit dual quaternion are given, which naturally result in a new kinematic control model with unit dual quaternion descriptors. Finally, as a case study, a generalized proportional control law using unit dual quaternion is developed.

LIPSCHITZ CONTINUITY OF AN APPROXIMATE SOLUTION MAPPING TO EQUILIBRIUM PROBLEMS

In this paper, with respect to Hausdorff metric, we establish the Lipschitz continuity of an approximate solution mapping for a parametric scalar equilibrium problem. Simultaneously, we give some applications to parametric optimization problems and parametric variational inequalities. Our main results are new and strengthen some results in the recent literature.

The Structure and Function of Highly Bent Toroidal DNA in Bacteriophage φ29

Tailed bacteriophages are highly efficient machines for infecting a host cell. A single virion must attach to the host surface, penetrate the cell wall, then release its double-stranded DNA genome. In these remarkable DNA delivery machines, controlling how and when the genome is released is a task of paramount importance. Recently, a three-dimensional cryo-electron microscopy (cryo-EM) reconstruction of mature bacteriophage φ29 revealed an intriguing toroidal DNA structure contained in a small cavity below the viral capsid. This highly bent toroidal DNA supercoil is thought to be 30-40 basepairs of dsDNA and its function remains unknown.In this study, we employ an elastic rod model to simulate highly strained DNA as it is compressed within the protein cavity. The model provides estimates of force and energy required to form the toroid as well as its equilibrium conformation. Results reveal that a toroid can indeed form under the biologically relevant forces for the viral packing motor (up to 100 pN). To understand the effects of the highly stressed toroid on DNA structure, we then employ molecular dynamics (MD) simulations starting with the rod model-computed equilibrium as the initial condition. Following equilibration in MD, we construct an approximate density map using the final predicted toroid to compare with the recently published cryo-EM data. The computed density map correctly predicts the major dimensions of the toroid as well as regions of high and low density. Finally, we simulate the start of the ejection process by integrating the rod model forward in time upon sudden removal of the protein “tail knob.” The resulting fast dynamic collapse of the toroid suggests that its function could be to prime the ejection of the remaining viral genome.

Multi-pose lipreading and audio-visual speech recognition

In this article, we study the adaptation of visual and audio-visual speech recognition systems to non-ideal visual conditions. We focus on overcoming the effects of a changing pose of the speaker, a problem encountered in natural situations where the speaker moves freely and does not keep a frontal pose with relation to the camera. To handle these situations, we introduce a pose normalization block in a standard system and generate virtual frontal views from non-frontal images. The proposed method is inspired by pose-invariant face recognition and relies on linear regression to find an approximate mapping between images from different poses. We integrate the proposed pose normalization block at different stages of the speech recognition system and quantify the loss of performance related to pose changes and pose normalization techniques. In audio-visual experiments we also analyze the integration of the audio and visual streams. We show that an audio-visual system should account for non-frontal poses and normalization techniques in terms of the weight assigned to the visual stream in the classifier.

Application of Thin-Plate Splines in Two Dimensions to Oceanographic Tracer Data

Abstract This study explores the utility of the thin-plate spline (TPS) as a mapping procedure for oceanographic sections of bottle data in comparison with objective mapping (OM), sometimes referred to as objective interpolation. Standard OM techniques in oceanography require a priori assumptions about the structure of the errors associated with mapping when interpolating irregularly spaced data. Alternatively, the TPS can be used to approximate mapping errors by fitting a nonparametric model using multiple covariates with a less rigid, physically consistent, spatial correlation structure. The case is made that these errors reflect the sparsity of the data coverage and quantify mapping error better than the estimates using OM. It is demonstrated that the maps from the TPS recreate the essential large-scale features of chlorofluorocarbon- or freon-11 (CFC-11) concentrations and inferred “ages,” but smooth over smaller-scale features, such as eddies. The TPS can outperform OM when either the distance between the samples is larger than the correlation length scale or the signal-to-noise ratio is small. With more data, OM and TPS estimates yield increasingly similar results, but differ most markedly where there are extrema in the mapped fields, particularly at the domain boundaries. The TPS is recommended over OM when the spatial domain is sparsely sampled but the full range of covariates is known to be spanned by these samples.

Correlation-based radio localization in an indoor environment

Abstract We investigate the feasibility of using correlation-based methods for estimating the spatial location of distributed receiving nodes in an indoor environment. Our algorithms do not assume any knowledge regarding the transmitter locations or the transmitted signal, but do assume that there are ambient signal sources whose location and properties are, however, not known. The motivation for this kind of node localization is to avoid interaction between nodes. It is most useful in non-line-of-sight propagation environments, where there is a lot of scattering. Correlation-based node localization is able to exploit an abundance of bandwidth of ambient signals, as well as the features of the scattering environment. The key idea is to compute pairwise cross correlations of the signals received at the nodes and use them to estimate the travel time between these nodes. By doing this for all pairs of receivers, we can construct an approximate map of their location using multidimensional scaling methods. We test this localization algorithm in a cubicle-style office environment based on both ray-tracing simulations, and measurement data from a radio measurement campaign using the Stanford broadband channel sounder. Contrary to what is seen in other applications of cross-correlation methods, the strongly scattering nature of the indoor environment complicates distance estimation. However, using statistical methods, the rich multipath environment can be turned partially into an advantage by enhancing ambient signal diversity and therefore making distance estimation more robust. The main result is that with our correlation-based statistical estimation procedure applied to the real data, assisted by multidimensional scaling, we were able to compute spatial antenna locations with an average error of about 2 m and pairwise distance estimates with an average error of 1.84 m. The theoretical resolution limit for the distance estimates is 1.25 m.

Extracting roads from dense point clouds in large scale urban environment

This paper describes a method for extracting roads from a large scale unstructured 3D point cloud of an urban environment consisting of many superimposed scans taken at different times. Given a road map and a point cloud, our system automatically separates road surfaces from the rest of the point cloud. Starting with an approximate map of the road network given in the form of 2D intersection locations connected by polylines, we first produce a 3D representation of the map by optimizing Cardinal splines to minimize the distances to points of the cloud under continuity constraints. We then divide the road network into independent patches, making it feasible to process a large point cloud with a small in-memory working set. For each patch, we fit a 2D active contour to an attractor function with peaks at small vertical discontinuities to predict the locations of curbs. Finally, we output a set of labeled points, where points lying within the active contour are tagged as “road” and the others are not. During experiments with a LIDAR point set containing almost a billion points spread over six square kilometers of a city center, our method provides 86% correctness and 94% completeness.

An Efficient Multi-Objective Optimization Method for Complicated Vehicle Random Vibration

In this paper, a new approach is proposed and addressed for designing vehicle suspension systems based on the scheme of multi-objective programming. For complicated vehicle random vibration, a linear model is used to describe the dynamic behavior of vehicles running on randomly profiled roads. The road irregularity is regarded as a Gaussian random process. Pesudo excitation method has been used to solve the dynamic responses. And a Kriging model is introduced to build the approximate mapping relationship between the design variables and the responses. Optimal solutions are derived by means of the method of centers for structural optimization with multiple objectives. Numerical examples are given, and compared with other optimization methods.

Medicinal plants in old-growth, degraded and re-growth forests of NW Pakistan

Many old-growth forest stands in northwest Pakistan have been structurally transformed as a consequence of logging and livestock grazing, some of which are thereafter left to secondary succession. These forests represent an important resource for local inhabitants who gather and sell medicinal plants as part of their livelihood. With this in mind, the main objectives of our study were: (1) to assess differences in the structure of the tree layer and the abundance of medicinal plants among differently transformed forests, (2) to evaluate the recovery potential of medicinal plants under re-growth forests, and (3) to assess relationships between tree stand structural characteristics and the occurrence of medicinal plants. The first step of the study involved creating an approximate map covering an area of 90 km 2 for five forest-use types (old-growth forest, forest degraded by logging, derived woodland, agroforest and re-growth forest). Fifteen plots per forest-use type were randomly allocated at altitudes ranging from 2200 m to 2400 m asl, within which the abundance of 10 locally important medicinal herb species was assessed. The study stands differed greatly in tree basal area, which was highest in old-growth forest (48 m 2 ha −1), lowest in agroforest areas (6 m 2 ha −1) and intermediate in re-growth forest (20 m 2 ha −1). All ten medicinal plant species were encountered in old-growth and in re-growth forests, but only five of these species also occurred on agroforest plots. The mean coverage of study medicinal plants was highest in old-growth forest (7%), low in forest degraded by logging, derived woodland and agroforest (0.3–2%), and intermediate in re-growth forest (4%). The Jaccard abundance based similarity index indicates a considerable similarity (0.6) between re-growth and old growth forest for both trees and medicinal plants. The overall abundance of medicinal plants increased with increasing tree basal area and canopy cover. The abundance of some particular species decreased; however, the most sought-after medicinal species Bergenia ciliata, Valeriana jatamansi and Viola cancescens increased with tree basal area within specific forest-use type and also across forest-use types. In conclusion, our data suggest that anthropogenic forest degradation leads to a reduction in the abundance of economically viable medicinal plants for the study region. It is further indicated that this can be reversed if degraded forests are allowed to regenerate.

Application of the dynamic mode decomposition to experimental data

The dynamic mode decomposition (DMD) is a data-decomposition technique that allows the extraction of dynamically relevant flow features from time-resolved experimental (or numerical) data. It is based on a sequence of snapshots from measurements that are subsequently processed by an iterative Krylov technique. The eigenvalues and eigenvectors of a low-dimensional representation of an approximate inter-snapshot map then produce flow information that describes the dynamic processes contained in the data sequence. This decomposition technique applies equally to particle-image velocimetry data and image-based flow visualizations and is demonstrated on data from a numerical simulation of a flame based on a variable-density jet and on experimental data from a laminar axisymmetric water jet. In both cases, the dominant frequencies are detected and the associated spatial structures are identified.

Computationally efficient design optimization of wideband planar antennas using Cauchy approximation and space mapping

Computationally efficient simulation-driven design of ultra-wideband planar antennas is presented using Cauchy-based surrogate models of the coarsely-discretized antenna electromagnetic models.Verification of the proposed methodology is performed with satisfactory designs obtained at a computational cost of a few evaluations of high-fidelity antenna models. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:618–622, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25814

Dynamics of a qubit coupled to a dissipative nonlinear quantum oscillator: An effective-bath approach

We consider a qubit coupled to a nonlinear quantum oscillator, the latter coupled to an Ohmic bath, and investigate the qubit dynamics. This composed system can be mapped onto that of a qubit coupled to an effective bath. An approximate mapping procedure to determine the spectral density of the effective bath is given. Specifically, within a linear response approximation the effective spectral density is given by the knowledge of the linear susceptibility of the nonlinear quantum oscillator. To determine the actual form of the susceptibility, we consider its periodically driven counterpart, the problem of the quantum Duffing oscillator within linear response theory in the driving amplitude. Knowing the effective spectral density, the qubit dynamics is investigated. In particular, an analytic formula for the qubit's population difference is derived. Within the regime of validity of our theory, a very good agreement is found with predictions obtained from a Bloch-Redfield master equation approach applied to the composite qubit-nonlinear oscillator system.

Continuity of approximate solution mappings for parametric equilibrium problems

In this paper, we obtain sufficient conditions for Hausdorff continuity and Berge continuity of an approximate solution mapping for a parametric scalar equilibrium problem. By using a scalarization method, we also discuss the Berge lower semicontinuity and Berge continuity of a approximate solution mapping for a parametric vector equilibrium problem.