Implicit Maps Research Articles

No differences in implicit hand maps among different degrees of autistic traits.

People with autism spectrum disorder (ASD) or higher levels of autistic traits have atypical characteristics in sensory processing. Atypicalities have been reported for proprioceptive judgments, which are tightly related to internal bodily representations underlying position sense. However, no research has directly investigated whether self-bodily representations are different in individuals with ASD. Implicit hand maps, estimated based on participants' proprioceptive sensations without sight of their hand, are known to be distorted such that the shape is stretched along the medio-lateral hand axis even for neurotypical participants. Here, with the view of ASD as falling on a continuous distribution among the general population, we explored differences in implicit body representations along with autistic traits by focusing on relationships between autistic traits and the magnitudes of the distortions in implicit hand maps (N ~ 100). We estimated the magnitudes of distortions in implicit hand maps both for fingers and hand surfaces on the dorsal and palmar sides of the hand. Autistic traits were measured by questionnaires (Autism Spectrum [AQ] and Empathy/Systemizing [EQ-SQ] Quotients). The distortions in implicit hand maps were replicated in our experimental situations. However, there were no significant relationships between autistic traits and the magnitudes of the distortions as well as within-individual variabilities in the maps and localization performances. Consistent results were observed from comparisons between IQ-matched samples of people with and without a diagnosis of ASD. Our findings suggest that there exist perceptual and neural processes for implicit body representations underlying position sense consistent across levels of autistic traits.

Analytical predictions of periodic oscillations in a piezoelectric energy harvester under combined aeroelastic and harmonic excitation.

This work studies a piezoelectric energy harvester subjected to both fluid flow and harmonic excitation. A lumped parameter model that incorporates fluid-structure interaction is presented to analyze the effects of both fluid flow and harmonic excitation on the proposed harvester. The method of implicit mapping is employed to calculate the periodic displacement, voltage, and velocity oscillations. Stabilities and bifurcations of periodic oscillations are determined based on the eigenvalues of the resultant matrix of mapping structures. The displacement and voltage nodes of the proposed energy harvester varying with excitation amplitude and frequency are investigated. The maximum eigenvalue magnitudes are illustrated. Utilizing the periodic nodes of the displacement and voltage, the harmonic amplitudes and phases are calculated using the fast Fourier transform. The harmonic amplitudes of both displacement and voltage varying with excitation frequency are depicted. For the stable periodic responses, the implicit maps and numerical simulations are presented to demonstrate the effectiveness of the energy harvesting system. The theoretical analysis presented in this study can be useful for the design and optimization of the proposed energy harvester.

Period-3 motions to chaos in a periodically forced nonlinear-spring pendulum.

In this paper, the complete bifurcation dynamics of period-3 motions to chaos are obtained semi-analytically through the implicit mapping method. Such an implicit mapping method employs discrete implicit maps to construct mapping structures of periodic motions to determine complex periodic motions. Analytical bifurcation trees of period-3 motions to chaos are determined through nonlinear algebraic equations generated through the discrete implicit maps, and the corresponding stability and bifurcations of periodic motions are achieved through eigenvalue analysis. To study the periodic motion complexity, harmonic amplitudes varying with excitation amplitudes are presented. Once more, significant harmonic terms are involved in periodic motions, and such periodic motions will be more complex. To illustrate periodic motion complexity, numerical and analytical solutions of periodic motions are presented for comparison, and the corresponding harmonic amplitudes and phases are also presented for such periodic motions in the bifurcation trees of period-3 motions to chaos. Similarly, other higher-order periodic motions and bifurcation dynamics for the nonlinear spring pendulum can be determined. The methods and analysis presented herein can be applied for other nonlinear dynamical systems.

An Algorithm for the SE(3)-Transformation on Neural Implicit Maps for Remapping Functions

Implicit representations are widely used for object reconstruction due to their efficiency and flexibility. In 2021, a novel structure named neural implicit map has been invented for incremental reconstruction. A neural implicit map alleviates the problem of inefficient memory cost of previous online 3D dense reconstruction while producing better quality. However, the neural implicit map suffers the limitation that it does not support remapping as the frames of scans are encoded into a deep prior after generating the neural implicit map. This means, that neither this generation process is invertible, nor a deep prior is transformable. The non-remappable property makes it not possible to apply loop-closure techniques. We present a neural implicit map based transformation algorithm to fill this gap. As our neural implicit map is transformable, our model supports remapping for this special map of latent features. Experiments show that our remapping module is capable to well-transform neural implicit maps to new poses. Embedded into a SLAM framework, our mapping model is able to tackle the remapping of loop closures and demonstrates high-quality surface reconstruction. Our implementation is available at github for the research community.

Bifurcations analysis in implicit maps through the dynamics of cumulated surface errors in milling

In this contribution, we examine the evolution of surface errors during consecutive milling operations. Its description is based on a nonlinear implicit map, which is suitable to investigate the surface quality. It describes the series of consecutive Surface Location Errors (SLE) in roughing operations. As one of the principal results of the paper, bifurcations related to the fixed point of the implicit map are analyzed via normal form theorem. We determined a formula for the criticality of the bifurcation, which allows the approximate computation of the arising period-two solution. The method is demonstrated for the surface error model of milling, and the results are verified by numerical computations. Although the amplitude of the SLE would be negligible, its derivatives has a great influence in the model, which can cause stability problems.

A unifying view of explicit and implicit feature maps of graph kernels

Non-linear kernel methods can be approximated by fast linear ones using suitable explicit feature maps allowing their application to large scale problems. We investigate how convolution kernels for structured data are composed from base kernels and construct corresponding feature maps. On this basis we propose exact and approximative feature maps for widely used graph kernels based on the kernel trick. We analyze for which kernels and graph properties computation by explicit feature maps is feasible and actually more efficient. In particular, we derive approximative, explicit feature maps for state-of-the-art kernels supporting real-valued attributes including the GraphHopper and graph invariant kernels. In extensive experiments we show that our approaches often achieve a classification accuracy close to the exact methods based on the kernel trick, but require only a fraction of their running time. Moreover, we propose and analyze algorithms for computing random walk, shortest-path and subgraph matching kernels by explicit and implicit feature maps. Our theoretical results are confirmed experimentally by observing a phase transition when comparing running time with respect to label diversity, walk lengths and subgraph size, respectively.

Periodic motions and chaos in power system including power disturbance

Single-machine infinite-bus power system is a nonlinear dynamic system with state variable in the sinusoidal function. With traditional analytical approaches, it is difficult to analyze such a nonlinear system since the rotor angle difference cannot always stay in an infinitesimal small value. In this paper, a single-machine infinite-bus power system with power disturbance will be discussed. The implicit discrete maps approach will be applied to solve the periodic motions for such a power system, and the stability condition will be discussed. The analytical expressions for periodic motions for such a single-machine infinite-bus power system can be recovered with a series of Fourier functions. The bifurcation diagram for such a system will be given to show the complexity of the motions when the frequency of the disturbance varies, and 2-D parameter map for chaotic motion will be obtained by calculating the Kolmogorov-Sinai entropy density. From analytical bifurcation for period-1 and period-2 motions, the evolution process of the periodic motion to chaos can be analytically explained.

Feedback control of unstable periodic motion for brushless motor with unsteady external torque

For dynamical systems, unstable periodic motion can play an important role, such as the walking behavior for human. Due to the dynamic characteristics, unstable periodic motion is difficult to stay on its limit orbit or equilibrium even when small disturbance occurs. Therefore, it is unusual to observe unstable periodic motions in the real world applications. At some specific circumferences, design a proper controller for a dynamic system properly when the unstable periodic motion is required becomes a problem to be solved. In this paper, a brushless motor model with unsteady external torque will be investigated. The analytic bifurcation of periodic motions will be obtained through a semi-analytic approach which is called as the discrete implicit maps algorithm. Based on the node points of the periodic motions, the analytic solution for the periodic motion can be expressed with a Fourier series. The stable and unstable analytical solutions will be verified by the numerical predictions. Then a feedback controller will be designed such that the unstable periodic motion can stay on its orbit permanently. The simulation with and without controller will be compared to show the effectiveness of the controller.

Sex differences in perceptual hand maps: A meta-analysis

A large body of research has suggested that localisation of the hand in external space relies on distorted representations of the hand. We developed a paradigm for measuring implicit perceptual maps of the hand (Longo & Haggard, 2010, Proc Natl Acad Sci USA, 107, 11727–11732), which show systematic deviation from actual hand shape, including overestimation of hand width and underestimation of finger length. Recently, Coelho and Gonzalez (in press, Psychol Res) reported sex differences in these perceptual hand maps, with women showing greater overestimation of hand width, but less underestimation of finger length than men. In the current study, I conducted a meta-analysis of 19 experiments using this paradigm by myself and my colleagues. The results replicated the sex differences reported by Coelho and Gonzalez. Importantly, however, these sex differences were not apparent when actual hand size was included as a covariate in analyses, suggesting that they may, at least in part, be due to women having smaller hands on average than men.

Semantic Prior Analysis for Salient Object Detection.

Salient object detection aims to detect the main objects in the given image. In this paper, we proposed an approach that integrates semantic priors into the salient object detection process. The method first obtains an explicit saliency map that is refined by the explicit semantic priors learned from data. Then an implicit saliency map is constructed using a trained model that maps the implicit semantic priors embedded into superpixel features with the saliency values. Next, the fusion saliency map is computed by adaptively fusing both the explicit and implicit semantic maps. The final saliency map is eventually computed via the post-processing refinement step. Experimental results have demonstrated the effectiveness of the proposed method, particularly, it achieves competitive performance with the state-of-the-art baselines on three challenging datasets, namely, ECSSD, HKUIS, and iCoSeg.

Nonlinear behavior for periodically excited brushless motor

PurposeDue to the coupling between the direct-axis current, quadrature-axis current and rotor speed, the dynamic response could be strongly nonlinear. Besides, if the working condition is severe, the loading is no longer constant and multiple harmonics could be introduced. In this paper, the periodic motions for brushless motor will be solved, and accurate analytic solution will be obtained through the proposed method. The purpose of this study is to provide accurate analytic solution of periodic motions for brushless motor with fluctuated loading, which is a dynamic system with strong nonlinearity.Design/methodology/approachA newly developed semi-analytic algorithm called discrete implicit maps is used to give analytic solutions for both stable and unstable motions for such a motor.FindingsThe accurate analytic expressions for stable and unstable periodic motions have been obtained. For unstable motion, it can stay on the unstable orbit for many periods without any controller. Through bifurcation analysis, the parameter sensitivity has been obtained which can be a suggestion for design and operation.Originality/valueThis paper provides all possible analytical solutions for period-1 motion as well as the unstable motions in a range of system parameters. It offers a chance to control the unstable motion for such a motor.

Stable and Unstable Behaviors for Brushless Motor with Harmonic Disturbance via Discrete Implicit Maps

Stable and Unstable Behaviors for Brushless Motor with Harmonic Disturbance via Discrete Implicit Maps

Free Function Theory Through Matrix Invariants

Abstract This paper concerns free function theory. Freemaps are free analogs of analytic functions in several complex variables and are defined in terms of freely noncommuting variables. A function of g noncommuting variables is a function on g-tuples of square matrices of all sizes that respects direct sums and simultaneous conjugation. Examples of such maps include noncommutative polynomials, noncommutative rational functions, and convergent noncommutative power series. In sharp contrast to the existing literature in free analysis, this article investigates free maps with involution, free analogs of real analytic functions. To get a grip on these, techniques and tools from invariant theory are developed and applied to free analysis. Here is a sample of the results obtained. A characterization of polynomial free maps via properties of their finite-dimensional slices is presented and then used to establish power series expansions for analytic free maps about scalar and non-scalar points; the latter are series of generalized polynomials for which an invarianttheoretic characterization is given. Furthermore, an inverse and implicit function theorem for free maps with involution is obtained. Finally, with a selection of carefully chosen examples it is shown that free maps with involution do not exhibit strong rigidity properties enjoyed by their involutionfree counterparts.

Periodic motions and chaos for a damped mobile piston system in a high pressure gas cylinder with P control

In this paper, the complex motions for a moving piston in a closed gas cylinder will be analyzed using the discrete implicit maps method. The strong nonlinearity of such system will be observed due to the large quadratic and cubic stiffness. Period-1 motions which contain high order of harmonic components will be presented. The periodic motions will be discretized into multiple continuous mappings, and such mapping can be analyzed via Newton–Raphson iteration. The stability analysis will be given and the analytic conditions for the saddle-node and period-doubling bifurcation will be determined. From the semi-analytic solution route, the possible motions without considering the impact of the piston with the end wall of the cylinder will be obtained analytically. The scheme to reduce the vibration of the piston can be obtained through the parameter studies.

Periodic Motions to Chaos in Pendulum

It is not easy to find periodic motions to chaos in a pendulum system even though the periodically forced pendulum is one of the simplest nonlinear systems. However, the inherent complex dynamics of the periodically forced pendulum is much beyond our imaginations through the traditional approach of linear dynamical systems. Until now, we did not know complex motions of pendulum yet. What are the mechanism and mathematics of such complex motions in the pendulum? The results presented herein give a new view of complex motions in the periodically forced pendulum. Thus, in this paper, periodic motions to chaos in a periodically forced pendulum are predicted analytically by a semi-analytical method. The method is based on discretization of differential equations of the dynamical system to obtain implicit maps. Using the implicit maps, mapping structures for specific periodic motions are developed, and the corresponding periodic motions can be predicted analytically through such mapping structures. Analytical bifurcation trees of periodic motions to chaos are obtained, and the corresponding stability and bifurcation analysis of periodic motions to chaos are carried out by eigenvalue analysis. From the analytical prediction of periodic motions to chaos, the corresponding frequency-amplitude characteristics are obtained for a better understanding of motions’ complexity in the periodically forced pendulum. Finally, numerical simulations of selected periodic motions are illustrated. The nontravelable and travelable periodic motions on the bifurcation trees are discovered. Through this investigation, the periodic motions to chaos in the periodically forced pendulums can be understood further. Based on the perturbation method, one cannot achieve the adequate solutions presented herein for periodic motions to chaos in the periodically forced pendulum.

Routes of periodic motions to chaos in a periodically forced pendulum

In this paper, with varying excitation amplitude, bifurcation trees of periodic motions to chaos in a periodically driven pendulum are obtained through a semi-analytical method. This method is based on the implicit discrete maps obtained from the midpoint scheme of the corresponding differential equation. Using the discrete maps, mapping structures are developed for specific periodic motions, and the corresponding nonlinear algebraic equations of such mapping structures are solved. Further, semi-analytical bifurcation trees of periodic motions to chaos are also obtained, and the corresponding eigenvalue analysis is carried out for the stability and bifurcation of the periodic motions. Finally, numerical illustrations of periodic motions on the bifurcation trees are presented in verification of the analytical prediction. Harmonic amplitude spectra are also presented for demonstrating harmonic effects on the periodic motions. The bifurcation trees of period-1 motions to chaos possess a double spiral structure. The two sets of solutions of period-\(2^{l}\) motions \((l=0,1,2,\ldots )\) to chaos are based on the center around \(2m\pi \) and \((2m-1)\pi (m=1,2,3,\ldots )\) in phase space. Other independent bifurcation trees of period-m motions to chaos are presented. Through this investigation, the motion complexity and nonlinearity of the periodically forced pendulum can be further understood.

Perceptual and Conceptual Distortions of Implicit Hand Maps.

Recent studies have revealed that human position sense relies on a massively distorted representation of hand size and shape. By comparing the judged location of landmarks on an occluded hand, Longo and Haggard (2010) constructed implicit perceptual maps of represented hand structure, showing large underestimation of finger length and overestimation of hand width. Here, we investigated the contribution of two potential sources of distortions to such effects: perceptual distortions reflecting spatial warping of the representation of bodily tissue itself, perhaps reflecting distortions of somatotopic cortical maps, and conceptual distortions reflecting mistaken beliefs about the locations of different landmarks within the body. In Experiment 1 we compared distorted hand maps to a task in which participants explicitly judged the location of their knuckles in a hand silhouette. The results revealed the conceptual distortions are responsible for at least part of the underestimation of finger length, but cannot explain overestimation of hand width. Experiment 2 compared distortions of the participant’s own hand based on position sense with a prosthetic hand based on visual memory. Underestimation of finger length was found for both hands, providing further evidence that it reflects a conceptual distortion. In contrast, overestimation of hand width was specific to representation of the participant’s own hand, confirming it reflects a perceptual distortion. Together, these results suggest that distorted body representations do not reflect a single underlying cause. Rather, both perceptual and conceptual distortions contribute to the overall configuration of the hand representation.

On complex periodic motions and bifurcations in a periodically forced, damped, hardening Duffing oscillator

In this paper, analytically predicted are complex periodic motions in the periodically forced, damped, hardening Duffing oscillator through discrete implicit maps of the corresponding differential equations. Bifurcation trees of periodic motions to chaos in such a hardening Duffing oscillator are obtained. The stability and bifurcation analysis of periodic motion in the bifurcation trees is carried out by eigenvalue analysis. The solutions of all discrete nodes of periodic motions are computed by the mapping structures of discrete implicit mapping. The frequency-amplitude characteristics of periodic motions are computed that are based on the discrete Fourier series. Thus, the bifurcation trees of periodic motions are also presented through frequency-amplitude curves. Finally, based on the analytical predictions, the initial conditions of periodic motions are selected, and numerical simulations of periodic motions are carried out for comparison of numerical and analytical predictions. The harmonic amplitude spectrums are also given for the approximate analytical expressions of periodic motions, which can also be used for comparison with experimental measurement. This study will give a better understanding of complex periodic motions in the hardening Duffing oscillator.

Posture modulates implicit hand maps.

Several forms of somatosensation require that afferent signals be informed by stored representations of body size and shape. Recent results have revealed that position sense relies on a highly distorted body representation. Changes of internal hand posture produce plastic alterations of processing in somatosensory cortex. This study therefore investigated how such postural changes affect implicit body representations underlying position sense. Participants localised the knuckles and tips of each finger in external space in two postures: the fingers splayed (Apart posture) or pressed together (Together posture). Comparison of the relative locations of the judgments of each landmark were used to construct implicit maps of represented hand structure. Spreading the fingers apart produced increases in the implicit representation of hand size, with no apparent effect on hand shape. Thus, changes of internal hand posture produce rapid modulation of how the hand itself is represented, paralleling the known effects on somatosensory cortical processing.

A Semi-analytical Prediction of Periodic Motions in Duffing Oscillator through Mapping Structures

In this paper, periodic motions in the Duffing oscillator are investigated through the mapping structures of discrete implicit maps. The discrete implicit maps are obtained from differential equation of the Duffing oscillator. From mapping structures, bifurcation trees of periodic motions are predicted analytically through nonlinear algebraic equations of implicit maps, and the corresponding stability and bifurcation analysis of periodic motion in the bifurcation trees are carried out. The bifurcation trees of periodic motions are also presented through the harmonic amplitudes of the discrete Fourier series. Finally, from the analytical prediction, numerical simulation results of periodic motions are performed to verify the analytical prediction. The harmonic amplitude spectra are also presented, and the corresponding analytical expression of periodic motions can be obtained approximately. The method presented in this paper can be applied to other nonlinear dynamical systems for bifurcation trees of periodic motions to chaos.