Configuration Space Model Research Articles

Equivariant Nerve Lemma, simplicial difference, and models for configuration spaces on simplicial complexes

Wiltshire-Gordon has introduced a homotopy model for ordered configuration spaces on a given simplicial complex. That author asserts that, after a suitable subdivision, his model also works for unordered configuration spaces. We supply details justifying Wiltshire-Gordon's assertion and, more importantly, uncover the equivariant properties of his more-general simplicial-difference model for the complement of a subcomplex inside a larger complex. This is achieved by proving an equivariant version of the Nerve Lemma. In addition, in the case of configuration spaces, we show that a slight variation of the model has better properties: it is regular and sits inside the configuration space as a strong and equivariant deformation retract. Our variant for the configuration-space model comes from a comparison, in the equivariant setting, between Wiltshire's simplicial difference and a well known model for the complement of a full subcomplex on a simplicial complex.

An Integrated Kinematic Calibration and Dynamic Identification Method With Only Static Measurements for Serial Robot

In this article, we propose an integrated calibration and identification method that can identify kinematic and dynamic parameters at the same time. Only a series of static experiments are required in this method, which can significantly simplify the experimental operation and improve the accuracy of identification. A novel calibration model based on axis configuration space and adjoint error model considering joint compliance with only position measurements is developed and both joint compliance and joint zero-offset errors are included in the proposed model. Identifiability analysis shows which joint compliance can be identified and the relationships between the identifiability of joint compliance and the number of measurement points. A recursive algorithm considering physical consistency is newly derived to obtain the derivatives of estimated inertial matrix and gravity vector with respect to joint twists. In this way, the coupling between kinematic and dynamic model is solved and the optimal kinematic and dynamic parameters can be derived using gradient-based optimizer. Comparative study with experiments are reported to show the effectiveness of our algorithm.

Complex Physical Properties of an Adaptive, Self-Organizing Biological System

Physical modeling of the functioning of the adaptive immune system, which has been thoroughly characterized on genetic and molecular levels, provides a unique opportunity to define an adaptive, self-organizing biological system in its entirety. This paper describes a configuration space model of immune function, where directed chemical potentials of the system constitute a space of interactions. A mathematical approach is used to define the system that couples the variance of Gaussian distributed interaction energies in its interaction space to the exponentially distributed chemical potentials of its effector molecules to maintain its steady state. The model is validated by identifying the thermodynamic and network variables analogous to the mathematical parameters and by applying the model to the humoral immune system. Overall, this statistical thermodynamics model of adaptive immunity describes how adaptive biological self-organization arises from the maintenance of a scale-free, directed molecular interaction network with fractal topology.

Configuration Space Decomposition for Scalable Proxy Collision Checking in Robot Planning and Control

Real-time robot motion planning in complex high-dimensional environments remains an open problem. Motion planning algorithms, and their underlying collision checkers, are crucial to any robot control stack. Collision checking takes up a large portion of the computational time in robot motion planning. Existing collision checkers make trade-offs between speed and accuracy and scale poorly to high-dimensional, complex environments. We present a novel space decomposition method using K-Means clustering in the Forward Kinematics space to accelerate proxy collision checking. We train individual configuration space models using Fastron, a kernel perceptron algorithm, on these decomposed subspaces, yielding compact yet highly accurate models that can be queried rapidly and scale better to more complex environments. We demonstrate this new method, called Decomposed Fast Perceptron (D-Fastron), on the 7-DOF Baxter robot producing on average 29x faster collision checks and up to 9.8x faster motion planning compared to state-of-the-art geometric collision checkers.

Mass spectrum of triply heavy baryon in the hypercentral quark model

In this study, we consider baryons as three-body bound systems according to hypercentral constituent quark model in configuration space and solve three-body Klein–Gordon equation. Then we analyze perturbative spin-dependent and isospin-dependent interaction effects. To find the analytical solution, we used screened potential and calculate the eigenfunctions and eigenvalues of triply heavy baryons by using Nikiforov–Uvarov method. We compute the ground and excited state masses of triply heavy baryons with quantum numbers [Formula: see text], [Formula: see text], [Formula: see text] via constituent quark model approach.

Investigation of Baryons in the Hypercentral Quark Model

In the present study, we consider baryons as three-body bound systems according to the hypercentral constituent quark model in configuration space and solve the three-body Klein-Gordon equation. Then, we analyze perturbative spin-dependent and isospin-dependent interaction effects. To find the analytical solution, we use screened potential and calculate the eigenfunctions and eigenvalues of some baryons. We consider exclusive semileptonic decays of bottom and charm baryons and apply the differential decay width with the Isgur-Wise function and arrive at the rates for some semileptonic baryon decays. The results prove more enhanced compared to recent works and comply well with the experimental data.

Bi-soft open sphere topology model of configuration space for reactive joint motion planning of unmanned vehicles

Bi-soft open sphere topology model of configuration space for reactive joint motion planning of unmanned vehicles

A Configuration Space Model for Intermediate‐Scale Ionospheric Structure

AbstractStochastic ionospheric structure is characterized by spectral density functions (SDFs), which are formally the average intensity of Fourier transformations of the electron density structure. Structure elongation along magnetic field lines is typically accommodated by constraining contours of constant spatial correlation to field‐aligned ellipsoidal surfaces. Structure realizations are generated by imposing the square root of the SDF onto uncorrelated random Fourier modes. The approach has been used successfully for interpreting both in situ and remote propagation diagnostics. However, the only connection to the field‐aligned structures generated by the underlying instability mechanism is the correlation scale. This paper introduces a configuration space model that constructs realizations as summations of field‐aligned elemental striations with a prescribed scale and peak electron density. We show that by choosing the contributing scales according to a bifurcation rule and imposing a power law intensity scaling, the corresponding SDF closely approximates an inverse power law. Thus, configuration space realizations can be structured to reproduce prescribed or measured SDFs from one‐dimensional scans. Stochastic variation comes from an imposed random distribution of striation locations, which are defined by their intercept in a reference slice plane. To conform more directly to physics‐based simulations, the striations can be interpreted as voids in the background electron density. The model is designed to support propagation simulations with arbitrary propagation angles relative to the local magnetic field direction. Relations between in situ structure and diagnostic measurements as well as phase screen equivalence can be explored.

An Explicit Two Step Quantization of Poisson Structures and Lie Bialgebras

We develop a new approach to deformation quantizations of Lie bialgebras and Poisson structures which goes in two steps. In the first step one associates to any Poisson (resp. Lie bialgebra) structure a so called quantizable Poisson (resp. Lie bialgebra) structure. We give explicit transcendental formulae for this correspondence. In the second step one deformation quantizes a quantizable Poisson (resp. Lie bialgebra) structure. We show again explicit transcendental formulae for this second step correspondence (as a byproduct we obtain configuration space models for biassociahedron and bipermutohedron). In the Poisson case the first step is the most non-trivial one and requires a choice of an associator while the second step quantization is essentially unique, it is independent of a choice of an associator and can be done by a trivial induction. We conjecture that similar statements hold true in the case of Lie bialgebras. The main new result is a surprisingly simple explicit universal formula (which uses only smooth differential forms) for universal quantizations of finite-dimensional Lie bialgebras.

Modelling the large-scale redshift-space 3-point correlation function of galaxies

We present a configuration-space model of the large-scale galaxy 3-point correlation function (3PCF) based on leading-order perturbation theory and including redshift space distortions (RSD). This model should be useful in extracting distance-scale information from the 3PCF via the Baryon Acoustic Oscillation (BAO) method. We include the first redshift-space treatment of biasing by the baryon-dark matter relative velocity. Overall, on large scales the effect of RSD is primarily a renormalization of the 3PCF that is roughly independent of both physical scale and triangle opening angle; for our adopted $\Omega_{\rm m}$ and bias values, the rescaling is a factor of $\sim 1.8$. We also present an efficient scheme for computing 3PCF predictions from our model, important for allowing fast exploration of the space of cosmological parameters in future analyses.

Using simulated annealing for computing cost-aware covering arrays

The configuration spaces of software systems are often too large to test exhaustively. Combinatorial interaction testing approaches, such as covering arrays, systematically sample the configuration space and test only the selected configurations. In an attempt to reduce the cost of testing, standard t-way covering arrays aim to cover all t-way combinations of option settings in a minimum number of configurations. By doing so, they simply assume that every configuration costs the same. When the cost varies from one configuration to another, however, minimizing the number of configurations is not necessarily the same as minimizing the cost. To overcome this issue, we have recently introduced cost-aware covering arrays. In a nutshell, a t-way cost-aware covering array is a standard t-way covering array that “minimizes” a given cost function modeling the actual cost of testing. In this work we develop a simulated annealing-based approach to compute cost-aware covering arrays, which takes as input a configuration space model enhanced with a cost function and computes a cost-aware covering array by using two alternating neighboring state generation strategies together with a fitness function expressed as a weighted sum of two objectives: covering all required t-way option setting combinations and minimizing the cost function. To the best of our knowledge, the proposed approach is the first approach that computes cost-aware covering arrays for general, non-additive linear cost functions with multiplicative interaction effects. We evaluate the approach both by conducting controlled experiments, in which we systematically vary the input models to study the sensitivity of the approach to various factors and by conducting experiments using real cost functions for real software systems. We also compare cost-aware covering arrays to standard covering arrays constructed by well-known algorithms and study how fast the construction costs are compensated by the cost reductions provided. Our empirical results suggest that the proposed approach is more effective and efficient than the existing approaches.

Nonlocal signaling in the configuration space model of quantum-classical interactions

When interactions are turned off, the theory of interacting quantum and classical ensembles due to Hall and Reginatto is shown to suffer from a nonlocal signaling effect that is effectively action at a distance. This limits the possible applicability of the theory. In its present form, it is restricted to those situations in which interactions are always on, such as classical gravity interacting with quantized matter.

Configuration Models For Moduli Spaces of Riemann surfaces with boundary

In this article we consider Riemann surfacesF of genus g ≥ 0 with n ≥ 1 incoming and m ≥ 1 outgoing boundary circles, where on each incoming circle a point is marked. For the moduli space mg*(m, n) of all suchF of genusg ≥ 0 a configuration space model Radh(m, n) is described: it consists of configurations of h = 2g-2+m+n pairs of radial slits distributed over n annuli; certain combinatorial conditions must be satisfied to guarantee the genusg and exactly m outgoing circles. Our main result is a homeomorphism between Radh(m, n) and Mg*(m,n). The space Radh(m, n) is a non-compact manifold, and the complement of a subcomplex in a finite cell complex. This can be used for homological calculations. Furthermore, the family of spaces Radh(m, n ) form an operad, acting on various spaces connected to conformai field theories.

Colloquium: Physically based fluid modeling of collisionally dominated low-temperature plasmas

This colloquium examines the theoretical modeling of nonequilibrium low-temperature (tens of thousands of degrees) plasmas, which involves a juxtaposition of three distinct fields: atomic and molecular physics, for the input of scattering cross sections; statistical mechanics, for the kinetic modeling; and electromagnetic theory, for the simultaneous solution of Maxwell's equations. Cross sections come either from single-scattering beam experiments or, at very low energies (<0.5 eV), from multiple-scattering experiments on swarms in gases—the free diffusion or large Debye length limit of a plasma, where they are embedded in transport coefficient data. The same Boltzmann kinetic theory that has been developed to a high level of sophistication over the past 50 years, specifically for the purpose of unfolding these transport data, can be employed for low-temperature plasmas with appropriate modification to allow for self-consistent rather than externally prescribed fields. A full kinetic treatment of low-temperature plasmas is, however, a daunting task and remains at the developmental level. Fortunately, since the accuracy requirements for modeling plasmas are generally much less stringent than for swarms, such a sophisticated phase-space treatment is not always necessary or desirable, and a computationally more efficient but correspondingly less accurate macroscopic theoretical model in configuration space at the fluid level is often considered sufficient. There has been a proliferation of such fluid modeling in recent times and this approach is now routinely used in the design and development of a large variety of plasma technologies, ranging from plasma display panels to plasma etching reactors for microelectronic device fabrication. However, many of these models have been developed empirically with specific applications in mind, and rigor and sophistication vary accordingly. In this colloquium, starting from the governing Boltzmann kinetic equation, a unified, general formulation of fluid equations is given for both ions and electrons in gaseous media with transparent and internally consistent approximations, all benchmarked against established results. Thereby a fluid model is obtained that is appropriate for practical application but at the same time is based on a firmer physical foundation.

Two-Gaussian excitations model for the glass transition

We develop a modified "two-state" model with Gaussian widths for the site energies of both ground and excited states, consistent with expectations for a disordered system. The thermodynamic properties of the system are analyzed in configuration space and found to bridge the gap between simple two-state models ("logarithmic" model in configuration space) and the random energy model ("Gaussian" model in configuration space). The Kauzmann singularity given by the random energy model remains for very fragile liquids but is suppressed or eliminated for stronger liquids. The sharp form of constant-volume heat capacity found by recent simulations for binary mixed Lennard-Jones and soft-sphere systems is reproduced by the model, as is the excess entropy and heat capacity of a variety of laboratory systems, strong and fragile. The ideal glass in all cases has a narrow Gaussian, almost invariant among molecular and atomic glassformers, while the excited-state Gaussian depends on the system and its width plays a role in the thermodynamic fragility. The model predicts the possibility of first-order phase transitions for fragile liquids. The analysis of laboratory data for toluene and o-terphenyl indicates that fragile liquids resolve the Kauzmann paradox by a first-order transition from supercooled liquid to ideal-glass state at a temperature between T(g) and Kauzmann temperature extrapolated from experimental data. We stress the importance of the temperature dependence of the energy landscape, predicted by the fluctuation-dissipation theorem, in analyzing the liquid thermodynamics.

Inertia Orbifolds, Configuration Spaces and the Ghost Loop Space

In this paper we define and study the ghost loop orbifold LsX of an orbifold X consisting of those loops that remain constant in the coarse moduli space of X .W econstruct a configuration space model for LsX using an idea of G. Segal. From this we exhibit the relation between the Hochschild and cyclic homologies of the inertia orbifold of X (that generate the so-called twisted sectors in string theory) and the ordinary and equivariant homologies of LsX .W ealso show how this clarifies the relation between Chen–Ruan orbifold cohomology, Hochschild homology, and periodic cyclic homology.

Inertia Orbifolds, Configuration Spaces and the Ghost Loop Space

In this paper we define and study the loop of an orbifold $X$ consisting of those loops that remain constant in the coarse moduli space of $X$. We construct a configuration space model for the ghost loop orbifold using an idea of G. Segal. From this we exhibit the relation between the Hochschild and cyclic homologies of the inertia orbifold of $X$ (that generate the so-called twisted sectors in string theory) and the ordinary and equivariant homologies of the ghost loop orbifold. We also show how this clarifies the relation between orbifold K-theory, Chen-Ruan orbifold cohomology, Hochschild homology, and periodic cyclic homology.

Mod p truncated configuration spaces

In this paper we study the homotopy types of mod p truncated configuration spaces. In particular, we investigate a finite dimensional configuration space model for the based loop space of mod p lens space as an application.

Configuration Space Models for Spaces of Maps from a Riemann Surface to Complex Projective Space

Let \mathrm{Map}_d^∗(\mathrm M_g, ℂ\mathrm{P}^{n−1}) denote the space consisting of all basepoint preserving continuous maps of degree d from a compact Riemann surface \mathrm M_g of genus g into an (n − 1) -dimensional complex projective space ℂ\mathrm{P}^{n−1} . In this paper, we construct a finite dimensional configuration space model \mathrm{SP}_n^d(\mathrm M'_g) for the infinite dimensional space \mathrm{Map}_d^∗(\mathrm M_g, ℂ\mathrm{P}^{n−1}) and show that the Atiyah–Jones type theorem (cf. [1], [12]) holds for this model.

The Role of Trp Side Chains in Tuning Single Proton Conduction through Gramicidin Channels

We present an extensive set of measurements of proton conduction through gramicidin A (gA), B (gB), and M (gM) homodimer channels which have 4, 3, or 0 Trp residues at each end of the channel, respectively. In gA we find a shoulder separating two domains of conductance increasing with concentration, confirming the results of Eisenman, G., B. Enos, J. Hagglund, and J. Sandblom. 1980. Ann. NY. Acad. Sci. 339:8–20. In gB, the shoulder is shifted by ∼½ pH unit to higher H + concentrations and is very sharply defined. No shoulder appears in the gM data, but an associated transition from sublinear to superlinear I- V values occurs at a 100-fold higher [H +] in gM than in gA. The data in the low concentration domain are analyzed using a configuration space model of single-proton conduction, assuming that the difference in the proton potential of mean force (PMF) between gA and its analogs is constant, similar to the results of Anderson, D., R. B. Shirts, T. A. Cross, and D. D. Busath. 2001. Biophys. J. 81:1255–1264. Our results suggest that the average amplitudes of the calculated proton PMFs are nearly correct, but that the water reorientation barrier calculated for gA by molecular dynamics using the PM6 water model (Pomès, R., and B. Roux. 1997. Biophys. J. 72:246 a) must be reduced in amplitude by 1.5 kcal/mol or more, and is not rate-limiting for gA.