Showing papers on "Configuration space published in 2010"

Adaptive and generic corner detection based on the accelerated segment test

Abstract: The efficient detection of interesting features is a crucial step for various tasks in Computer Vision. Corners are favored cues due to their two dimensional constraint and fast algorithms to detect them. Recently, a novel corner detection approach, FAST, has been presentedwhich outperforms previous algorithms in both computational performance and repeatability. We will show how the accelerated segment test, which underlies FAST, can be significantly improved by making it more generic while increasing its performance.We do so by finding the optimal decision tree in an extended configuration space, and demonstrating how specialized trees can be combined to yield an adaptive and generic accelerated segment test. The resulting method provides high performance for arbitrary environments and so unlike FAST does not have to be adapted to a specific scene structure. We will also discuss how different test patterns affect the corner response of the accelerated segment test.

Sampling-Based Path Planning on Configuration-Space Costmaps

Abstract: This paper addresses path planning to consider a cost function defined over the configuration space. The proposed planner computes low-cost paths that follow valleys and saddle points of the configuration-space costmap. It combines the exploratory strength of the Rapidly exploring Random Tree (RRT) algorithm with transition tests used in stochastic optimization methods to accept or to reject new potential states. The planner is analyzed and shown to compute low-cost solutions with respect to a path-quality criterion based on the notion of mechanical work. A large set of experimental results is provided to demonstrate the effectiveness of the method. Current limitations and possible extensions are also discussed.

Coordinate-dependent diffusion in protein folding.

Abstract: Diffusion on a low-dimensional free-energy surface is a remarkably successful model for the folding dynamics of small single-domain proteins. Complicating the interpretation of both simulations and experiments is the expectation that the effective diffusion coefficient D will in general depend on the position along the folding coordinate, and this dependence may vary for different coordinates. Here we explore the position dependence of D, its connection to protein internal friction, and the consequences for the interpretation of single-molecule experiments. We find a large decrease in D from unfolded to folded, for reaction coordinates that directly measure fluctuations in Cartesian configuration space, including those probed in single-molecule experiments. In contrast, D is almost independent of Q, the fraction of native amino acid contacts: Near the folded state, small fluctuations in position cause large fluctuations in Q, and vice versa for the unfolded state. In general, position-dependent free energies and diffusion coefficients for any two good reaction coordinates that separate reactant, product, and transition states, are related by a simple transformation, as we demonstrate. With this transformation, we obtain reaction coordinates with position-invariant D. The corresponding free-energy surfaces allow us to justify the assumptions used in estimating the speed limit for protein folding from experimental measurements of the reconfiguration time in the unfolded state, and also reveal intermediates hidden in the original free-energy projection. Lastly, we comment on the design of future single-molecule experiments that probe the position dependence of D directly.

Modifying the Sum Over Topological Sectors and Constraints on Supergravity

Abstract: The standard lore about the sum over topological sectors in quantum field theory is that locality and cluster decomposition uniquely determine the sum over such sectors, thus leading to the usual θ-vacua. We show that without changing the local degrees of freedom, a theory can be modified such that the sum over instantons should be restricted; e.g. one should include only instanton numbers which are divisible by some integer p. This conclusion about the configuration space of quantum field theory allows us to carefully reconsider the quantization of parameters in supergravity. In particular, we show that FI-terms and nontrivial Kahler forms are quantized. This analysis also leads to a new derivation of recent results about linearized supergravity.

Coordinated Motion Design on Lie Groups

Abstract: The present paper proposes a unified geometric framework for coordinated motion on Lie groups It first gives a general problem formulation and analyzes ensuing conditions for coordinated motion Then, it introduces a precise method to design control laws in fully actuated and underactuated settings with simple integrator dynamics It thereby shows that coordination can be studied in a systematic way once the Lie group geometry of the configuration space is well characterized Applying the proposed general methodology to particular examples allows to retrieve control laws that have been proposed in the literature on intuitive grounds A link with Brockett's double bracket flows is also made The concepts are illustrated on SO(3) , SE(2) and SE(3)

The VCI-P code: an iterative variation–perturbation scheme for efficient computations of anharmonic vibrational levels and IR intensities of polyatomic molecules

Abstract: A variation–perturbation scheme called VCI-P code is proposed. It is developed mainly for the efficient and accurate theoretical description of vibrational resonances in polyatomic molecules. This state-specific process consists of the iterative construction of small matrices for each vibrational state, using the most important configurations contributing to that state. The weak couplings are considered perturbationally. The keypoint of this paper is a recipe that allows the massive truncation of the vibrational configuration space with minimum error in the calculated energies. The anharmonic frequencies and IR/vibrational absorption (VA) intensities obtained using VCI-P for methane and formaldehyde are compared to their full VCI counterparts. The convergence of the VCI-P results with respect to configuration selection is also discussed from the examples of trans-difluoroethylene and ethylene oxide (also called oxirane). A parallelization scheme for the 3N − 5 calculations on distributed memory computers is proposed. Representative computational times are presented for molecules ranging in size from 4 to 15 atoms.

Crystal fingerprint space – a novel paradigm for studying crystal‐structure sets

Abstract: The initial aim of the crystal fingerprint project was to solve a very specific problem: to classify and remove duplicate crystal structures from the results generated by the evolutionary crystal-structure predictor USPEX. These duplications decrease the genetic diversity of the population used by the evolutionary algorithm, potentially leading to stagnation and, after a certain time, reducing the likelihood of predicting essentially new structures. After solving the initial problem, the approach led to unexpected discoveries: unforeseen correlations, useful derived quantities and insight into the structure of the overall set of results. All of these were facilitated by the project's underlying idea: to transform the structure sets from the physical configuration space to an abstract, high-dimensional space called the fingerprint space. Here every structure is represented as a point whose coordinates (fingerprint) are computed from the crystal structure. Then the space's distance measure, interpreted as structure `closeness', enables grouping of structures into similarity classes. This model provides much flexibility and facilitates access to knowledge and algorithms from fields outside crystallography, e.g. pattern recognition and data mining. The current usage of the fingerprint-space model is revealing interesting properties that relate to chemical and crystallographic attributes of a structure set. For this reason, the mapping of structure sets to fingerprint space could become a new paradigm for studying crystal-structure ensembles and global chemical features of the energy landscape.

Spin-adapted open-shell random phase approximation and time-dependent density functional theory. I. Theory.

Abstract: The spin-adaptation of single-reference quantum chemical methods for excited states of open-shell systems has been nontrivial. The primary reason is that the configuration space, generated by a truncated rank of excitations from only one component of a reference multiplet, is spin-incomplete. Those "missing" configurations are of higher ranks and can, in principle, be recaptured by a particular class of excitation operators. However, the resulting formalisms are then quite involved and there are situations [e.g., time-dependent density functional theory (TD-DFT) under the adiabatic approximation] that prevent one from doing so. To solve this issue, we propose here a tensor-coupling scheme that invokes all the components of a reference multiplet (i.e., a tensor reference) rather than increases the excitation ranks. A minimal spin-adapted n-tuply excited configuration space can readily be constructed by tensor products between the n-tuple tensor excitation operators and the chosen tensor reference. Further combined with the tensor equation-of-motion formalism, very compact expressions for excitation energies can be obtained. As a first application of this general idea, a spin-adapted open-shell random phase approximation is first developed. The so-called "translation rule" is then adopted to formulate a spin-adapted, restricted open-shell Kohn-Sham (ROKS)-based TD-DFT (ROKS-TD-DFT). Here, a particular symmetry structure has to be imposed on the exchange-correlation kernel. While the standard ROKS-TD-DFT can access only excited states due to singlet-coupled single excitations, i.e., only some of the singly excited states of the same spin (S(i)) as the reference, the new scheme can capture all the excited states of spin S(i)-1, S(i), or S(i)+1 due to both singlet- and triplet-coupled single excitations. The actual implementation and computation are very much like the (spin-contaminated) unrestricted Kohn-Sham-based TD-DFT. It is also shown that spin-contaminated spin-flip configuration interaction approaches can easily be spin-adapted via the tensor-coupling scheme.

The Theory of (Exclusively) Local Beables

Abstract: It is shown how, starting with the de Broglie–Bohm pilot-wave theory, one can construct a new theory of the sort envisioned by several of QM’s founders: a Theory of Exclusively Local Beables (TELB). In particular, the usual quantum mechanical wave function (a function on a high-dimensional configuration space) is not among the beables posited by the new theory. Instead, each particle has an associated “pilot-wave” field (living in physical space). A number of additional fields (also fields on physical space) maintain what is described, in ordinary quantum theory, as “entanglement.” The theory allows some interesting new perspective on the kind of causation involved in pilot-wave theories in general. And it provides also a concrete example of an empirically viable quantum theory in whose formulation the wave function (on configuration space) does not appear—i.e., it is a theory according to which nothing corresponding to the configuration space wave function need actually exist. That is the theory’s raison d’etre and perhaps its only virtue. Its vices include the fact that it only reproduces the empirical predictions of the ordinary pilot-wave theory (equivalent, of course, to the predictions of ordinary quantum theory) for spinless non-relativistic particles, and only then for wave functions that are everywhere analytic. The goal is thus not to recommend the TELB proposed here as a replacement for ordinary pilot-wave theory (or ordinary quantum theory), but is rather to illustrate (with a crude first stab) that it might be possible to construct a plausible, empirically viable TELB, and to recommend this as an interesting and perhaps-fruitful program for future research.

Symplectic topology of Mañé's critical values

Abstract: We study the dynamics and symplectic topology of energy hypersurfaces of mechanical Hamiltonians on twisted cotangent bundles. We pay particular attention to periodic orbits, displaceability, stability and the contact type property, and the changes that occur at the Mane critical value c . Our main tool is Rabinowitz Floer homology. We show that it is defined for hypersurfaces that are either stable tame or virtually contact, and that it is invariant under homotopies in these classes. If the configuration space admits a metric of negative curvature, then Rabinowitz Floer homology does not vanish for energy levels k > c and, as a consequence, these level sets are not displaceable. We provide a large class of examples in which Rabinowitz Floer homology is nonzero for energy levels k > c but vanishes for k < c , so levels above and below c cannot be connected by a stable tame homotopy. Moreover, we show that for strictly 1=4‐pinched negative curvature and nonexact magnetic fields all sufficiently high energy levels are nonstable, provided that the dimension of the base manifold is even and different from two. 53D40; 37D40

Phase-space dynamics of runaway electrons in tokamaks

Abstract: The phase-space dynamics of runaway electrons is studied, including the influence of loop voltage, radiation damping, and collisions. A theoretical model and a numerical algorithm for the runaway dynamics in phase space are developed. Instead of standard integrators, such as the Runge-Kutta method, a variational symplectic integrator is applied to simulate the long-term dynamics of a runaway electron. The variational symplectic integrator is able to globally bound the numerical error for arbitrary number of time-steps, and thus accurately track the runaway trajectory in phase space. Simulation results show that the circulating orbits of runaway electrons drift outward toward the wall, which is consistent with experimental observations. The physics of the outward drift is analyzed. It is found that the outward drift is caused by the imbalance between the increase of mechanical angular momentum and the input of toroidal angular momentum due to the parallel acceleration. An analytical expression of the outward drift velocity is derived. The knowledge of trajectory of runaway electrons in configuration space sheds light on how the electrons hit the first wall, and thus provides clues for possible remedies.

A quadratic regulator-based heuristic for rapidly exploring state space

Abstract: Kinodynamic planning algorithms like Rapidly-Exploring Randomized Trees (RRTs) hold the promise of finding feasible trajectories for rich dynamical systems with complex, nonconvex constraints. In practice, these algorithms perform very well on configuration space planning, but struggle to grow efficiently in systems with dynamics or differential constraints. This is due in part to the fact that the conventional distance metric, Euclidean distance, does not take into account system dynamics and constraints when identifying which node in the existing tree is capable of producing children closest to a given point in state space. We show that an affine quadratic regulator (AQR) design can be used to approximate the exact minimum-time distance pseudometric at a reasonable computational cost. We demonstrate improved exploration of the state spaces of the double integrator and simple pendulum when using this pseudometric within the RRT framework, but this improvement drops off as systems' nonlinearity and complexity increase. Future work includes exploring methods for approximating the exact minimum-time distance pseudometric that can reason about dynamics with higher-order terms.

Generalized Møller-Plesset Partitioning in Multiconfiguration Perturbation Theory.

Abstract: Two perturbation (PT) theories are developed starting from a multiconfiguration (MC) zero-order function. To span the configuration space, the theories employ biorthogonal vector sets introduced in the MCPT framework. At odds with previous formulations, the present construction operates with the full Fockian corresponding to a principal determinant, giving rise to a nondiagonal matrix of the zero-order resolvent. The theories provide a simple, generalized Moller-Plesset (MP) second-order correction to improve any reference function, corresponding either to a complete or incomplete model space. Computational demand of the procedure is determined by the iterative inversion of the Fockian, similarly to the single reference MP theory calculated in a localized basis. Relation of the theory to existing multireference (MR) PT formalisms is discussed. The performance of the present theories is assessed by adopting the antisymmetric product of strongly orthogonal geminal (APSG) wave functions as the reference function.

Configuring software product line feature models based on Stakeholders' soft and hard requirements

Abstract: Feature modeling is a technique for capturing commonality and variability. Feature models symbolize a representation of the possible application configuration space, and can be customized based on specific domain requirements and stakeholder goals. Most feature model configuration processes neglect the need to have a holistic approach towards the integration and satisfaction of the stakeholder's soft and hard constraints, and the application-domain integrity constraints. In this paper, we will show how the structure and constraints of a feature model can be modeled uniformly through Propositional Logic extended with concrete domains, called P(N). Furthermore, we formalize the representation of soft constraints in fuzzy P(N) and explain how semi-automated feature model configuration is performed. The model configuration derivation process that we propose respects the soundness and completeness properties.

Quantum cosmological metroland model

Abstract: Relational particle mechanics is useful for modelling whole-universe issues such as quantum cosmology or the problem of time in quantum gravity, including some aspects outside the reach of comparably complex mini-superspace models. In this paper, we consider the mechanics of pure shape and not scale of four particles on a line, so that the only physically significant quantities are ratios of relative separations between the constituents' physical objects. Many of our ideas and workings extend to the N-particle case. As such models' configurations resemble depictions of metro lines in public transport maps, we term them 'N-stop metrolands'. This 4-stop model's configuration space is a 2-sphere, from which our metroland mechanics interpretation is via the 'cubic' tessellation. This model yields conserved quantities which are mathematically SO(3) objects like angular momenta but are physically relative dilational momenta (i.e. coordinates dotted with momenta). We provide and interpret various exact and approximate classical and quantum solutions for 4-stop metroland; from these results one can construct expectations and spreads of shape operators that admit interpretations as relative sizes and the 'homogeneity of the model universe's contents', and also objects of significance for the problem of time in quantum gravity (e.g. in the naive Schrodinger and records theory timeless approaches).

Singularity problem and phase-space noncanonical noncommutativity

Abstract: The Wheeler-DeWitt equation arising from a Kantowski-Sachs model is considered for a Schwarzschild black hole under the assumption that the scale factors and the associated momenta satisfy a noncanonical noncommutative extension of the Heisenberg-Weyl algebra. An integral of motion is used to factorize the wave function into an oscillatory part and a function of a configuration space variable. The latter is shown to be normalizable using asymptotic arguments. It is then shown that on the hypersurfaces of constant value of the argument of the wave function's oscillatory piece, the probability vanishes in the vicinity of the black hole singularity.

On the relation between operator constraint, master constraint, reduced phase space and path integral quantization

Abstract: Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space formulation. In this paper we review this rather involved procedure in full generality. Moreover, we demonstrate that the reduced phase space path integral formulation formally agrees with the Dirac's operator constraint quantization and, more specifically, with the master constraint quantization for first-class constraints. For first-class constraints with nontrivial structure functions the equivalence can only be established by passing to Abelian(ized) constraints which is always possible locally in phase space. Generically, the correct configuration space path integral measure deviates from the exponential of the Lagrangian action. The corrections are especially severe if the theory suffers from second-class secondary constraints. In a companion paper we compute these corrections for the Holst and Plebanski formulations of GR on which current spin foam models are based.

Homotopic Path Planning on Manifolds for Cabled Mobile Robots

Abstract: We present two path planning algorithms for mobile robots that are connected by cable to a fixed base. Our algorithms efficiently compute the shortest path and control strategy that lead the robot to the target location considering cable length and obstacle interactions. First, we focus on cable-obstacle collisions.We introduce and formally analyze algorithms that build and search an overlapped configuration space manifold. Next, we present an extension that considers cable-robot collisions. All algorithms are experimentally validated using a real robot.

Characteristic Classes and Integrable Systems. General Construction

Abstract: We consider topologically non-trivial Higgs bundles over elliptic curves with marked points and construct corresponding integrable systems. In the case of one marked point we call them the modified Calogero-Moser systems (MCM systems). Their phase space has the same dimension as the phase space of the standard CM systems with spin, but less number of particles and greater number of spin variables. Topology of the holomorphic bundles are defined by their characteristic classes. Such bundles occur if G has a non-trivial center, i.e. classical simply-connected groups, $E_6$ and $E_7$. We define the conformal version CG of G - an analog of GL(N) for SL(N), and relate the characteristic classes with degrees of CG-bundles. Starting with these bundles we construct Lax operators, quadratic Hamiltonians, define the phase spaces and the Poisson structure using dynamical r-matrices. To describe the systems we use a special basis in the Lie algebras that generalizes the basis of t'Hooft matrices for sl(N). We find that the MCM systems contain the standard CM systems related to some (unbroken) subalgebras. The configuration space of the CM particles is the moduli space of the holomorphic bundles with non-trivial characteristic classes.

Probabilistically complete planning with end-effector pose constraints

Abstract: We present a proof for the probabilistic completeness of RRT-based algorithms when planning with constraints on end-effector pose Pose constraints can induce lower-dimensional constraint manifolds in the configuration space of the robot, making rejection sampling techniques infeasible RRT-based algorithms can overcome this problem by using the sample-project method: sampling coupled with a projection operator to move configuration space samples onto the constraint manifold Until now it was not known whether the sample-project method produces adequate coverage of the constraint manifold to guarantee probabilistic completeness The proof presented in this paper guarantees probabilistic completeness for a class of RRT-based algorithms given an appropriate projection operator This proof is valid for constraint manifolds of any fixed dimensionality

Hot plug process in a distributed interconnect bus

Abstract: A distributed PCIe adapted to support a hot-plug process triggered by any change in a status of a distributed link, comprises an upstream bus unit including a first bridge connected to a root component and adapted to maintain a first configuration space and a copy of a second configuration space, the first configuration space bridge includes at least hot-plug registers specifying at least capabilities and status of a slot of the first bridge; and a second bridge connected to an endpoint component and adapted to maintain the second configuration space, the second configuration space includes at least hot-plug registers specifying at least capabilities and status of a slot of the second bridge.

Study of the noise-induced transition and the exploration of the phase space for the Kuramoto?Sivashinsky equation using the minimum action method

Abstract: Noise-induced transition in the solutions of the Kuramoto–Sivashinsky (K–S) equation is investigated using the minimum action method derived from the large deviation theory. This is then used as a starting point for exploring the configuration space of the K–S equation. The particular example considered here is the transition between a stable fixed point and a stable travelling wave. Five saddle points, up to constants due to translational invariance, are identified based on the information given by the minimum action path. Heteroclinic orbits between the saddle points are identified. Relations between noise-induced transitions and the saddle points are examined.

Characterizing Graphs with Convex and Connected Cayley Configuration Spaces

Abstract: We define and study exact, efficient representations of realization spaces Euclidean Distance Constraint Systems (EDCS), which include Linkages and Frameworks. These are graphs with distance assignments on the edges (frameworks) or graphs with distance interval assignments on the edges. Each representation corresponds to a choice of non-edge (squared) distances or Cayley parameters. The set of realizable distance assignments to the chosen parameters yields a parametrized Cayley configuration space. Our notion of efficiency is based on the convexity and connectedness of the Cayley configuration space, as well as algebraic complexity of sampling realizations, i.e., sampling the Cayley configuration space and obtaining a realization from the sample (parametrized) configuration. Significantly, we give purely graph-theoretic, forbidden minor characterizations for 2D and 3D EDCS that capture (i) the class of graphs that always admit efficient Cayley configuration spaces and (ii) the possible choices of representation parameters that yield efficient Cayley configuration spaces for a given graph. We show that the easy direction of the 3D characterization extends to arbitrary dimension d and is related to the concept of d-realizability of graphs. Our results automatically yield efficient algorithms for obtaining exact descriptions of the Cayley configuration spaces and for sampling realizations, without missing extreme or boundary realizations. In addition, our results are tight: we show counterexamples to obvious extensions. This is the first step in a systematic and graded program of combinatorial characterizations of efficient Cayley configuration spaces. We discuss several future theoretical and applied research directions. In particular, the results presented here are the first to completely characterize EDCS that have connected, convex and efficient Cayley configuration spaces, based on precise and formal measures of efficiency. It should be noted that our results do not rely on genericity of the EDCS. Some of our proofs employ an unusual interplay of (a) classical analytic results related to positive semi-definiteness of Euclidean distance matrices, with (b) recent forbidden minor characterizations and algorithms related to d-realizability of graphs. We further introduce a novel type of restricted edge contraction or reduction to a graph minor, a “trick” that we anticipate will be useful in other situations.

Study of coordinated motions of the human hand for robotic applications

Abstract: This paper presents an acquisition method that comprehensively looks for the mimic configurations of the human hand. The data obtained through this process is further analyzed, transformed, and then used to synthesize a reduced configuration space of a robot anthropomorphic hand. The method rely on a dimensionality reduction technique that provides a new basis of the full configuration space, from which one can select a subset of the vectors forming that basis, and finally obtaining a simpler configuration subspace. These vectors are called Principal Motion Directions, and represent the coordinated motions captured by a sensorized glove on a human hand and transferred to the robot hand. The characteristics and limitations of the subspace are discussed, as well as its application in several scenarios within robotics such as the motion planning of robot hands, where the subspace has been successfully implemented and executed.

Relational mechanics of shape and scale

Abstract: Relational particle mechanics models (RPM's) are useful models for the problem of time in quantum gravity and other foundational issues in quantum cosmology. Some concrete examples of scalefree RPM's have already been studied, but it is the case with scale that is needed for the semiclassical and dilational internal time approaches to the problem of time. In this paper, I show that the scaled RPM's configuration spaces are the cones over the scalefree RPM's configuration spaces, which are spheres in 1-d and complex projective spaces in 2-d for plain shapes, and these quotiented by Z_2 for oriented shapes. I extend the method of physical interpretation by tessellation of the configuration space and the description in terms of geometrical quantities to the cases with scale and/or orientation. I show that there is an absence of monopole issues for RPM's and point out a difference between quantum cosmological operator ordering and that used in molecular physics. I use up RPM's freedom of the form of the potential to more closely parallel various well-known cosmologies, and begin the investigation of the semiclassical approach to the problem of time for such models.

Re-examining the directional-ordering transition in the compass model with screw-periodic boundary conditions

Abstract: We study the directional-ordering transition in the two-dimensional classical and quantum compass models on the square lattice by means of Monte Carlo simulations. An improved algorithm is presented which builds on the Wolff cluster algorithm in one-dimensional subspaces of the configuration space. This improvement allows us to study classical systems up to L=512. Based on this algorithm, we give evidence for the presence of strongly anomalous scaling for periodic boundary conditions which is much worse than anticipated before. We propose and study alternative boundary conditions for the compass model which do not make use of extended configuration spaces and show that they completely remove the problem with finite-size scaling. In the last part, we apply these boundary conditions to the quantum problem and present a considerably improved estimate for the critical temperature which should be of interest for future studies on the compass model. Our investigation identifies a strong one-dimensional magnetic ordering tendency with a large correlation length as the cause of the unusual scaling and moreover allows for a precise quantification of the anomalous length scale involved.