Showing papers on "Configuration space published in 2017"

Finding near-optimal configurations in product lines by random sampling

Abstract: Software Product Lines (SPLs) are highly configurable systems. This raises the challenge to find optimal performing configurations for an anticipated workload. As SPL configuration spaces are huge, it is infeasible to benchmark all configurations to find an optimal one. Prior work focused on building performance models to predict and optimize SPL configurations. Instead, we randomly sample and recursively search a configuration space directly to find near-optimal configurations without constructing a prediction model. Our algorithms are simpler and have higher accuracy and efficiency.

Tessellating cushions: four-point functions in N $$ \mathcal{N} $$ = 4 SYM

Abstract: We consider a class of planar tree-level four-point functions in $$ \mathcal{N} $$ = 4 SYM in a special kinematic regime: one BMN operator with two scalar excitations and three half-BPS operators are put onto a line in configuration space; additionally, for the half-BPS operators a co-moving frame is chosen in flavour space. In configuration space, the four-punctured sphere is naturally triangulated by tree-level planar diagrams. We demonstrate on a number of examples that each tile can be associated with a modified hexagon form-factor in such a way as to efficiently reproduce the tree-level four-point function. Our tessellation is not of the OPE type, fostering the hope of finding an independent, integrability-based approach to the computation of planar four-point functions.

Unwinding the Amplituhedron in Binary

Abstract: We present new, fundamentally combinatorial and topological characterizations of the amplituhedron. Upon projecting external data through the amplituhedron, the resulting configuration of points has a specified (and maximal) generalized 'winding number'. Equivalently, the amplituhedron can be fully described in binary: canonical projections of the geometry down to one dimension have a specified (and maximal) number of 'sign flips' of the projected data. The locality and unitarity of scattering amplitudes are easily derived as elementary consequences of this binary code. Minimal winding defines a natural 'dual' of the amplituhedron. This picture gives us an avatar of the amplituhedron purely in the configuration space of points in vector space (momentum-twistor space in the physics), a new interpretation of the canonical amplituhedron form, and a direct bosonic understanding of the scattering super-amplitude in planar N = 4 SYM as a differential form on the space of physical kinematical data.

Transfer learning for improving model predictions in highly configurable software

Abstract: Modern software systems are built to be used in dynamic environments using configuration capabilities to adapt to changes and external uncertainties. In a self-adaptation context, we are often interested in reasoning about the performance of the systems under different configurations. Usually, we learn a black-box model based on real measurements to predict the performance of the system given a specific configuration. However, as modern systems become more complex, there are many configuration parameters that may interact and we end up learning an exponentially large configuration space. Naturally, this does not scale when relying on real measurements in the actual changing environment. We propose a different solution: Instead of taking the measurements from the real system, we learn the model using samples from other sources, such as simulators that approximate performance of the real system at low cost. We define a cost model that transform the traditional view of model learning into a multi-objective problem that not only takes into account model accuracy but also measurements effort as well. We evaluate our cost-aware transfer learning solution using real-world configurable software including (i) a robotic system, (ii) 3 different stream processing applications, and (iii) a NoSQL database system. The experimental results demonstrate that our approach can achieve (a) a high prediction accuracy, as well as (b) a high model reliability.

In-medium similarity renormalization group for closed and open-shell nuclei

Abstract: We present a pedagogical introduction to the In-Medium Similarity Renormalization Group (IM-SRG) framework for ab initio calculations of nuclei. The IM-SRG performs continuous unitary transformations of the nuclear many-body Hamiltonian in second-quantized form, which can be implemented with polynomial computational effort. Through suitably chosen generators, it is possible to extract eigenvalues of the Hamiltonian in a given nucleus, or drive the Hamiltonian matrix in configuration space to specific structures, e.g., band- or block-diagonal form. Exploiting this flexibility, we describe two complementary approaches for the description of closed- and open-shell nuclei: The first is the Multireference IM-SRG (MR-IM-SRG), which is designed for the efficient calculation of nuclear ground-state properties. The second is the derivation of nonempirical valence-space interactions that can be used as input for nuclear Shell model (i.e., configuration interaction (CI)) calculations. This IM-SRG+Shell model approach provides immediate access to excitation spectra, transitions, etc., but is limited in applicability by the factorial cost of the CI calculations. We review applications of the MR-IM-SRG and IM-SRG+Shell model approaches to the calculation of ground-state properties for the oxygen, calcium, and nickel isotopic chains or the spectroscopy of nuclei in the lower $sd$ shell, respectively, and present selected new results, e.g., for the ground- and excited state properties of neon isotopes.

A two-level approach for solving the inverse kinematics of an extensible soft arm considering viscoelastic behavior

Abstract: Soft compliant materials and novel actuation mechanisms ensure flexible motions and high adaptability for soft robots, but also increase the difficulty and complexity of constructing control systems. In this work, we provide an efficient control algorithm for a multi-segment extensible soft arm in 2D plane. The algorithm separate the inverse kinematics into two levels. The first level employs gradient descent to select optimized arm's pose (from task space to configuration space) according to designed cost functions. With consideration of viscoelasticity, the second level utilizes neural networks to figure out the pressures from each segment's pose (from configuration space to actuation space). In experiments with a physical prototype, the control accuracy and effectiveness are validated, where the control algorithm is further improved by an optional feedback strategy.

Parallel tempering algorithm for integration over Lefschetz thimbles

Abstract: The algorithm based on integration over Lefschetz thimbles is a promising method to resolve the sign problem for complex actions. However, this algorithm often meets a difficulty in actual Monte Carlo calculations because the configuration space is not easily explored due to the infinitely high potential barriers between different thimbles. In this paper, we propose to use the flow time of the antiholomorphic gradient flow as an auxiliary variable for the highly multimodal distribution. To illustrate this, we implement the parallel tempering method by taking the flow time as a tempering parameter. In this algorithm, we can take the maximum flow time to be sufficiently large such that the sign problem disappears there, and two separate modes are connected through configurations at small flow times. To exemplify that this algorithm does work, we investigate the (0+1)-dimensional massive Thirring model at finite density and show that our algorithm correctly reproduces the analytic results for large flow times such as T=2.

Our Fundamental Physical Space: An Essay on the Metaphysics of the Wave Function

Abstract: The mathematical structure of realist quantum theories has given rise to an interesting ongoing debate about how our ordinary 3-dimensional space is related to the 3N-dimensional configuration space on which the wave function is defined. Which of the two spaces is our (more) fundamental physical space? In this essay, I review the debate between the 3N-Fundamentalists (wave function realists) and the 3D-Fundamentalists (primitive ontologists). Instead of framing the debate as putting different weights on different kinds of evidence, I shall evaluate them on how they are overall supported on the basis of: (1) the dynamical structure of the quantum theory, (2) our perceptual evidence of the 3D-space, and (3) mathematical symmetries in the wave function. I show that the common arguments based on (1) and (2) are either unsound or incomplete. Completing the arguments, it seems to me, render the overall considerations based on (1) and (2) roughly in favor of 3D-Fundamentalism. A more decisive argument, however, is found when we consider which view leads to a deeper understanding of the physical world. In fact, given the deeper topological explanation from the unordered configurations to the Symmetrization Postulate, we have strong reasons counting in favor of 3D-Fundamentalism. I therefore conclude that our current overall evidence strongly favors the view that our fundamental physical space in a quantum world is 3-dimensional rather than 3N-dimensional. I also outline future lines of research where the evidential balance can be restored or reversed. To push the analysis further, I draw some lessons from this case study to the debate on theoretical equivalence.

Parallel tempering algorithm for integration over Lefschetz thimbles

Abstract: The algorithm based on integration over Lefschetz thimbles is a promising method to resolve the sign problem for complex actions. However, this algorithm often meets a difficulty in actual Monte Carlo calculations because the configuration space is not easily explored due to the infinitely high potential barriers between different thimbles. In this paper, we propose to use the flow time of the antiholomorphic gradient flow as an auxiliary variable for the highly multimodal distribution. To illustrate this, we implement the parallel tempering method by taking the flow time as a tempering parameter. In this algorithm, we can take the maximum flow time to be sufficiently large such that the sign problem disappears there, and two separate modes are connected through configurations at small flow times. To exemplify that this algorithm does work, we investigate the (0+1)-dimensional massive Thirring model at finite density and show that our algorithm correctly reproduces the analytic results for large flow times such as T=2.

Betti numbers and stability for configuration spaces via factorization homology

Abstract: Using factorization homology, we realize the rational homology of the unordered configuration spaces of an arbitrary manifold $M$, possibly with boundary, as the homology of a Lie algebra constructed from the compactly supported cohomology of $M$. By locating the homology of each configuration space within the Chevalley-Eilenberg complex of this Lie algebra, we extend theorems of Bodigheimer-Cohen-Taylor and Felix-Thomas and give a new, combinatorial proof of the homological stability results of Church and Randal-Williams. Our method lends itself to explicit calculations, examples of which we include.

A deep reinforcement learning approach for dynamically stable inverse kinematics of humanoid robots

Abstract: Real time calculation of inverse kinematics (IK) with dynamically stable configuration is of high necessity in humanoid robots as they are highly susceptible to lose balance. This paper proposes a methodology to generate joint-space trajectories of stable configurations for solving inverse kinematics using Deep Reinforcement Learning (RL). Our approach is based on the idea of exploring the entire configuration space of the robot and learning the best possible solutions using Deep Deterministic Policy Gradient (DDPG). The proposed strategy was evaluated on the highly articulated upper body of a humanoid model with 27 degree of freedom (DoF). The trained model was able to solve inverse kinematics for the end effectors with 90% accuracy while maintaining the balance in double support phase.

Three-Dimensional Localized-Delocalized Anderson Transition in the Time Domain.

Abstract: Systems which can spontaneously reveal periodic evolution are dubbed time crystals. This is in analogy with space crystals that display periodic behavior in configuration space. While space crystals are modeled with the help of space periodic potentials, crystalline phenomena in time can be modeled by periodically driven systems. Disorder in the periodic driving can lead to Anderson localization in time: the probability for detecting a system at a fixed point of configuration space becomes exponentially localized around a certain moment in time. We here show that a three-dimensional system exposed to a properly disordered pseudoperiodic driving may display a localized-delocalized Anderson transition in the time domain, in strong analogy with the usual three-dimensional Anderson transition in disordered systems. Such a transition could be experimentally observed with ultracold atomic gases.

Low-Energy Fock-Space Localization for Attractive Hard-Core Particles in Disorder

Abstract: We study a one-dimensional quantum system with an arbitrary number of hard-core particles on the lattice, which are subject to a deterministic attractive interaction as well as a random potential. Our choice of interaction is suggested by the spectral analysis of the XXZ quantum spin chain. The main result concerns a version of high-disorder Fock-space localization expressed here in the configuration space of hard-core particles. The proof relies on an energetically motivated Combes–Thomas estimate and an effective one-particle analysis. As an application, we show the exponential decay of the two-point function in the infinite system uniformly in the particle number.

G 2 -structures and quantization of non-geometric M-theory backgrounds

Abstract: We describe the quantization of a four-dimensional locally non-geometric M-theory background dual to a twisted three-torus by deriving a phase space star product for deformation quantization of quasi-Poisson brackets related to the nonassociative algebra of octonions. The construction is based on a choice of G 2-structure which defines a nonassociative deformation of the addition law on the seven-dimensional vector space of Fourier momenta. We demonstrate explicitly that this star product reduces to that of the three-dimensional parabolic constant R-flux model in the contraction of M-theory to string theory, and use it to derive quantum phase space uncertainty relations as well as triproducts for the nonassociative geometry of the four-dimensional configuration space. By extending the G 2-structure to a Spin(7)-structure, we propose a 3-algebra structure on the full eight-dimensional M2-brane phase space which reduces to the quasi-Poisson algebra after imposing a particular gauge constraint, and whose deformation quantisation simultaneously encompasses both the phase space star products and the configuration space triproducts. We demonstrate how these structures naturally fit in with previous occurences of 3-algebras in M-theory.

Anderson localization of a Rydberg electron along a classical orbit

Abstract: Anderson localization is related to exponential localization of a particle in the configuration space in the presence of a disorder potential. Anderson localization can be also observed in the momentum space and corresponds to quantum suppression of classical diffusion in systems that are classically chaotic. Another kind of Anderson localization has been recently proposed, i.e. localization in the time domain due to the presence of {\it disorder} in time. That is, the probability density for the detection of a system at a fixed position in the configuration space is localized exponentially around a certain moment of time if a system is driven by a force that fluctuates in time. We show that an electron in a Rydberg atom, perturbed by a fluctuating microwave field, Anderson localizes along a classical periodic orbit. In other words the probability density for the detection of an electron at a fixed position on an orbit is exponentially localized around a certain time moment. This phenomenon can be experimentally observed.

Poincaré's equations for Cosserat media : application to shells

Abstract: In 1901 Henri Poincare discovered a new set of equations for mechanics. These equations are a generalization of Lagrange's equations for a system whose configuration space is a Lie group which is not necessarily commutative. Since then, this result has been extensively refined through the Lagrangian reduction theory. In the present contribution, we extend these equations from classical mechanical systems to continuous Cosserat media, i.e. media in which the usual point particles are replaced by small rigid bodies, called micro-structures. In particular, we will see how the Shell balance equations used in nonlinear structural dynamics, can be easily derived from this extension of the Poincare's result.

Decoding heat capacity features from the energy landscape.

Abstract: A general scheme is derived to connect transitions in configuration space with features in the heat capacity. A formulation in terms of occupation probabilities for local minima that define the potential energy landscape provides a quantitative description of how contributions arise from competition between different states. The theory does not rely on a structural interpretation for the local minima, so it is equally applicable to molecular energy landscapes and the landscapes defined by abstract functions. Applications are presented for low-temperature solid-solid transitions in atomic clusters, which involve just a few local minima with different morphologies, and for cluster melting, which is driven by the landscape entropy associated with the more numerous high-energy minima. Analyzing these features in terms of the balance between states with increasing and decreasing occupation probabilities provides a direct interpretation of the underlying transitions. This approach enables us to identify a qualitatively different transition that is caused by a single local minimum associated with an exceptionally large catchment volume in configuration space for a machine learning landscape.

Structure and decays of nuclear three-body systems: The Gamow coupled-channel method in Jacobi coordinates

Abstract: Background: Weakly bound and unbound nuclear states appearing around particle thresholds are prototypical open quantum systems. Theories of such states must take into account configuration mixing effects in the presence of strong coupling to the particle continuum space.Purpose: To describe structure and decays of three-body systems, we developed a Gamow coupled-channel (GCC) approach in Jacobi coordinates by employing the complex-momentum formalism. We benchmarked the complex-energy Gamow shell model (GSM) against the new framework.Methods: The GCC formalism is expressed in Jacobi coordinates, so that the center-of-mass motion is automatically eliminated. To solve the coupled-channel equations, we use hyperspherical harmonics to describe the angular wave functions while the radial wave functions are expanded in the Berggren ensemble, which includes bound, scattering, and Gamow states.Results: We show that the GCC method is both accurate and robust. Its results for energies, decay widths, and nucleon-nucleon angular correlations are in good agreement with the GSM results.Conclusions: We have demonstrated that a three-body GSM formalism explicitly constructed in the cluster-orbital shell model coordinates provides results similar to those with a GCC framework expressed in Jacobi coordinates, provided that a large configuration space is employed. Our calculations for $A=6$ systems and $^{26}\mathrm{O}$ show that nucleon-nucleon angular correlations are sensitive to the valence-neutron interaction. The new GCC technique has many attractive features when applied to bound and unbound states of three-body systems: it is precise, is efficient, and can be extended by introducing a microscopic model of the core.

A Local Order Parameter-Based Method for Simulation of Free Energy Barriers in Crystal Nucleation.

Abstract: While global order parameters have been widely used as reaction coordinates in nucleation and crystallization studies, their use in nucleation studies is claimed to have a serious drawback. In this work, a local order parameter is introduced as a local reaction coordinate to drive the simulation from the liquid phase to the solid phase and vice versa. This local order parameter holds information regarding the order in the first- and second-shell neighbors of a particle and has different well-defined values for local crystallites and disordered neighborhoods but is insensitive to the type of the crystal structure. The order parameter is employed in metadynamics simulations to calculate the solid–liquid phase equilibria and free energy barrier to nucleation. Our results for repulsive soft spheres and the Lennard-Jones potential, LJ(12–6), reveal better-resolved solid and liquid basins compared with the case in which a global order parameter is used. It is also shown that the configuration space is sampled m...

Repeatable Motion Planning for Redundant Robots Over Cyclic Tasks

Abstract: We consider the problem of repeatable motion planning for redundant robotic systems performing cyclic tasks in the presence of obstacles. For this open problem, we present a control-based randomized planner, which produces closed collision-free paths in configuration space and guarantees continuous satisfaction of the task constraints. The proposed algorithm, which relies on bidirectional search and loop closure in the task-constrained configuration space, is shown to be probabilistically complete. A modified version of the planner is also devised for the case in which configuration-space paths are required to be smooth. Finally, we present planning results in various scenarios involving both free-flying and nonholonomic robots to show the effectiveness of the proposed method.

$G_2$-structures and quantization of non-geometric M-theory backgrounds

Abstract: We describe the quantization of a four-dimensional locally non-geometric M-theory background dual to a twisted three-torus by deriving a phase space star product for deformation quantization of quasi-Poisson brackets related to the nonassociative algebra of octonions. The construction is based on a choice of $G_2$-structure which defines a nonassociative deformation of the addition law on the seven-dimensional vector space of Fourier momenta. We demonstrate explicitly that this star product reduces to that of the three-dimensional parabolic constant $R$-flux model in the contraction of M-theory to string theory, and use it to derive quantum phase space uncertainty relations as well as triproducts for the nonassociative geometry of the four-dimensional configuration space. By extending the $G_2$-structure to a $Spin(7)$-structure, we propose a 3-algebra structure on the full eight-dimensional M2-brane phase space which reduces to the quasi-Poisson algebra after imposing a particular gauge constraint, and whose deformation quantisation simultaneously encompasses both the phase space star products and the configuration space triproducts. We demonstrate how these structures naturally fit in with previous occurences of 3-algebras in M-theory.

Emergent facilitation behavior in a distinguishable-particle lattice model of glass

Abstract: We propose an interacting lattice gas model of structural glass characterized by particle distinguishability and site-particle-dependent random nearest-neighboring particle interactions. This incorporates disorder quenched in the configuration space rather than in the physical space. The model exhibits nontrivial energetics while still admitting exact equilibrium states directly constructible at arbitrary temperature and density. The dynamics is defined by activated hopping following standard kinetic Monte Carlo approach without explicit facilitation rule. Kinetic simulations show emergent dynamic facilitation behaviors in the glassy phase in which motions of individual voids are significant only when accelerated by other voids nearby. This provides a microscopic justification for the dynamic facilitation picture of structural glass.

Homology groups for particles on one-connected graphs

Abstract: We present a mathematical framework for describing the topology of configuration spaces for particles on one-connected graphs. In particular, we compute the homology groups over integers for different classes of one-connected graphs. Our approach is based on some fundamental combinatorial properties of the configuration spaces, Mayer-Vietoris sequences for different parts of configuration spaces, and some limited use of discrete Morse theory. As one of the results, we derive the closed-form formulae for ranks of the homology groups for indistinguishable particles on tree graphs. We also give a detailed discussion of the second homology group of the configuration space of both distinguishable and indistinguishable particles. Our motivation is the search for new kinds of quantum statistics.

Noninteracting constrained motion planning and control for robot manipulators

Abstract: In this paper we present a novel geometric approach to motion planning for constrained robot systems. This problem is notoriously hard, as classical sampling-based methods do not easily apply when motion is constrained in a zero-measure submanifold of the configuration space. Based on results on the functional controllability theory of dynamical systems, we obtain a description of the complementary spaces where rigid body motions can occur, and where interaction forces can be generated, respectively. Once this geometric setting is established, the motion planning problem can be greatly simplified. Indeed, we can relax the geometric constraint, i.e., replace the lower-dimensional constraint manifold with a full-dimensional boundary layer. This in turn allows us to plan motion using state-of-the-art methods, such as RRT∗, on points within the boundary layer, which can be efficiently sampled. On the other hand, the same geometric approach enables the design of a completely decoupled control scheme for interaction forces, so that they can be regulated to zero (or any other desired value) without interacting with the motion plan execution. A distinguishing feature of our method is that it does not use projection of sampled points on the constraint manifold, thus largely saving in computational time, and guaranteeing accurate execution of the motion plan. An explanatory example is presented, along with an experimental implementation of the method on a bimanual manipulation workstation.

Simulation of the experimental imaging results for the OH + CHD3 reaction with a simple and accurate theoretical approach.

Abstract: The OH + CHD3 reaction is among the largest one ever studied at the high-resolution level permitted by imaging techniques [B. Zhang et al., J. Phys. Chem. A, 2005, 109, 8989]. This process involves eighteen configuration space coordinates, which are large enough to make exact quantum scattering calculations beyond reach. Moreover, freezing some degrees-of-freedom in order to render these calculations feasible may lead to unrealistic predictions. However, we have found it possible to reproduce for the first time the pair-correlated measurements of Zhang et al. at a nearly quantitative level by means of full-dimensional classical trajectory calculations in a quantum spirit on a recent ab initio potential energy surface. These calculations combine the classical description of the dynamics, well suited to polyatomic systems, with Bohr quantization of both reagent and product vibrational motions. While this pseudo-quantization is exactly imposed to the reagents, it is approximately imposed to the products in a first step through energy-based Gaussian binning (1GB). In a second step, we show that the original action-based Gaussian binning (GB), long thought to be inapplicable in practice to polyatomic reactions, yields in fact results comparable in accuracy and numerical cost to those obtained by means of 1GB, provided that Gaussian weights are properly widened. This new finding clearly extends the scope of GB in theoretical reactive scattering.

Evaluation of 4-D Reaction Integrals in the Method of Moments: Coplanar Element Case

Abstract: Recently, the benefits of simultaneously treating source and testing integrals in the numerical evaluation of 4-D reaction integrals have been reported. The reported schemes usually first transform the reaction integral to parametric coordinates, and some combination of radial, angular, and/or line segment integrals is then used to treat coincident, edge-adjacent, or vertex-adjacent triangular source and test element pairs. However, advantages of the reported approaches are tempered by their lack of generality and severely degraded performance on poorly shaped elements, the latter caused primarily by the parametric transformations’ severe distortion of the kernel’s circularly concentric level contours. Here, for coplanar element pairs and kernels with 1/ $R$ singularities, we apply the surface divergence theorem twice to obtain a novel formula for 4-D reaction integrals, generalizing earlier schemes while retaining their benefits and without distorting the original configuration space. Numerical results illustrate the method’s efficiency, which is improved by employing appropriate transformations to further smooth the resulting integrands and hence accelerate their convergence. The reaction integral formula can be extended to noncoplanar elements.

Lie algebra type noncommutative phase spaces are Hopf algebroids

Abstract: For a noncommutative configuration space whose coordinate algebra is the universal enveloping algebra of a finite-dimensional Lie algebra, it is known how to introduce an extension playing the role of the corresponding noncommutative phase space, namely by adding the commuting deformed derivatives in a consistent and nontrivial way; therefore, obtaining certain deformed Heisenberg algebra. This algebra has been studied in physical contexts, mainly in the case of the kappa-Minkowski space-time. Here, we equip the entire phase space algebra with a coproduct, so that it becomes an instance of a completed variant of a Hopf algebroid over a noncommutative base, where the base is the enveloping algebra.

Kinematic Cartography and the Efficiency of Viscous Swimming

Abstract: The apparent “distance” between two configurations of a system and the “length” of trajectories through its configuration space can be significantly distorted by plots that use “natural” or intuitively selected coordinates. This effect is similar to the way that a latitude–longitude plot of the Earth distorts the size and shape of the continents. In this paper, we explore how ideas from cartography can be used to identify system parameterizations that better reflect the effort costs of changing configuration. We then apply these new parameters to provide geometric insight about two aspects of moving in dissipative environments such as low Reynolds number fluids: The shape of the optimal gait cycle for a three-link swimmer and the fundamentally superior efficiency of a serpenoid swimmer as compared to the classic three-link system.