Reduced Configuration Space Research Articles

ETune: Efficient configuration tuning for big-data software systems via configuration space reduction

Configuration tuning for big-data software systems is generally challenging due to the complex configuration space and costly performance evaluation. The workload changes over time in the context of big data making this problem even more difficult. To address the low efficiency issue caused by the need to retune from scratch after workload changes, we present ETune based on a combination of an Bayesian Optimization (BO) based tuner and configuration space reduction techniques to efficiently find high-performance configurations for big-data systems. For configuration space reduction, we develop two approaches: (1) shrinking the configuration space by trading off the exploitation and exploration between the impactful parameters and other parameters in the tuning process, (2) generating the promising regions of configuration space by transferring knowledge across past tuning tasks. The two configuration space reduction methods aim to reduce the huge configuration space to a compact but promising one, and searching in the reduced configuration space can further accelerate the configuration tuning. The extensive experiments show that our configuration space reduction methods considerably boost the BO-based tuner, and ETune significantly improves the tuning efficiency compared with the transfer learning based state-of-the-arts.

Quasi-canonicalization for linear homogeneous nonholonomic systems**Project supported by the National Natural Science Foundation of China (Grant Nos. 11972177, 11972122, 11802103, 11772144, 11872030, and 11572034) and the Scientific Research Starting Foundation for Scholars with Doctoral Degree of Guangdong Medical University (Grant Nos. B2019042 and B2019021).

For conservative linear homogeneous nonholonomic systems, there exists a cotangent bundle with the symplectic structure dπμ ∧ dξμ, in which the motion equations of the system can be written into the form of the canonical equations by the set of quasi-coordinates πμ and quasi-momenta ξμ. The key to construct this cotangent bundle is to define a set of suitable quasi-coordinates πμ by a first-order linear mapping, so that the reduced configuration space of the system is a Riemann space with no torsion. The Hamilton–Jacobi method for linear homogeneous nonholonomic systems is studied as an application of the quasi-canonicalization. The Hamilton–Jacobi method can be applied not only to Chaplygin nonholonomic systems, but also to non-Chaplygin nonholonomic systems. Two examples are given to illustrate the effectiveness of the quasi-canonicalization and the Hamilton–Jacobi method.

Averaging, symplectic reduction, and central extensions

We show that the averaged equation for a one-frequency fast-oscillating Hamiltonian system is the result of symplectic reduction of a certain natural system on the corresponding S1-bundle with respect to the circle action. Furthermore, if the reduced configuration space happens to be a group, then under natural assumptions the averaged system turns out to be the Euler equation on a central extension of that group. This gives a new explanation of the drift, common in averaged system, as a similar shift is typically present in symplectic reductions and central extensions.

Motion Planning of a Second-Order Nonholonomic Chained Form System Based on Holonomy Extraction

This paper proposes a motion planning algorithm for dynamic nonholonomic systems represented in a second-order chained form. The proposed approach focuses on the so-called holonomy resulting from a kind of motion that traverses a closed path in a reduced configuration space of the system. According to the author’s literature survey, control approaches that make explicit use of holonomy exist for kinematic nonholonomic systems but does not exist for dynamic nonholonomic systems. However, the second-order chained form system is controllable. Also, the structure of the second-order chained form system analogizes with the one of the first-order chained form for kinematic nonholonomic systems. These survey and perspectives brought a hypothesis that there exists a specific control strategy for extracting holonomy of the second-order chained form system to the author. To verify this hypothesis, this paper shows that the holonomy of the second-order chained form system can be extracted by combining two appropriate pairs of sinusoidal inputs. Then, based on such holonomy extraction, a motion planning algorithm is constructed. Furthermore, the effectiveness is demonstrated through some simulations including an application to an underactuated manipulator.

Quantum gravity in timeless configuration space

On the path towards quantum gravity we find friction between temporal relations in quantum mechanics (QM) (where they are fixed and field-independent), and in general relativity (where they are field-dependent and dynamic). This paper aims to attenuate that friction, by encoding gravity in the timeless configuration space of spatial fields with dynamics given by a path integral. The framework demands that boundary conditions for this path integral be uniquely given, but unlike other approaches where they are prescribed—such as the no-boundary and the tunneling proposals—here I postulate basic principles to identify boundary conditions in a large class of theories. Uniqueness arises only if a reduced configuration space can be defined and if it has a profoundly asymmetric fundamental structure. These requirements place strong restrictions on the field and symmetry content of theories encompassed here; shape dynamics is one such theory. When these constraints are met, any emerging theory will have a Born rule given merely by a particular volume element built from the path integral in (reduced) configuration space. Also as in other boundary proposals, Time, including space-time, emerges as an effective concept; valid for certain curves in configuration space but not assumed from the start. When some such notion of time becomes available, conservation of (positive) probability currents ensues. I show that, in the appropriate limits, a Schrödinger equation dictates the evolution of weakly coupled source fields on a classical gravitational background. Due to the asymmetry of reduced configuration space, these probabilities and currents avoid a known difficulty of standard WKB approximations for Wheeler DeWitt in minisuperspace: the selection of a unique Hamilton–Jacobi solution to serve as background. I illustrate these constructions with a simple example of a full quantum gravitational theory (i.e. not in minisuperspace) for which the formalism is applicable, and give a formula for calculating gravitational semi-classical relative probabilities in it.

Faster discovery of faster system configurations with spectral learning

Despite the huge spread and economical importance of configurable software systems, there is unsatisfactory support in utilizing the full potential of these systems with respect to finding performance-optimal configurations. Prior work on predicting the performance of software configurations suffered from either (a) requiring far too many sample configurations or (b) large variances in their predictions. Both these problems can be avoided using the WHAT spectral learner. WHAT's innovation is the use of the spectrum (eigenvalues) of the distance matrix between the configurations of a configurable software system, to perform dimensionality reduction. Within that reduced configuration space, many closely associated configurations can be studied by executing only a few sample configurations. For the subject systems studied here, a few dozen samples yield accurate and stable predictors--less than 10% prediction error, with a standard deviation of less than 2%. When compared to the state of the art, WHAT (a) requires 2---10 times fewer samples to achieve similar prediction accuracies, and (b) its predictions are more stable (i.e., have lower standard deviation). Furthermore, we demonstrate that predictive models generated by WHAT can be used by optimizers to discover system configurations that closely approach the optimal performance.

Online Semisingularity Avoidance for Three-Axis Tracking Pedestals

Three-axis tracking pedestals eliminate the keyhole problem and are widely used in whole-space-tracking missions. Owing to their rotary limits, however, such pedestals have semisingular postures. In these postures, they cannot follow targets moving in certain directions. More critically, when using common unilateral constraint avoidance approaches, there always exists a target movement for which the pedestal will be guided into semisingular configurations. This is a fatal defect when tracking noncooperative targets. To solve this serious problem, we propose a novel online solution for semisingularity avoidance. A reduced configuration space is developed so that the pedestal does not have semisingularity. We propose a general method to derive such a configuration space for the three-axis tracking pedestal under arbitrary elevation and heeling-motion limits. Experimental results clearly show that, with the proposed approach, the pedestal can effectively avoid semisingularity with a very smooth posture trajectory.

Calculating Watson-Crick to Hoogsteen Transition Kinetics in DNA with Langevin Dynamics and Fokker-Planck Diffusion in Reduced Configuration Space

Previous studies have shown that an important aspect of designing drugs for RNA drug targets, in particular, the transactivation response element (TAR) from HIV type 1 (HIV-1), is the determination of the thermodynamics and kinetics for WC to HG (Watson-Crick to Hoogsteen) conformation transitions. Previous work by Eunae Kim and Ioan Andricioaei successfully implemented umbrella sampling to produce a two-dimensional free energy surface for WC to HG transitions, where the two independent variables are the “flip-over” angle and “flip-out” angle of the adenine moiety undergoing the transition. The current study builds upon the work of Kim and Andricioaei by exploring the kinetics that arise from the time evolution of the probability density function of configurations, subjected to this potential energy surface. A position-dependent diffusion matrix was first calculated from the umbrella sampling data, in order to accurately describe diffusive motions in this reduced space. Next, a 2D polynomial of order 20 was fit to the energy surface, in order to obtain an analytical expression for the 2D surface. The diffusion matrix and analytical function describing the 2D surface were then used to carry out Langevin dynamics. Numerous Langevin trajectories between states were then analyzed in multiple ways, including calculating first passage time distributions between WC and HG configurations, and determination of regions in configuration space of maximum flux. In order to make the system numerically tractable for a Fokker-Planck approach to diffusion, the energy surface was also fit to a simpler 2D analytical function with a 20 term Fourier series solely in the “flip-over” dimension and a separate harmonic term approximating the “flip-out” dimension. Both approaches were utilized to determine favorable pathways for WC/HG transitions, and their respective time scales.

Grasp planning to maximize task coverage

This paper proposes a task-oriented grasp quality metric based on distribution of task disturbance, which could be used to search for a grasp that covers the most significant part of the disturbance distribution. Rather than using a uniformly distributed task wrench space, this paper models a manipulation task with a non-parametric statistical distribution model built from the disturbance data captured during the task demonstrations. The grasp resulting from maximizing the proposed grasp quality criterion is prone to increasing the coverage of most frequent disturbances. To reduce the computational complexity of the search in a high-dimensional robotic hand configuration space, as well as to avoid the correspondence problem, the candidate grasps are computed from a reduced configuration space that is confined by a set of given thumb placements and thumb directions. The proposed approach has been tested both in simulation and on a real robotic system. In simulation, the approach was validated with a Barrett hand and a Shadow hand in several manipulation tasks. Experiments on a physical robotic platform verified the consistency between the proposed grasp metric and the success rate.

Characterizing the configuration space of the 3-SPS-S spatial orientation parallel manipulator

In this paper, a complete analysis of configuration space entities of a three-degree-of-freedom spatial orientation manipulator is presented. In particular, the 3-SPS-S architecture with fixed joints located on an orthogonal frame is studied. At the design stage, the evaluation of the workspace of the manipulator constitutes an important issue. Besides, obtaining other entities such as joint space, in which the inputs are established, or the reduced configuration space, entity that relates inputs and outputs, gives an overall idea of the characteristics offered by each design. Comparison among different designs of the 3-SPS-S is carried out, analyzing the ability of transitioning between solutions and its influence on the resultant workspace.

Assembly Mode Changing in the Cuspidal Analytic 3-R $\underline{\hbox{P}}$R

In this paper, the analytic 3-RPR platform studied by Wenger and Chablat in 2009 will be analyzed regarding its cuspidality condition. Many investigations have paid great attention to the cuspidality phenomena that arise for some designs of the 3-RPR parallel manipulator. Nevertheless, most of them focus on obtaining the cusp points of direct kinematic singularity curves on a section of the joint space, meaning that one of the input variables must remain constant. The authors, in this paper, obtain the locus of cusp points of the manipulator under study in a complete analytic way and in 3-D joint space. This way, the three inputs can be actuated to perform a nonsingular transition that encircles one of the curves that belong to the locus of cusp points. It will be shown that the duplicity of one of the output variables of this manipulator causes the overlapping of two different cusp points in the joint space. In order to visualize this characteristic, initially, transitions in a section of the joint space will be analyzed using, additionally, the reduced configuration space. Then, transitions in the 3-D joint space will be performed, showing that, in order to ensure a feasible nonsingular transition, it is necessary to represent the direct kinematic singularity surface and assess the evolution of the three output variables along the trajectory.

Computing the Configuration Space for Tracing Paths Between Assembly Modes

In this paper, the authors present a general methodology for computing the configuration space for three-degree-of-freedom parallel manipulators so that the relation between input and output variables can be easily assessed. Making use of an entity called the reduced configuration space, all solutions of the direct kinematic problem in parallel manipulators are solved. The graphical representation of this entity enables the location of the direct kinematic solutions to be analyzed so as to make use of a wider operational workspace by means of path planning. A descriptive study is presented regarding the diverse possible paths that allow changing between direct kinematic solutions, thus, enlarging the manipulator’s range of motion.

A Strategy to Simulate the Dynamics of Molecular Assemblies Over Long Times

AbstractWe propose a strategy to simulate the dynamics of molecular assemblies over long times, provided they have a hierarchical and modular nature. In the scheme, fast fluctuations are averaged into a set of effective potentials (fluctuation softened potentials or FSPs), and the remaining slower dynamics are propagated in a drastically reduced configuration space (coupled energy landscapes or CEL). As a preliminary validation of the FSPs we compute the free energy of binding of a protein complex (RNase:barstar) for different relative positionings of the proteins. As a demonstration of CEL, we simulate the dynamics of microtubule unraveling upon hydrolysis of bound nucleotides. The method should allow the use of time steps hundreds to thousands of times longer than in conventional molecular dynamics, so that with only atomic structures and interactions as input, motions over human time scales (>ms) could be simulated.

From multi-body to many-body dynamics

This article provides a brief historical review of multi-body dynamics analysis, initiated by the Newtonian axioms through constrained ( removed degrees of freedom) Lagrangian dynamics or restrained ( resisted degrees of freedom) Newton—Euler formulation. It provides a generic formulation method, based on system dynamics in a reduced configuration space, which encompasses both the aforementioned methods and is applicable to any cluster of material points. A detailed example is provided to show the integration of other physical phenomena such as flexibility and acoustic wave propagation into multi-body dynamics analysis. It is shown that in the scale of minutiae, when the action potentials deviate from Newtonian laws, the forces are often described by empirical or stochastic functions of separation and the medium of interactions. These make for complex analyses and distinguish a host of many body problems from Newtonian laws of motion. A simple example is provided to demonstrate this. It is suggested that unification of many-body analysis with that of multi-body dynamics is incumbent on the fundamental understanding of interaction potentials at close separations.

Simulations of hydrogen diffusion at grain boundaries in aluminum

Long-timescale simulations of hydrogen atom diffusion in aluminum at low concentration were carried out to study the effect grain boundaries can have on the diffusion mechanism and diffusion rate. Three different grain boundaries were studied: Σ 5 twist, Σ 5 tilt and general, twist + tilt, grain boundaries. The adaptive kinetic Monte Carlo method was used to simulate the system over time intervals spanning tens of microseconds. A potential function of the effective medium form was parametrized to density functional theory calculations and used to describe the atomic interactions. The twist boundary turns out to block diffusion across the boundary – only a few high-energy sites are found in the boundary layer. However, diffusion parallel to the boundary is slightly enhanced because of the reduced configuration space. The twist and twist + tilt grain boundaries have strong binding sites within the boundary layer, up to 0.1 and 0.3 eV stronger, respectively, than binding sites in the crystal. In the latter case, the H atom spends more than 99% of the time in the grain boundary layer and diffusion parallel to the grain boundary occurs only when the H atom re-enters a crystal grain. Because of the trapping, the diffusion is reduced by more than an order of magnitude compared with the crystal.

On the topology of the reduced classical configuration space of lattice QCD

We study the topological structure of the quotient X of SU ( 3 ) × SU ( 3 ) by diagonal conjugation. This is the simplest nontrivial example for the classical reduced configuration space of chromodynamics on a spatial lattice in the Hamiltonian approach. We construct a cell complex structure of X in such a way that the closures of strata are subcomplexes and compute the homology and cohomology groups of the strata and their closures.

NOETHER SYMMETRY APPROACH TO SCALAR-FIELD-DOMINATED COSMOLOGY WITH DYNAMICALLY EVOLVING G AND Λ

This paper studies the cosmological equations for a scalar field φ in the framework of a quantum gravity modified Einstein–Hilbert Lagrangian where G and Λ are dynamical variables. It is possible to show that there exists a Noether symmetry for the point Lagrangian describing this scheme in a FRW universe. Our main result is that the Noether Symmetry Approach fixes both Λ = Λ(G) and the potential V = V(φ) of the scalar field. The method does not lead, however, to easily solvable equations, by virtue of the higher dimensionality of the reduced configuration space involved, the additional variable being the running Newton coupling.

Dynamical hydrogen atom tunneling in dichlorotropolone: A combined quantum, semiclassical, and classical study

Based on the Cartesian Reaction Surface framework we construct a four-dimensional potential for the tropolone derivative 3,7-dichlorotropolone, a molecule with an intramolecular O-H...O hydrogen bond. The reduced configuration space involves the in-plane hydrogen atom coordinates, a symmetric O-O vibrational mode, and an antisymmetric mode related to deformations of the seven-membered ring. The system is characterized in terms of quantum mechanical computations of the low-lying eigenstates as well as a classical and semiclassical analysis of spectra obtained via Fourier transforming autocorrelation functions. For the semiclassical analysis we utilize the amplitude-free correlation function method [K. Hotta and K. Takatsuka, J. Phys. A 36, 4785 (2003)]. Our results demonstrate substantial anharmonic couplings leading to highly correlated wave functions even at moderate energies. Furthermore, the importance of dynamical tunneling in tropolone is suggested since many low-lying states--including the ground state--lie above the classical saddle point but nevertheless appear as split pairs.

The topology of the planar three-body problem with zero total angular momentum and the existence of periodic orbits

We consider the planar three-body problem (3BP) with a Newtonian-like potential of the form with and also the Newtonian case . We study the least action principle on the manifold defined by the vanishing of the total angular momentum. Using the topology of the reduced configuration space we are able to find a class of trajectories on which a generalization of the Poincaré inequality holds, this then enables us to apply the direct method of calculus of variations. We prove the existence of a periodic solution: for the Newtonian potential , this periodic solution has at most a finite number of collisions. For the solution is in the homotopic class of the trajectories that go through at least three different collinear configurations. This result is a direct consequence of the first homotopy group of the reduced configuration space without coincidence set, this group is isomorphic to the free-generated group .

Gauge fields in the separation of rotations andinternal motions in the n-body problem

The problem of separating rotations from internal motions in systems such as macroscopic flexible bodies, atoms, molecules, nuclei, and solar systems is an old one, with many applications in physics, chemistry, and engineering. A new element, however, which has not been appreciated until fairly recently, is the existence of certain gauge fields on the reduced configuration space for such systems. These (non-Abelian) gauge fields arise in the ``falling cat'' problem, in which changes in shape induce changes in external orientation; but they also have a dynamical significance, and enter as gauge potentials in the Lagrangian or Hamiltonian describing the internal or reduced dynamics. Physically these gauge fields represent Coriolis effects. This review concentrates on the case of nonrelativistic, n-body systems not subject to external torques, and develops the gauge theory of rotations and internal motions in detail. Both classical and quantum treatments are given. The gauge theory is developed from the standpoint of classical, coordinate-based tensor analysis; more abstract mathematical notation is generally not used, although the basic geometrical ideas of fiber-bundle theory are developed as needed. Certain old results, such as the Wilson-Howard-Watson Hamiltonian of molecular physics, are examined from a gauge-theoretical standpoint; and several new results are presented, including field equations of the Kaluza-Klein type satisfied by the gauge fields, and geometrical interpretations of the Eckart frame.