Iterative Path Research Articles

Equilibrium Analysis of Pin-Jointed Steel Structures under Large Variations of Configuration

In the paper an equilibrium analysis of pin-jointed steel structures is described. The attention is focused on the non-linearity problem that characterizes this type of steel structures under large displacements. A matrix method is developed, starting from a balanced and congruent configuration. Firstly, the analysis is conducted on the single bar; the, the behaviour of the global structure is analysed through the re-assembling and the final non-linear relationships between the variation of loads and the configuration are identified in order to proceed to the iterative solution path.

Node localization over small world WSNs using constrained average path length reduction

Small world characteristics have been observed and studied in social networks in the context of information dissemination in important applications like disease spread among communities. However, the significance of small world characteristics in wireless sensor network (WSN) applications has hitherto not been investigated. This work investigates the significance of introducing small world characteristics in a conventional WSN for improving the node localization accuracy. In this context, a novel constrained iterative average path length reduction algorithm is proposed to introduce small world characteristics into a conventional WSN. This method utilizes a novel frequency selective approach for the introduction of small world phenomena. The frequency selective approach utilizes two frequency bands for link addition and pruning to create an optimized small world WSN. Subsequently, a constrained least squares node localization method over the small world WSN is developed using both model-based and model-free signal propagation approaches. The proposed constrained iterative average path length reduction method provides reduced average path length and a high average clustering coefficient when compared to conventional WSN. Constrained least squares node localization over the small world WSN yields improved localization performance when compared to node localization over conventional WSN. Performance analysis in terms of localization error, power consumption, bandwidth and anchors required for node localization is also discussed. Cramer-Rao lower bound analysis for node location parameters is also used to provide insights into the error bounds obtained using the proposed method. The experimental results obtained are motivating enough for the introduction of small world phenomena in conventional WSN for applications like node localization and related applications.

Coarse-grained representation of the quasi adiabatic propagator path integral for the treatment of non-Markovian long-time bath memory.

The description of non-Markovian effects imposed by low frequency bath modes poses a persistent challenge for path integral based approaches like the iterative quasi-adiabatic propagator path integral (iQUAPI) method. We present a novel approximate method, termed mask assisted coarse graining of influence coefficients (MACGIC)-iQUAPI, that offers appealing computational savings due to substantial reduction of considered path segments for propagation. The method relies on an efficient path segment merging procedure via an intermediate coarse grained representation of Feynman-Vernon influence coefficients that exploits physical properties of system decoherence. The MACGIC-iQUAPI method allows us to access the regime of biological significant long-time bath memory on the order of hundred propagation time steps while retaining convergence to iQUAPI results. Numerical performance is demonstrated for a set of benchmark problems that cover bath assisted long range electron transfer, the transition from coherent to incoherent dynamics in a prototypical molecular dimer and excitation energy transfer in a 24-state model of the Fenna-Matthews-Olson trimer complex where in all cases excellent agreement with numerically exact reference data is obtained.

Iterative blip-summed path integral for quantum dynamics in strongly dissipative environments.

The iterative decomposition of the blip-summed path integral [N. Makri, J. Chem. Phys. 141, 134117 (2014)] is described. The starting point is the expression of the reduced density matrix for a quantum system interacting with a harmonic dissipative bath in the form of a forward-backward path sum, where the effects of the bath enter through the Feynman-Vernon influence functional. The path sum is evaluated iteratively in time by propagating an array that stores blip configurations within the memory interval. Convergence with respect to the number of blips and the memory length yields numerically exact results which are free of statistical error. In situations of strongly dissipative, sluggish baths, the algorithm leads to a dramatic reduction of computational effort in comparison with iterative path integral methods that do not implement the blip decomposition. This gain in efficiency arises from (i) the rapid convergence of the blip series and (ii) circumventing the explicit enumeration of between-blip path segments, whose number grows exponentially with the memory length. Application to an asymmetric dissipative two-level system illustrates the rapid convergence of the algorithm even when the bath memory is extremely long.

Finite-temperature time-dependent variation with multiple Davydov states.

The Dirac-Frenkel time-dependent variational approach with Davydov Ansätze is a sophisticated, yet efficient technique to obtain an accurate solution to many-body Schrödinger equations for energy and charge transfer dynamics in molecular aggregates and light-harvesting complexes. We extend this variational approach to finite temperature dynamics of the spin-boson model by adopting a Monte Carlo importance sampling method. In order to demonstrate the applicability of this approach, we compare calculated real-time quantum dynamics of the spin-boson model with that from numerically exact iterative quasiadiabatic propagator path integral (QUAPI) technique. The comparison shows that our variational approach with the single Davydov Ansätze is in excellent agreement with the QUAPI method at high temperatures, while the two differ at low temperatures. Accuracy in dynamics calculations employing a multitude of Davydov trial states is found to improve substantially over the single Davydov Ansatz, especially at low temperatures. At a moderate computational cost, our variational approach with the multiple Davydov Ansatz is shown to provide accurate spin-boson dynamics over a wide range of temperatures and bath spectral densities.

A structure-preserving pivotal method for affine variational inequalities

Affine variational inequalities (AVI) are an important problem class that subsumes systems of linear equations, linear complementarity problems and optimality conditions for quadratic programs. This paper describes PathAVI, a structure-preserving pivotal approach, that can efficiently process (solve or determine infeasible) large-scale sparse instances of the problem with theoretical guarantees and at high accuracy. PathAVI implements a strategy known to process models with good theoretical properties without reducing the problem to specialized forms, since such reductions may destroy sparsity in the models and can lead to very long computational times. We demonstrate formally that PathAVI implicitly follows the theoretically sound iteration paths, and can be implemented in a large scale setting using existing sparse linear algebra and linear programming techniques without employing a reduction. We also extend the class of problems that PathAVI can process. The paper illustrates the effectiveness of our approach by comparison to the Path solver used on a complementarity reformulation of the AVI in the context of applications in friction contact and Nash Equilibria. PathAVI is a general purpose solver, and freely available under the same conditions as Path.

Monitoring Environmental Performance During the Design Process of a Complex System

A large part of impacts that will be generated by a system / product during its life cycle are allocated during the earliest stages of the design process. In this paper we propose to trace the evolution of environmental impacts throughout a complex system design process through an industrial case. We follow the stages of a boat design process for maintenance of offshore wind farms. The different architectures sketched throughout the design process are evaluated in order to measure the impact of design decisions on the environmental performance of the system. The problematic of taking into account environmental constraints upstream of the design process abound methods but they often prove inadequate for complex systems whose subsystems interact in complex ways leading to conflicts in the decision of the right parameters. To meet the stakeholders’ needs, that appear (during the design project) in the iterative design process, the initial design is modified to fit the specifications. This iterative path between designers and users leads to uncertainties over the environmental impact of the system. It is then necessary to use smart design support tools allowing a negotiation in definition phase of system specifications. Thus the preliminary design is modified to incorporate changes and contributions occurred during the negotiation phase functional.

Deterministic polishing of freeform optical surface by iterative intersection tool path in an off-axial three-mirror anastigmat imaging system

Deterministic polishing as the final step of freeform surface machining can acquire preferable form accuracy. In this article, a deterministic polishing model based on iterative intersection tool path is presented to meet the requirement of high-form accuracy in freeform surface. In the polishing process, on-machine measurement and point set registration method are adopted for installation error extraction and form error calculation. The iterative polishing can be finished without discharging of workpiece by on-machine measurement strategy, which will reduce the processing time and improve the machining efficiency. In addition, a boundary extension method is employed to diminish the surface edge collapse generated by edge effect. Finally, the polishing experiment of freeform optical surface in an off-axial three-mirror anastigmat imaging system is conducted to verify the effectiveness of the proposed model.

Formula omitted] regularized multiplicative iterative path algorithm for non-negative generalized linear models

In regression modeling, often a restriction that regression coefficients are non-negative is faced. The problem of model selection in non-negative generalized linear models (NNGLM) is considered using lasso, where regression coefficients in the linear predictor are subject to non-negative constraints. Thus, non-negatively constrained regression coefficient estimation is sought by maximizing the penalized likelihood (such as the l1-norm penalty). An efficient regularization path algorithm is proposed for generalized linear models with non-negative regression coefficients. The algorithm uses multiplicative updates which are fast and simultaneous. Asymptotic results are also developed for the constrained penalized likelihood estimates. Performance of the proposed algorithm is shown in terms of computational time, accuracy of solutions and accuracy of asymptotic standard deviations.

Iterative quantum-classical path integral with dynamically consistent state hopping.

We investigate the convergence of iterative quantum-classical path integral calculations in sluggish environments strongly coupled to a quantum system. The number of classical trajectories, thus the computational cost, grows rapidly (exponentially, unless filtering techniques are employed) with the memory length included in the calculation. We argue that the choice of the (single) trajectory branch during the time preceding the memory interval can significantly affect the memory length required for convergence. At short times, the trajectory branch associated with the reactant state improves convergence by eliminating spurious memory. We also introduce an instantaneous population-based probabilistic scheme which introduces state-to-state hops in the retained pre-memory trajectory branch, and which is designed to choose primarily the trajectory branch associated with the reactant at early times, but to favor the product state more as the reaction progresses to completion. Test calculations show that the dynamically consistent state hopping scheme leads to accelerated convergence and a dramatic reduction of computational effort.

Toward An Integration of the Behavioral and Cognitive Influences on the Entrepreneurship Process

Research summaryEntrepreneurs develop innovations, fulfill customer needs, and spur economic growth by recognizing, evaluating, and exploiting opportunities. Despite progress, scholarly understanding of how entrepreneurs achieve these objectives may be incomplete. For instance, little explanation exists for why entrepreneurs may pursue activities seemingly at random, nor is there a clear endpoint to the entrepreneurship process. To address these concerns, we present a framework that integrates sensemaking and structuration perspectives to specify the cognitive and behavioral influences on the entrepreneurship process. Within this framework, entrepreneurs ultimately pursue opportunities through developing and deploying capabilities to create value for customers.Managerial summaryWhile entrepreneurs' initial insights regarding innovations and customer needs are important, these insights are only the beginning of an interactive, iterative path that ends with the formation of an organization that can reliably produce value for customers. One of entrepreneurs' most important tools along this path is their set of scripts. Scripts help define how entrepreneurs act and interact so they can fully understand market needs and develop the means for solving these needs. In this paper, our objective is to describe how these scripts help entrepreneurs do the hard work of thinking and acting to effectively create new venture capabilities and to explain how entrepreneurs, who may possess similar sets of scripts, may nevertheless conceptualize different opportunities and solutions.

On iterative path integral calculations for a system interacting with a shifted dissipative bath.

Real-time path integral calculations for the propagation of a system in contact with a harmonic dissipative environment often employ the iterative quasi-adiabatic propagator path integral (i-QuAPI) methodology. We compare two simple ways of applying this methodology to a bath initially in equilibrium with the localized state of the system (e.g., the donor in the case of charge transfer). The first way involves modifying the phase of the system via a time-local phase given in terms of integrals of the spectral density or in terms of the coefficients entering the QuAPI-discretized influence functional. In the iterative decomposition of the path integral, this approach requires consistent memory truncation to avoid extremely slow convergence. The second, alternative approach involves shifting the coordinate of the system, to bring the donor state in equilibrium with the bath, and requires no further modification of the i-QuAPI algorithm.

Iterative path attacks on networks

We investigate a path-attack process on model networks and real-world networks. Based on the local topological structure of a path, we propose an attack centrality measure with a control parameter α for quantifying the influence of a path. In the path-attack process, we iteratively remove the path with the largest attack centrality from a network. Results demonstrate that, for a specific network, there is an optimal α which results in maximum attack efficiency. The denser and more homogeneous the networks, the more robust the networks are against iterative path attacks. Our work helps to explain the vulnerability of networks and provides some clues about the protection and design of real complex systems.

A stochastic algorithm for makespan minimized multi-agent path planning in discrete space

Makespan minimized multi-agent path planning (MAPP) requires the minimization of the time taken by the slowest agents to reach its destination. The resulting minimax objective function is non-smooth and the search for an optimal solution in MAPP can be intractable. In this work, a maximum entropy function is adopted to approximate the minimax objective function. An iterative algorithm named probabilistic iterative makespan minimization (PIMM) is then proposed to approximate a makespan minimized MAPP solution by solving a sequence of computationally hard MAPP minimization problems with a linear objective function. At each iteration, a novel local search algorithm called probabilistic iterative path coordination (PIPC) is used to find a sufficiently good solution for each MAPP minimization problem. Experimental results from comparative studies with existing MAPP algorithms show that the proposed algorithm strikes a good tradeoff between the quality of the makespan minimized solution and the computational cost incurred.

Decentralised hybrid workflow scheduling algorithm for minimum end-to-end delay in heterogeneous computing environment

This paper considers a decentralised hybrid algorithm for scheduling scientific workflow applications onto an underlying distributed computing environment with heterogeneous resources for minimum end-to-end delay EED. Distributed scientific workflow applications modelled as directed acyclic graphs DAGs are widely applied to various research areas to enable efficient knowledge discovery by automated data processing. Owing to the NP-hardness of this problem, heuristic algorithms are commonly proposed to achieve the EED. Our algorithm combines iterative critical path search and layer-based priority techniques HICPP to achieve the minimum EED. Four representative mapping and scheduling algorithms for minimum EED are compared with HICPP. Our simulation results illustrate that HICPP consistently achieves the smallest EED with a low algorithm running time observed from many different scales of simulated test cases.

Multipath Discovery Algorithms for VoD Streaming In Wireless Mesh Network

Transmission and routing of video data over wireless network is a challenging task because of wireless interferences. To improve the performance of video on demand transmission over wireless networks multipath algorithms are used. IPD/S (Iterative path discovery/selection) PPD/S (Parallel Path discovery/selection) are two algorithms which is used for discovering maximum number of edge disjoint paths from source to destination, for each VoD request by considering the effects of wireless interferences. In this paper performance evaluation of these multipath discovery algorithms for VoD (Video on demand) streaming in wireless mesh network is presented. These algorithms are evaluated on the bases of Number of Path discovers, Packet drop ratio and delay. Simulation result shows that PPD/S works batter as compared to IPD/S because it’s able to discover more paths than IPD/S under same circumstances.

Modeling flow information of loops using compositional condition of controls

This paper proposes a flow analysis approach to provide accurate flow facts such as number of loop iterations and infeasible paths for WCET analysis. To achieve this, a novel approach to model program flows of given loops as compositional condition of controls that can model the program flow of the sequence of basic blocks on an execution path through a single loop iteration is proposed. The proposed approach builds distinct symbolic expressions each representing a path condition as conjunctions of branch conditions along the path. Then, the path conditions are formed via substituting all constituent variables of the branch conditions with symbolic expressions computing the value of these variables. The final symbolic expression will contain variables denoting theirs value at the loop entry point. Considering the change in the value of the loop variables of the path condition, the feasible values of these variables are computed and consequently the number of the loop iterations along the iteration path is determined. Applying a SMT solver to the symbolic expressions representing each path condition, all the infeasible paths along the loop body are detected. The results of applying our flow analysis approach to a number of programs addressed in the Malardalen benchmark suite reveal the capability and efficiency of our proposed approach.

Stochastic optimal control to a nonlinear differential game

The paper studies the optimal control of a nonlinear stochastic differential game of two persons subjected to noisy measurements. The logarithmic transformation to the value function is used in trying to find the solution of the problem. The conversion of a quasilinear partial differential equation to an ordinary linear differential equation is considered. Lastly, the iterative optimal control path estimates for the minimization maximization differential game are attained.

Exploiting classical decoherence in dissipative quantum dynamics: Memory, phonon emission, and the blip sum

The mechanisms that lead to the quenching of the coherence of a quantum system interacting with a dissipative environment are analyzed within the path integral/influence functional framework. Classical and quantum contributions are identified and linked to stimulated and spontaneous phonon emission processes. Three ways of exploiting decoherence in numerical calculations are discussed. The first is based on the decay of memory effects with time separation and leads to well-known iterative quasi-adiabatic propagator path integral (i-QuAPI) schemes. The other two mechanisms exploit the prominent role of classical decoherence. Removal of classical memory is possible through the introduction of auxiliary variables, leading to efficient and accurate quantum–classical path integral (QCPI) methods. A third way is proposed, which involves systematic corrections to the fully incoherent limit. An efficient procedure for summing all paths associated with ‘blips’ (short off-diagonal path pair segments) is described. The ideas are illustrated with numerical calculations of tunneling dynamics.

Iterative path integral summation for nonequilibrium quantum transport

We have developed a numerically exact approach to compute real‐time path integral expressions for quantum transport problems out of equilibrium. The scheme is based on a deterministic iterative summation of the path integral (ISPI) for the generating function of nonequilibrium observables of interest. We apply the scheme to compute the charge current or dynamical quantities of small strongly correlated quantum systems as a quantum dot or molecules that are tunnel coupled to leads. Self‐energies due to the leads, being nonlocal in time, are fully taken into account within a finite memory time, thereby including non‐Markovian effects. Numerical results are extrapolated first to vanishing (Trotter) time discretization and, second, to infinite memory time. The method is applied to nonequilibrium transport through a single‐impurity Anderson dot in the first place. We benchmark our results in various regimes of the rich parameter space. In the respective regime of validity, iterative summation of real‐time path integrals (ISPI) results are shown to match those of other state‐of‐the art methods. Especially, we have chosen the mixed valence regime of the Anderson model to compare ISPI to time dependent density matrix renormalization group (tDMRG) and functional RG calculations. Secondly, we determine the nonequilibrium current through a molecular junction in presence of a vibrational mode. We have found an exact mapping of the single impurity Anderson–Holstein model to an effective spin‐1 problem. In analytically tractable regimes, as the adiabatic phonon or weak molecule‐lead coupling regime, we reproduce known perturbative results. Studying the crossover regime between those limits shows that the Franck–Condon blockade persists in the quantum limit. At low temperature, the Franck–Condon steps in the characteristics are smeared due to nonequilibrium conditions. The third system under investigation here is the magnetic Anderson model which consists of a spinful single‐orbital quantum dot with an incorporated quantum mechanical spin–1/2 magnetic impurity. Coulomb interaction together with the exchange coupling of the magnetic impurity with the electron spins strongly influence the dynamics. We investigate the nonequilibrium tunneling current through the system as a function of exchange and Coulomb interaction as well as the real‐time impurity polarization. From the real‐time evolution of physical observables, we are able to determine characteristics of the time‐dependent nonequilibrium current and the relaxation dynamics of the impurity. These examples illustrate that the ISPI technique is particularly well suited for the quantum regime, when all time and energy scales are of the same order of magnitude.