Recursive Step Research Articles

Terminating constraint set satisfiability and simplification algorithms for context-dependent overloading

Abstract Algorithms for constraint set satisfiability and simplification of Haskell type class constraints are used during type inference in order to allow the inference of more accurate types and to detect ambiguity. Unfortunately, both constraint set satisfiability and simplification are in general undecidable, and the use of these algorithms may cause non-termination of type inference. This paper presents algorithms for these problems that terminate on any given input, based on the use of a criterion that is tested on each recursive step. The use of this criterion eliminates the need of imposing syntactic conditions on Haskell type class and instance declarations in order to guarantee termination of type inference in the presence of multi-parameter type classes, and allows program compilation without the need of compiler flags for lifting such restrictions. Undecidability of the problems implies the existence of instances for which the algorithm incorrectly reports unsatisfiability, but we are not aware of any practical example where this occurs.

Adaptive fuzzy output feedback dynamic surface sliding mode control for a nonlinear dynamic system

Friction and deadzone nonlinearities in the nonlinear dynamic systems act often the main obstacles for higher motion control. It is difficult to achieve effective motion compensation for these types of nonlinearities by traditional linear control methodology without the aid of a proper estimation scheme on nonlinearity. Here, we present an adaptive fuzzy dynamic surface control scheme combined with state and nonlinearity observer and sliding mode control to estimate immeasurable state and compensate undesirable uncertainty on motion control for a strict output feedback nonlinear dynamic system. The adaptive laws of the fuzzy, friction and deadzone observer are derived from the recursive steps of the dynamic surface control. The boundedness and convergence of the closed-loop system are guaranteed by a Lyapunov stability analysis. The performance of the proposed control scheme is verified through simulation and experiment on the robot manipulator.

Adaptive Fuzzy Dynamic Surface Sliding Mode Position Control for a Robot Manipulator with Friction and Deadzone

Precise tracking positioning performance in the presence of both the deadzone and friction of a robot manipulator actuator is difficult to achieve by traditional control methodology without proper nonlinear compensation schemes. In this paper, we present a dynamic surface sliding mode control scheme combined with an adaptive fuzzy system, state observer, and parameter estimator to estimate the uncertainty, friction, and deadzone nonlinearities of a robot manipulator system. We design a dynamic surface sliding mode basic controller by systematic recursive design steps that yields several adaptive laws for the compensation of nonlinear friction, deadzone, and other unknown nonlinear dynamics. The boundedness and convergence of this closed-loop system are guaranteed by the Lyapunov stability theorem. Experiments on the Scorbot robot manipulator demonstrate the validity and effectiveness of the proposed control scheme.

An integrated approach to support the joint design of machine tools and process planning

The configuration of machine tools and process planning problem are traditionally managed as independent stages, where the process plan is designed by considering a number of machine tool solutions available from catalogue. This strategy presents a number of disadvantages in terms of process results and machine capabilities fully exploitation. The current paper proposes an integrated approach for jointly configuring machine tools and process planning. The approach is structured in 4 major recursive steps that eventually ensure the accomplishment of the best trade-off between the machine tool static and dynamic behaviour, the process quality and the resulting economic efficiency. The benefits of the approach have been evaluated for a test case application in the railway and automotive sectors.

Adaptive fuzzy backstepping dynamic surface control for output-constrained non-smooth nonlinear dynamic system

Output-constrained backstepping dynamic surface control (DSC) is proposed for the purpose of output constraint and precise output positioning of a strict feedback single-input, single-output dynamic system in the presence of deadzone and uncertainty. A symmetric barrier Lyapunov function (BLF) is employed to meet the output constraint requirement using DSC as an alternative method of backstepping control that is adopted mainly to deal with the BLF’s constraint control. However, using the ordinary DSC method with the BLF limits the selection of the control gain whereas this limitation does not exist in the backstepping structure. To remove this limitation, we propose a partial backstepping DSC method in which backstepping control is added only in the first recursive DSC design step. For precise positioning, an inverse deadzone method and adaptive fuzzy system are introduced to handle unknown deadzone and unmodeled nonlinear functions. We show that the semiglobal boundedness of the overall closed-loop signals is guaranteed, the tracking error converges within the prescribed region, and precise positioning performance is ensured. The proposed control scheme is experimentally evaluated using a robot manipulator.

The Weighted Averages Algorithm Revisited

The classic weighted averages (WA) algorithm for the evaluation of Sommerfeld-like integrals is reviewed and reappraised. As a result, a new version of the WA algorithm, called generalized WA, is introduced. The new version can be considered as a generalization of the well established Hölder and Cèsaro means, used to sum divergent series. Generalized WA exhibits a more compact formulation, devoid of iterative and recursive steps, and a wider range of applications. It is more robust, as it provides a unique formulation, valid for monotonic and oscillating functions. The implementation of the new version is easier and more economical in terms of basic operations. Preliminary numerical examples show that generalized WA also outperforms in terms of accuracy the classic WA algorithm, which is currently recognized as the most competitive algorithm to evaluate Sommerfeld integral tails.

The data‐driven approach as an operational real‐time flood forecasting model

AbstractAccurate water level forecasts are essential for flood warning. This study adopts a data‐driven approach based on the adaptive network–based fuzzy inference system (ANFIS) to forecast the daily water levels of the Lower Mekong River at Pakse, Lao People's Democratic Republic. ANFIS is a hybrid system combining fuzzy inference system and artificial neural networks. Five ANFIS models were developed to provide water level forecasts from 1 to 5 days ahead, respectively. The results show that although ANFIS forecasts of water levels up to three lead days satisfied the benchmark, four‐ and five‐lead‐day forecasts were only slightly better in performance compared with the currently adopted operational model. This limitation is imposed by the auto‐ and cross‐correlations of the water level time series. Output updating procedures based on the autoregressive (AR) and recursive AR (RAR) models were used to enhance ANFIS model outputs. The RAR model performed better than the AR model. In addition, a partial recursive procedure that reduced the number of recursive steps when applying the AR or the RAR model for multi‐step‐ahead error prediction was superior to the fully recursive procedure. The RAR‐based partial recursive updating procedure significantly improved three‐, four‐ and five‐lead‐day forecasts. Our study further shows that for long lead times, ANFIS model errors are dominated by lag time errors. Although the ANFIS model with the RAR‐based partial recursive updating procedure provided the best results, this method was able to reduce the lag time errors significantly for the falling limbs only. Improvements for the rising limbs were modest. Copyright © 2011 John Wiley & Sons, Ltd.

International Participatory Research Framework: triangulating procedures to build health research capacity in Brazil.

This study advances Community-based Participatory Research (CBPR) by presenting a set of triangulated procedures (steps and actions) that can facilitate participatory research in myriad international settings. By using procedural triangulation-the combination of specific steps and actions as the basis for the International Participatory Research Framework (IPRF)-our approach can improve the abilities of researchers and practitioners worldwide to systematize the development of research partnerships. The IPRF comprises four recursive steps: (i) contextualizing the host country; (ii) identifying collaborators in the host country; (iii) seeking advice and endorsement from gatekeepers and (iv) matching partners' expertise, needs and interests. IPRF includes the following sets of recursive participatory actions: (A(1)) becoming familiar with local languages and culture; (A(2)) sharing power, ideas, influence and resources; (A(3)) gathering oral and written information about partners; (A(4)) establishing realistic expectations and (A(5)) resolving personal and professional differences. We show how these steps and actions were used recursively to build a partnership to study the roles of community health workers (CHWs) in Brazil's Family Health Program (PSF). The research conducted using IPRF focused on HIV prevention, and it included nearly 200 CHWs. By using the IPRF, our partnership achieved several participatory outcomes: community-defined research aims, capacity for future research and creation of new policies and programs. We engaged CHWs who requested that we study their training needs, and we engaged CHWs' supervisors who used the data collected to modify CHW training. Data collected from CHWs will form the basis for a grant to test CHW training curricula. Researchers and community partners can now use the IPRF to build partnerships in different international contexts. By triangulating steps and actions, the IPRF advances knowledge about the use of CBPR methods/procedures for international health research.

Identifying Regions of Interest in Medical Images Using Self-Organizing Maps

Advances in data acquisition, processing and visualization techniques have had a tremendous impact on medical imaging in recent years. However, the interpretation of medical images is still almost always performed by radiologists. Developments in artificial intelligence and image processing have shown the increasingly great potential of computer-aided diagnosis (CAD). Nevertheless, it has remained challenging to develop a general approach to process various commonly used types of medical images (e.g., X-ray, MRI, and ultrasound images). To facilitate diagnosis, we recommend the use of image segmentation to discover regions of interest (ROI) using self-organizing maps (SOM). We devise a two-stage SOM approach that can be used to precisely identify the dominant colors of a medical image and then segment it into several small regions. In addition, by appropriately conducting the recursive merging steps to merge smaller regions into larger ones, radiologists can usually identify one or more ROIs within a medical image.

Iterative data-parallel mark&sweep on a GPU

Automatic memory management makes programming easier. This is also true for general purpose GPU computing where currently no garbage collectors exist. In this paper we present a parallel mark-and-sweep collector to collect GPU memory on the GPU and tune its performance. Performance is increased by: (1) data-parallel marking and sweeping of regions of memory, (2) marking all elements of large arrays in parallel, (3) trading recursion over parallelism to match deeply linked data structures. (1) is achieved by coarsely processing all potential objects in a region of memory in parallel. When during (1) a large array is detected, it is put aside and a parallel-for is later issued on the GPU to mark its elements. For a data-structure that is a large linked list, we dynamically switch to a marking version with less overhead by performing a few recursive steps sequentially (and multiple lists in parallel). The collector achieves a speedup of a factor of up-to 11 over a sequential collector on the same GPU.

Construction of Mutually Orthogonal Zero Correlation Zone Polyphase Sequence Sets

In this paper, two constructions of mutually orthogonal zero correlation zone polyphase sequence sets are presented. The first one is based on DFT matrices and interleaving iteration. After each recursive step, the period of sequence and the length of zero-correlation zone are two times larger than that in the last step. The second method, based on DFT matrices and orthogonal matrices, can generate numbers of mutually orthogonal optimal ZCZ sequence sets whose parameters reach the theoretical bounds by using interleaving and shifting techniques. As a result, the algorithms proposed can provide more sequences for the QS-CDMA (quasi-synchronous CDMA) systems.

Geometric sensitivity of statically determinate planar truss families

We define a truss family Ti by a statically determinate truss T0 and a recursive step Ti+1=f(Ti), such that Ti+1Ti and that step f(Ti) keeps static determinacy. Such recursive algorithms have been broadly discussed in the literature, e.g. the Henneberg operation 1 is a well-known example. Earlier we introduced the concept of geometric sensitivity index rg of trusses, here we investigate the sensitivity of truss families, in particular, the limit sensitivity (Ti).

Algorithms for fast computation of Zernike moments and their numerical stability

Accuracy, speed and numerical stability are among the major factors restricting the use of Zernike moments (ZMs) in numerous commercial applications where they are a tool of significant utility. Often these factors are conflicting in nature. The direct formulation of ZMs is prone to numerical integration error while in the recent past many fast algorithms are developed for its computation. On the other hand, the relationship between geometric moments (GMs) and ZMs reduces numerical integration error but it is observed to be computation intensive. We propose fast algorithms for both the formulations. In the proposed method, the order of time complexity for GMs-to-ZMs formulation is reduced and further enhancement in speed is achieved by using quasi-symmetry property of GMs. The existing q-recursive method for direct formulation is further modified by incorporating the recursive steps for the computation of trigonometric functions. We also observe that q-recursive method provides numerical stability caused by finite precision arithmetic at high orders of moment which is hitherto not reported in the literature. Experimental results on images of different sizes support our claim.

Renormalizing the NN interaction with multiple subtractions

The aim of this work is to show how to renormalize the nucleon-nucleon interaction at next-to-next-to-leading order using a systematic subtractive renormalization approach with multiple subtractions. As an example, we calculate the phase shifts for the partial waves with total angular momentum J = 2 . The intermediate driving terms at each recursive step as well as the renormalized T-matrix are also shown. We conclude that our method is reliable for singular potentials such as the two-pion exchange and derivative contact interactions.

SER bound for ordered ZF-SIC receiver in M-QAM MIMO system

With the advances of the 4th generation (4G) mobile communications targeting multi-user QoS-guaranteed multimedia services, multiple input multiple output (MIMO) combined with multi-level quadrature amplitude modulation (M-QAM) technique gains great popularity for its capability of supporting high data rate. In this article, the statistical distribution of signal to noise plus interference ratio (SINR) in each recursive step of optimal ordered zero-forcing perfect successive interference cancellation (ZF-OOPSIC) detection is deduced based on order statistics theory. The symbol error rate (SER) of M-QAM MIMO system with ZF-OOPSIC detector is analyzed under flat Rayleigh fading channel. This precise analytical SER result could be taken as the lower bound of various zero-forcing ordered successive interference cancellation (ZF-OSIC) receivers. Combining the analytical SER expression for linear zero-forcing (ZF) receiver as upper bound, the rough range of SER for various ZF-OSIC detectors could be obtained. Monte Carlo (MC) simulations validate the analytical results and prove the conclusions.

An SDP-Based Divide-and-Conquer Algorithm for Large-Scale Noisy Anchor-Free Graph Realization

We propose the DISCO algorithm for graph realization in $\mathbb{R}^d$, given sparse and noisy short-range intervertex distances as inputs. Our divide-and-conquer algorithm works as follows. When a group has a sufficiently small number of vertices, the basis step is to form a graph realization by solving a semidefinite program. The recursive step is to break a large group of vertices into two smaller groups with overlapping vertices. These two groups are solved recursively, and the subconfigurations are stitched together, using the overlapping atoms, to form a configuration for the larger group. At intermediate stages, the configurations are improved by gradient descent refinement. The algorithm is applied to the problem of determining protein moleculer structure. Tests are performed on molecules taken from the Protein Data Bank database. For each molecule, given 20-30% of the inter-atom distances less than 6A that are corrupted by a high level of noise, DISCO is able to reliably and efficiently reconstruct the conformation of large molecules. In particular, given 30% of distances with 20% multiplicative noise, a 13000-atom conformation problem is solved within an hour with a root mean square deviation of 1.6A.

Cut-and-paste of quadriculated disks and arithmetic properties of the adjacency matrix

We define cut-and-paste, a construction which, given a quadriculated disk obtains a disjoint union of quadriculated disks of smaller total area. We provide two examples of the use of this procedure as a recursive step. Tilings of a disk Δ receive a parity: we construct a perfect or near-perfect matching of tilings of opposite parities. Let B Δ be the black-to-white adjacency matrix: we factor B Δ = L D ∼ U , where L and U are lower and upper triangular matrices, D ∼ is obtained from a larger identity matrix by removing rows and columns and all entries of L , D ∼ and U are equal to 0 , 1 or - 1 .

Spectral tripartitioning of networks

We formulate a spectral graph-partitioning algorithm that uses the two leading eigenvectors of the matrix corresponding to a selected quality function to split a network into three communities in a single step. In so doing, we extend the recursive bipartitioning methods developed by Newman [M. E. J. Newman, Proc. Natl. Acad. Sci. U.S.A. 103, 8577 (2006); Phys. Rev. E 74, 036104 (2006)] to allow one to consider the best available two-way and three-way divisions at each recursive step. We illustrate the method using simple "bucket brigade" examples and then apply the algorithm to examine the community structures of the coauthorship graph of network scientists and of U. S. Congressional networks inferred from roll call voting similarities.

Generating restricted classes of involutions, Bell and Stirling permutations

We present a recursive generating algorithm for unrestricted permutations which is based on both the decomposition of a permutation as a product of transpositions and that as a union of disjoint cycles. It generates permutations at each recursive step and slight modifications of it produce generating algorithms for Bell permutations and involutions. Further refinements yield algorithms for these classes of permutations subject to additional restrictions: a given number of cycles or/and fixed points. We obtain, as particular cases, generating algorithms for permutations counted by the Stirling numbers of the first and second kind, even permutations, fixed-point-free involutions and derangements. All of these algorithms run in constant amortized time.

Is there a structural limit to ‘branch’ recursively between more than two tasks?

The term 'branching' refers to processes needed for successful reuptake of a task after interruption by another task. Based on a model of human prefrontal cognitive architecture, it has been postulated that people cannot branch recursively between more than two tasks due to a capacity limit built into the cognitive architecture (Koechlin and Hyafil in Science 318:594-598, 2007). As an alternative to a structural limit for recursive branching between more than two tasks we put forward the hypothesis that working memory capacity is the limiting factor in recursive branching. We tested this hypothesis by independently varying working memory load and number of recursive branching steps. Successful branching between up to four tasks was observed, as long as working memory load was kept low. Our data, thus, do not support the proposition of a structural limit to recursive branching beyond two tasks. Instead, they suggest that working memory capacity limit is the most important factor that limits the capacity for branching. We further observed that the requirement to retain task sets and task contents additively contributed to the difficulty of recursive branching. In a broader context, our data thus support working memory models that conceptualize working memory and executive functions not as separate modules, but as tightly interactive processes.