Multiple Recursion Research Articles

Research on Photoelectric Detection and Identification System Based on ThreeStage Multiple Innovation Recursive Least Squares Algorithm

Research on Photoelectric Detection and Identification System Based on ThreeStage Multiple Innovation Recursive Least Squares Algorithm

A Novel Online Scheduling Algorithm and Hierarchical Protocol for Large-Scale EV Charging Coordination

For electric vehicle (EV) charging coordination, relaxation and approximation methods are usually employed to improve scheduling efficiency in solving integer linear programming (ILP) problems. Nevertheless, they have a few inherent flaws, such as frequent charging interruption and large deviation in final SOC. Based on the recursive method, this paper proposes a search-swapping algorithm (SSA) for optimal approximation. It leverages the non-aftereffect property of charging scheduling to approximate the optimal solution as well as uses single recursion instead of multiple recursion to reduce computation cost from exponential time to polynomial time. Compared with the conventional algorithms, it has much higher efficiency, less charging interruption, and better final SOC uniformity. Furthermore, a single-round interactive protocol is designed for hierarchical coordinated framework to achieve power dispatch. Numerous simulations show that the SSA has outstanding efficiency and satisfactory optimality.

Locality Transformations for Nested Recursive Iteration Spaces

There has been a significant amount of effort invested in designing scheduling transformations such as loop tiling and loop fusion that rearrange the execution of dynamic instances of loop nests to place operations that access the same data close together temporally. In recent years, there has been interest in designing similar transformations that operate on recursive programs, but until now these transformations have only considered simple scenarios: multiple recursions to be fused, or a recursion nested inside a simple loop. This paper develops the first set of scheduling transformations for nested recursions: recursive methods that call other recursive methods. These are the recursive analog to nested loops. We present a transformation called recursion twisting that automatically improves locality at all levels of the memory hierarchy, and show that this transformation can yield substantial performance improvements across several benchmarks that exhibit nested recursion.

Locality Transformations for Nested Recursive Iteration Spaces

There has been a significant amount of effort invested in designing scheduling transformations such as loop tiling and loop fusion that rearrange the execution of dynamic instances of loop nests to place operations that access the same data close together temporally. In recent years, there has been interest in designing similar transformations that operate on recursive programs, but until now these transformations have only considered simple scenarios: multiple recursions to be fused, or a recursion nested inside a simple loop. This paper develops the first set of scheduling transformations for nested recursions: recursive methods that call other recursive methods. These are the recursive analog to nested loops. We present a transformation called recursion twisting that automatically improves locality at all levels of the memory hierarchy, and show that this transformation can yield substantial performance improvements across several benchmarks that exhibit nested recursion.

Recursion Removal as an Instructional Method to Enhance the Understanding of Recursion Tracing

Recursion is one of the most difficult programming topics for students. In this paper, an instructional method is proposed to enhance students' understanding of recursion tracing. The proposal is based on the use of rules to translate linear recursion algorithms into equivalent, iterative ones. The paper has two main contributions: the instructional method itself, and its evaluation, which is based on previous works of other authors on mental models of recursion. As a result, an enhancement was measured in the viability of mental models exhibited by students (both for linear and multiple recursion), but no significant improvement was detected in their skills for designing recursive algorithms. Evidence was also obtained of the fact that many students with (relatively) viable mental models for linear recursion have unviable mental models for multiple recursion. Finally, it was noticed that many students adopt inaccurate mental models if those models are adequate to handle the given algorithm.

Tutte polynomials for benzenoid systems with one branched hexagon

Benzenoid systems are natural graph representation of benzenoid hydrocarbons. Many chemically and combinatorially interesting indices and polynomials for bezenoid systems have been widely researched by both chemists and graph theorists. The Tutte polynomial of benzenoid chains without branched hexagons has already been computed by the recursive method. In this paper, by multiple recursion schema, an explicit expression for the Tutte polynomial of benzenoid systems with exactly one branched hexagon is obtained in terms of the number of hexagons on three linear or kinked chains. As a by-product, the number of spanning trees for these kind of benzenoid systems is determined.

Real-time multiply recursive reflections and refractions using hybrid rendering

We present a new method for real-time rendering of multiple recursions of reflections and refractions. The method uses the strengths of real-time ray tracing for objects close to the camera, by sto...

Research on Classification of Partial Discharge of Switchgear Cabinets Based on a Novel Association Rule Algorithm

In order to assess switchgear insulation status, a novel association rule mining (ARM) algorithm is presented. It is used to recognize the severity of switchgear cabinet partial discharge. The algorithm uses fuzzy C-means clustering (FCM) to divide partial discharge feature interval, candidate sets meeting minimum support and minimum confidence are sought based on an improved Apriori algorithm. Multiple recursions and scans are performed on candidate sets to generate association rules library for classification. Fuzzy reasoning based on association rules are performed over multiple needle corona partial discharge signals sampled in 10KV switchgear cabinets. The results show that partial discharge classification rate using association rules is high and classification conclusions are accurate. It has provided theoretical basis and practical value for insulation status assessment of switchgear cabinets.

Cosmopolitics: The Kiss of Life

Abstract A portrait of Australian flying fox life in the Anthropocene illuminates startlingly familiar stories. These animals are participants in most of the major catastrophic events of contemporary life on Earth: warfare, man-made mass death, famine, expukion, urbanisation, emerging dkeases, climate change, and biosecurity. At the same time they are the targets of conservation action and local/international NGO aid. They are endangered, and are involved in all the major factors causing extinctions. Equally, they are a keystone species and their looming extinction portends wider waves of extinction. My account of flying foxes in Australia focuses on the plan to expel them from the Royal Botanic Gardens in Sydney. Whilst arguing for an urban cosmopolitics of emergent convivialities, my study is required to move in a darker direction. I am inspired by Stengers's account of cosmopolitics and her definition of politics which focuses on who is entitled to speak about questions of our common destiny. Research with flying foxes shows that in advance of the question of who speaks, determinations involving terror and expulsion depend on severing any sense that there is or could be a common destiny. Radical social exclusion, phrased in righteously banal terms, precedes and comes to authorise the species cleansing involved in expulsion. Peace, if it can grasped at all in such a context, requires multiple recursions across a terrain in which we name and resist the acts of terror that purport to separate us out into divergent destinies. Keywords cosmopolitics, mutualism, symbiosis, multispecies encounters, terror, Pteropus spp I YET ANOTHER LOVE STORY I sat in the backyard of a dilapidated bungalow in south-west Sydney wondering how I could possibly get used to living in this huge, hideous, dysfunctional city. I sat there often, brooding, and I continued to brood until the day the Grevillea Robusta burst into flower. This large relatively nondescript tree, also known as silky oak, has a Cinderella moment when it decks itself out with bright orange heavily nectared flowers. I was sitting there worrying, and suddenly I heard chattery quarrelsome sounds and smelled a glorious muskiness. I felt my senses come alive, and when I looked up and saw that unmistakeable shape in the evening sky I knew for sure that flying foxes were abroad, bringing their blessings even into my backyard. I caught a glimpse of a 'nourishing terrain', of a city in which multispecies gifts of life are on the move, and I thought: 'if you guys can live here, I can too!' The next step was a research project to learn more about the lives of flying foxes in Sydney and other urban areas. I have written about Australian Aboriginal people's relationships with 'country', and I have spent years in the bush learning from Aboriginal people, many of whom are kin to flying foxes.1 1 hadn't expected to find myself washed up on a distant urban shore where no life but the human seemed to find purchase. And yet, as I came to understand, flying foxes are living an urban life rich with both perils and possibilities, a life that challenges humans to develop a more inclusive cosmopolitics. Isabelle Stengers' concept of cosmopolitics is articulated in an open and generous way that arises from a fundamental proposition that 'we are not alone in the world'.2 She states that she is aiming toward an 'experimental togetherness that makes peace a challenge'. The place of cosmopolitics is to define 'peace as an ecological production of actual togetherness, where 'ecological' means that the aim is not toward a unity beyond differences...'.3 That experimental togetherness is, or has the potential to be, a form of symbiosis: 'a relation between two heterogeneous ways of being, both needing the other because without the other none of them would be able to achieve its own pathways and goals'.4 Flying foxes in Sydney seem to be living (or trying to live) just such a multispecies symbiotic cosmopolitics, and my aim is to articulate ways in which humans might rise to the challenges of peace. …

Simply terminating rewrite systems with long derivations

A term rewrite system is called simply terminating if its termination can be shown by means of a simplification ordering. According to a result of Weiermann, the derivation length function of any simply terminating finite rewrite system is eventually dominated by a Hardy function of ordinal less than the small Veblen ordinal. This bound had appeared to be of rather theoretical nature, because all known examples had had multiple recursive complexities, until recently Touzet constructed simply (and even totally) terminating examples with complexities beyond multiple recursion. This was established by simulating the Hydra battle for all ordinal segments below the proof-theoretic ordinal of Peano arithmetic. By extending this result to the small Veblen ordinal we prove the huge bound of Weiermann to be sharp. As a spin-off we can show that total termination allows for complexities as high as those of simple termination.

Use of recursion forests in the sequential screening process: consensus selection by multiple recursion trees.

The application of Cheminformatics to High-Throughput Screening (HTS) data requires the use of robust modeling methods. Robust models must be able to accommodate false positive and false negative data yet retain good explanatory and predictive power. Recursive Partitioning has been shown to accommodate false positive and false negative data in the model building phase but suffers from a high false positive rate in the prediction phase, especially with sparse data sets such as HTS data. Here, we introduce Consensus Selection as a procedure to decrease the false positive rate of Recursive Partitioning-based models. Consensus Selection by Multiple Recursion Trees can increase the hit rate of a High-Throughput Screen in excess of 30-fold while significantly reducing the false positive rate relative to single Recursion Tree models.

Computability. Computable Functions, Logic, and the Foundations of Mathematics

Philosophy and mathematics. Some paradoxes. Whole numbers. Functions. An introduction to the nature of a proof. Infinite collections? Hilbert: on the infinite. Computability. Turing machines. The most amazing fact and Church's thesis. Primitive recursive functions. The Grzegorczyk hierarchy. Multiple recursion and recursion on order types. The least search operator. Partial recursion functions. Numbering the partial recursive functions. Listability. Turing machine computable = partial recursive. Logic and arithmetic, part 1: propositional logic. Logic and arithmetic, part 2: a review. Logic and arithmetic, part 3: first-order arithmetic. Functions representable in formal arithmetic. The undecidability of arithmetic. The unprovability of consistency. Church's thesis. Constructivist view of mathematics. Bibliography. Index of notation. Index.

Efficient parallel execution of irregular recursive programs

Programs whose parallelism stems from multiple recursion form an interesting subclass of parallel programs with many practical applications. The highly irregular shape of many recursion trees makes it difficult to obtain good load balancing with small overhead. We present a system, called REAPAR, that executes recursive C programs in parallel on SMP machines. Based on data from a single profiling run of the program, REAPAR selects a load-balancing strategy that is both effective and efficient and it generates parallel code implementing that strategy. The performance obtained by REAPAR on a diverse set of benchmarks matches that published for much more complex systems requiring high-level problem-oriented explicitly parallel constructs. A case study even found REAPAR to be competitive to handwritten (low-level, machine-oriented) thread-parallel code.

An object‐oriented software life cycle of an intelligent tutoring system

Abstract This paper describes the application of an object‐oriented model of life cycle in the development of an intelligent tutoring system for secondary students in the domain of algebraic powers. The system is called EasyMath and has been developed using the Rational Unified Process, which is an object‐oriented process proposed for use with the Unified Modelling Language. The Rational Unified Process supports multiple recursions of the phases of the software life cycle. This has been enriched to include empirical studies and formative evaluations appropriate for knowledge‐based educational software.

Multiple Recursion Conjugate Gradient Algorithms Part I: Sufficient Conditions

In this paper we show that a conjugate gradient method can be implemented using a short multiple recursion for a wider class of matrices than that demonstrated by Faber and Manteuffel [ SIAM J. Numer. Anal., 21 (1984), pp. 352--362]. In part I of this paper, sufficient conditions are determined in order that a conjugate gradient method can be implemented using this form of multiple recursion. Part II of this paper addresses necessary conditions. This is the first known short recursion for a conjugate gradient method that can be applied to a nonnormal matrix of nontrivial degree.

Term rewriting theory for the primitive recursive functions

The termination of rewrite systems for parameter recursion, simple nested recursion and unnested multiple recursion is shown by using monotone interpretations both on the ordinals below the first primitive recursively closed ordinal and on the natural numbers. We show that the resulting derivation lengths are primitive recursive. As a corollary we obtain transparent and illuminating proofs of the facts that the schemata of parameter recursion, simple nested recursion and unnested multiple recursion lead from primitive recursive functions to primitive recursive functions.

Motion compensated image interpolation

Field skipping is a variable technique for reducing drastically the bit rate necessary to transmit a television signal. All fields have to be reconstructed at the receiver end, but nearest-neighbor or linear interpolations give poor performances when significant scene activity is present; therefore, some motion compensation scheme is mandatory. Although any of the algorithms proposed for motion estimation can be used for motion compensated interpolation, in this paper only the pel-recursive algorithm is considered. Past experience is briefly summarized and, based on criticism, improvements to the basic algorithm are proposed that seem to lead to an estimated motion field that is accurate enough. Multiple recursions and appropriate selection rules are proposed to counteract streaking effects of the recursive algorithm when it crosses image boundaries. The estimation of a forward and a backward motion field is used to identify image areas where occlusion effects are present. Experimental results are presented that seem to indicate that the proposed interpolation scheme has good performance.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Increase of the complexity of functions by an application of multiple recursion

Increase of the complexity of functions by an application of multiple recursion

Computational Complexity of Multiple Recursive Schemata

The computational complexity properties of a hierarchy of classes of subrecursive schemata are investigated. The schemata are derived from the multiple recursive operators of Peter. Concrete complexity measures based on specific computation rules and an underlying random-access stored-program machine (RASP) model are defined and the complexity properties induced by certain structural features are studied.It is shown to be undecidable whether two schemata have identical complexity. Upper bounds for the complexity of schemata are then given in terms of a hierarchy of multiple recursive function classes and lower bounds are given which demonstrate that multiple recursion is a thoroughly unfeasible computational tool in practice. Specifically, it is shown that a pure multiple recursive schema capable of defining nonprimitive recursive functions must have at least exponential complexity in terms of its arguments for all interpretations. We also show it undecidable whether a schema has the minimal complexity of...

Multiple recursions bounded in the class of primitive recursive functions

Multiple recursions bounded in the class of primitive recursive functions