Dutta, Soumitra
1988-01-01
Much of human reasoning is approximate in nature. Formal models of reasoning traditionally try to be precise and reject the fuzziness of concepts in natural use and replace them with non-fuzzy scientific explicata by a process of precisiation. As an alternate to this approach, it has been suggested that rather than regard human reasoning processes as themselves approximating to some more refined and exact logical process that can be carried out with mathematical precision, the essence and power of human reasoning is in its capability to grasp and use inexact concepts directly. This view is supported by the widespread fuzziness of simple everyday terms (e.g., near tall) and the complexity of ordinary tasks (e.g., cleaning a room). Spatial reasoning is an area where humans consistently reason approximately with demonstrably good results. Consider the case of crossing a traffic intersection. We have only an approximate idea of the locations and speeds of various obstacles (e.g., persons and vehicles), but we nevertheless manage to cross such traffic intersections without any harm. The details of our mental processes which enable us to carry out such intricate tasks in such apparently simple manner are not well understood. However, it is that we try to incorporate such approximate reasoning techniques in our computer systems. Approximate spatial reasoning is very important for intelligent mobile agents (e.g., robots), specially for those operating in uncertain or unknown or dynamic domains.
Approximate Assertional Reasoning Over Expressive Ontologies
Tserendorj, Tuvshintur
2010-01-01
In this thesis, approximate reasoning methods for scalable assertional reasoning are provided whose computational properties can be established in a well-understood way, namely in terms of soundness and completeness, and whose quality can be analyzed in terms of statistical measurements, namely recall and precision. The basic idea of these approximate reasoning methods is to speed up reasoning by trading off the quality of reasoning results against increased speed.
An approximate reasoning-based method for screening high-level-waste tanks for flammable gas
The in situ retention of flammable gas produced by radiolysis and thermal decomposition in high-level waste can pose a safety problem if the gases are released episodically into the dome space of a storage tank. Screening efforts at the Hanford site have been directed at identifying tanks in which this situation could exist. Problems encountered in screening motivated an effort to develop and improved screening methodology. Approximate reasoning (AR) is a formalism designed to emulate the kinds of complex judgments made by subject matter experts. It uses inductive logic structures to build a sequence of forward-chaining inferences about a subject. Approximate-reasoning models incorporate natural language expressions known as linguistic variables to represent evidence. The use of fuzzy sets to represent these variables mathematically makes it practical to evaluate quantitative and qualitative information consistently. In a pilot study to investigate the utility of AR for flammable gas screening, the effort to implement such a model was found to be acceptable, and computational requirements were found to be reasonable. The preliminary results showed that important judgments about the validity of observational data and the predictive power of models could be made. These results give new insights into the problems observed in previous screening efforts
An Approximate Reasoning-Based Method for Screening High-Level-Waste Tanks for Flammable Gas
The in situ retention of flammable gas produced by radiolysis and thermal decomposition in high-level waste can pose a safety problem if the gases are released episodically into the dome space of a storage tank. Screening efforts at the Hanford site have been directed at identifying tanks in which this situation could exist. Problems encountered in screening motivated an effort to develop an improved screening methodology. Approximate reasoning (AR) is a formalism designed to emulate the kinds of complex judgments made by subject matter experts. It uses inductive logic structures to build a sequence of forward-chaining inferences about a subject. Approximate-reasoning models incorporate natural language expressions known as linguistic variables to represent evidence. The use of fuzzy sets to represent these variables mathematically makes it practical to evaluate quantitative and qualitative information consistently. In a pilot study to investigate the utility of AR for flammable gas screening, the effort to implement such a model was found to be acceptable, and computational requirements were found to be reasonable. The preliminary results showed that important judgments about the validity of observational data and the predictive power of models could be made. These results give new insights into the problems observed in previous screening efforts
Owladeghaffari, H; Saeedi, G H R
2008-01-01
Approximately more than 90% of all coal production in Iranian underground mines is derived directly longwall mining method. Out of seam dilution is one of the essential problems in these mines. Therefore the dilution can impose the additional cost of mining and milling. As a result, recognition of the effective parameters on the dilution has a remarkable role in industry. In this way, this paper has analyzed the influence of 13 parameters (attributed variables) versus the decision attribute (dilution value), so that using two approximate reasoning methods, namely Rough Set Theory (RST) and Self Organizing Neuro- Fuzzy Inference System (SONFIS) the best rules on our collected data sets has been extracted. The other benefit of later methods is to predict new unknown cases. So, the reduced sets (reducts) by RST have been obtained. Therefore the emerged results by utilizing mentioned methods shows that the high sensitive variables are thickness of layer, length of stope, rate of advance, number of miners, type of...
Approximate Reasoning with Fuzzy Booleans
Broek, van den P.M.; Noppen, J.A.R.
2004-01-01
This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp ante
An approximate-reasoning-based method for screening high-level waste tanks for flammable gas
The in situ retention of flammable gas produced by radiolysis and thermal decomposition in high-level waste can pose a safety problem if the gases are released episodically into the dome space of a storage tank. Screening efforts at Hanford have been directed at identifying tanks in which this situation could exist. Problems encountered in screening motivated an effort to develop an improved screening methodology. Approximate reasoning (AR) is a formalism designed to emulate the kinds of complex judgments made by subject matter experts. It uses inductive logic structures to build a sequence of forward-chaining inferences about a subject. AR models incorporate natural language expressions known as linguistic variables to represent evidence. The use of fuzzy sets to represent these variables mathematically makes it practical to evaluate quantitative and qualitative information consistently. The authors performed a pilot study to investigate the utility of AR for flammable gas screening. They found that the effort to implement such a model was acceptable and that computational requirements were reasonable. The preliminary results showed that important judgments about the validity of observational data and the predictive power of models could be made. These results give new insights into the problems observed in previous screening efforts
An approximate-reasoning-based method for screening flammable gas tanks
Eisenhawer, S.W.; Bott, T.F.; Smith, R.E.
1998-03-01
High-level waste (HLW) produces flammable gases as a result of radiolysis and thermal decomposition of organics. Under certain conditions, these gases can accumulate within the waste for extended periods and then be released quickly into the dome space of the storage tank. As part of the effort to reduce the safety concerns associated with flammable gas in HLW tanks at Hanford, a flammable gas watch list (FGWL) has been established. Inclusion on the FGWL is based on criteria intended to measure the risk associated with the presence of flammable gas. It is important that all high-risk tanks be identified with high confidence so that they may be controlled. Conversely, to minimize operational complexity, the number of tanks on the watchlist should be reduced as near to the true number of flammable risk tanks as the current state of knowledge will support. This report presents an alternative to existing approaches for FGWL screening based on the theory of approximate reasoning (AR) (Zadeh 1976). The AR-based model emulates the inference process used by an expert when asked to make an evaluation. The FGWL model described here was exercised by performing two evaluations. (1) A complete tank evaluation where the entire algorithm is used. This was done for two tanks, U-106 and AW-104. U-106 is a single shell tank with large sludge and saltcake layers. AW-104 is a double shell tank with over one million gallons of supernate. Both of these tanks had failed the screening performed by Hodgson et al. (2) Partial evaluations using a submodule for the predictor likelihood for all of the tanks on the FGWL that had been flagged previously by Whitney (1995).
An approximate-reasoning-based method for screening flammable gas tanks
High-level waste (HLW) produces flammable gases as a result of radiolysis and thermal decomposition of organics. Under certain conditions, these gases can accumulate within the waste for extended periods and then be released quickly into the dome space of the storage tank. As part of the effort to reduce the safety concerns associated with flammable gas in HLW tanks at Hanford, a flammable gas watch list (FGWL) has been established. Inclusion on the FGWL is based on criteria intended to measure the risk associated with the presence of flammable gas. It is important that all high-risk tanks be identified with high confidence so that they may be controlled. Conversely, to minimize operational complexity, the number of tanks on the watchlist should be reduced as near to the true number of flammable risk tanks as the current state of knowledge will support. This report presents an alternative to existing approaches for FGWL screening based on the theory of approximate reasoning (AR) (Zadeh 1976). The AR-based model emulates the inference process used by an expert when asked to make an evaluation. The FGWL model described here was exercised by performing two evaluations. (1) A complete tank evaluation where the entire algorithm is used. This was done for two tanks, U-106 and AW-104. U-106 is a single shell tank with large sludge and saltcake layers. AW-104 is a double shell tank with over one million gallons of supernate. Both of these tanks had failed the screening performed by Hodgson et al. (2) Partial evaluations using a submodule for the predictor likelihood for all of the tanks on the FGWL that had been flagged previously by Whitney (1995)
Richtárik, Peter
2008-01-01
In this paper we propose and analyze a variant of the level method [4], which is an algorithm for minimizing nonsmooth convex functions. The main work per iteration is spent on 1) minimizing a piecewise-linear model of the objective function and on 2) projecting onto the intersection of the feasible region and a polyhedron arising as a level set of the model. We show that by replacing exact computations in both cases by approximate computations, in relative scale, the theoretical ...
A comparison of approximate reasoning results using information uncertainty
Chavez, Gregory [Los Alamos National Laboratory; Key, Brian [Los Alamos National Laboratory; Zerkle, David [Los Alamos National Laboratory; Shevitz, Daniel [Los Alamos National Laboratory
2009-01-01
An Approximate Reasoning (AR) model is a useful alternative to a probabilistic model when there is a need to draw conclusions from information that is qualitative. For certain systems, much of the information available is elicited from subject matter experts (SME). One such example is the risk of attack on a particular facility by a pernicious adversary. In this example there are several avenues of attack, i.e. scenarios, and AR can be used to model the risk of attack associated with each scenario. The qualitative information available and provided by the SME is comprised of linguistic values which are well suited for an AR model but meager for other modeling approaches. AR models can produce many competing results. Associated with each competing AR result is a vector of linguistic values and a respective degree of membership in each value. A suitable means to compare and segregate AR results would be an invaluable tool to analysts and decisions makers. A viable method would be to quantify the information uncertainty present in each AR result then use the measured quantity comparatively. One issue of concern for measuring the infornlation uncertainty involved with fuzzy uncertainty is that previously proposed approaches focus on the information uncertainty involved within the entire fuzzy set. This paper proposes extending measures of information uncertainty to AR results, which involve only one degree of membership for each fuzzy set included in the AR result. An approach to quantify the information uncertainty in the AR result is presented.
Approximation methods in probability theory
Čekanavičius, Vydas
2016-01-01
This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.
Uncertainty and approximate reasoning in waste pretreatment planning
Waste pretreatment process planning within the DOE complex must consider many different outcomes in order to perform the tradeoffs necessary to accomplish this important national mission. One of the difficulties encountered by many who assess these tradeoffs is that the complexity of this problem taxes the abilities of any single person or small group of individuals. For example, uncertainties in waste composition as well as process efficiency are well known yet incompletely considered in the search for optimum solutions. This paper describes a tool, the pre-treatment Process Analysis Tool (PAT), for evaluating tank waste pretreatment options at Hanford, Oak Ridge, Idaho National Environmental and Engineering Laboratory, and Savannah River Sites. The PAT propagates uncertainty in both tank waste composition and process partitioning into a set of ten outcomes. These outcomes are, for example, total cost, Cs-137 in iLAW, iHLW MT, and so on. Tradeoffs among outcomes are evaluated or scored by means of an approximate reasoning module that uses linguistic bases to evaluate tradeoffs for each process based on user valuations of outcomes
System reliability assessment with an approximate reasoning model
Eisenhawer, S.W.; Bott, T.F.; Helm, T.M.; Boerigter, S.T.
1998-12-31
The projected service life of weapons in the US nuclear stockpile will exceed the original design life of their critical components. Interim metrics are needed to describe weapon states for use in simulation models of the nuclear weapons complex. The authors present an approach to this problem based upon the theory of approximate reasoning (AR) that allows meaningful assessments to be made in an environment where reliability models are incomplete. AR models are designed to emulate the inference process used by subject matter experts. The emulation is based upon a formal logic structure that relates evidence about components. This evidence is translated using natural language expressions into linguistic variables that describe membership in fuzzy sets. The authors introduce a metric that measures the acceptability of a weapon to nuclear deterrence planners. Implication rule bases are used to draw a series of forward chaining inferences about the acceptability of components, subsystems and individual weapons. They describe each component in the AR model in some detail and illustrate its behavior with a small example. The integration of the acceptability metric into a prototype model to simulate the weapons complex is also described.
Artificial neural networks and approximate reasoning for intelligent control in space
Berenji, Hamid R.
1991-01-01
A method is introduced for learning to refine the control rules of approximate reasoning-based controllers. A reinforcement-learning technique is used in conjunction with a multi-layer neural network model of an approximate reasoning-based controller. The model learns by updating its prediction of the physical system's behavior. The model can use the control knowledge of an experienced operator and fine-tune it through the process of learning. Some of the space domains suitable for applications of the model such as rendezvous and docking, camera tracking, and tethered systems control are discussed.
Information processing systems, reasoning modules, and reasoning system design methods
Hohimer, Ryan E.; Greitzer, Frank L.; Hampton, Shawn D.
2016-08-23
Information processing systems, reasoning modules, and reasoning system design methods are described. According to one aspect, an information processing system includes working memory comprising a semantic graph which comprises a plurality of abstractions, wherein the abstractions individually include an individual which is defined according to an ontology and a reasoning system comprising a plurality of reasoning modules which are configured to process different abstractions of the semantic graph, wherein a first of the reasoning modules is configured to process a plurality of abstractions which include individuals of a first classification type of the ontology and a second of the reasoning modules is configured to process a plurality of abstractions which include individuals of a second classification type of the ontology, wherein the first and second classification types are different.
Information processing systems, reasoning modules, and reasoning system design methods
Hohimer, Ryan E.; Greitzer, Frank L.; Hampton, Shawn D.
2015-08-18
Information processing systems, reasoning modules, and reasoning system design methods are described. According to one aspect, an information processing system includes working memory comprising a semantic graph which comprises a plurality of abstractions, wherein the abstractions individually include an individual which is defined according to an ontology and a reasoning system comprising a plurality of reasoning modules which are configured to process different abstractions of the semantic graph, wherein a first of the reasoning modules is configured to process a plurality of abstractions which include individuals of a first classification type of the ontology and a second of the reasoning modules is configured to process a plurality of abstractions which include individuals of a second classification type of the ontology, wherein the first and second classification types are different.
Information processing systems, reasoning modules, and reasoning system design methods
Hohimer, Ryan E; Greitzer, Frank L; Hampton, Shawn D
2014-03-04
Information processing systems, reasoning modules, and reasoning system design methods are described. According to one aspect, an information processing system includes working memory comprising a semantic graph which comprises a plurality of abstractions, wherein the abstractions individually include an individual which is defined according to an ontology and a reasoning system comprising a plurality of reasoning modules which are configured to process different abstractions of the semantic graph, wherein a first of the reasoning modules is configured to process a plurality of abstractions which include individuals of a first classification type of the ontology and a second of the reasoning modules is configured to process a plurality of abstractions which include individuals of a second classification type of the ontology, wherein the first and second classification types are different.
Approximation methods for stochastic petri nets
Jungnitz, Hauke Joerg
1992-01-01
Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay
Dynamical equations and approximation methods
The integral equations approach to the three-body problem, decisively stimulated by Faddeev's formulation, provides the most powerful tool for studying the internal structure of this system. An essential step towards a detailed understanding of composite particle dynamics has been done in this way. The search for adequate extensions to the general N-body situation therefore represented, and still represents a natural challenge. For various reasons this transition is non-trivial and non-unique. Emphasizing different aspects of the three-body theory, different generalizations have been found. In particular, it was the concept of connectedness of the (iterated) integral kernel which allows for an arbitrary number of formulations, many of them being presumably only mathematically correct, but physically rather unsatisfactory. Therefore, the present status of the N-body theory is reviewed in a less technical way. Starting from the basic, physically convincing definitions of scattering states, the defining equations are replaced by more appropriate matrix relations. This is done in a reversible way, thus preserving in every step the original structure and information. In order to be as close as possible to the basic definitions, all relations are first derived for scattering states or half-on-shell transition amplitudes. The ambiguity in going over to corresponding operator identities (fully off-shell equations) is demonstrated. (Auth.)
Evaluation of high-level waste pretreatment processes with an approximate reasoning model
The development of an approximate-reasoning (AR)-based model to analyze pretreatment options for high-level waste is presented. AR methods are used to emulate the processes used by experts in arriving at a judgment. In this paper, the authors first consider two specific issues in applying AR to the analysis of pretreatment options. They examine how to combine quantitative and qualitative evidence to infer the acceptability of a process result using the example of cesium content in low-level waste. They then demonstrate the use of simple physical models to structure expert elicitation and to produce inferences consistent with a problem involving waste particle size effects
A Linear Approximation Method for Probabilistic Inference
Shachter, Ross D.
2013-01-01
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on the Gaussian influence diagram, iterates over linear approximations to the inference problem.
A New Method for Reasoning about Action
杨杰
1996-01-01
Reasoning about action is an important aspect of common sense reasoning and planning.It gives rise to three classical problems:the frame problem,the qualification problem and the ramification problem.Existing approaches cannot deal with these problems efficiently.This paper presents a new method which uses the stratified ATMS for reasoning about action to overcome the limitations of these approaches.
Scientific Facts and Methods in Public Reason
Jønch-Clausen, Karin; Kappel, Klemens
2016-01-01
Should scientific facts and methods have an epistemically privileged status in public reason? In Rawls’s public reason account he asserts what we will label the Scientific Standard Stricture: citizens engaged in public reason must be guided by non-controversial scientific methods, and public reason......’s Scientific Standards Stricture. We then use Rawls’s general theoretical framework to examine various potential justifications for privileging these ‘non-controversial’ scientific methods and conclusions. We conclude that no viable justification is available to Rawls....... must be in line with non-controversial scientific conclusions. The Scientific Standard Stricture is meant to fulfill important tasks such as enabling the determinateness and publicity of the public reason framework. However, Rawls leaves us without elucidation with regard to when science is and is not...
Approximate error conjugation gradient minimization methods
Kallman, Jeffrey S
2013-05-21
In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.
Approximate path integral methods for partition functions
We review several approximate methods for evaluating quantum mechanical partition functions with the goal of obtaining a method that is easy to implement for multidimensional systems but accurately incorporates quantum mechanical corrections to classical partition functions. A particularly promising method is one based upon an approximation to the path integral expression of the partition function. In this method, the partition-function expression has the ease of evaluation of a classical partition function, and quantum mechanical effects are included by a weight function. Anharmonicity is included exactly in the classical Boltzmann average and local quadratic expansions around the centroid of the quantum paths yield a simple analytic form for the quantum weight function. We discuss the relationship between this expression and previous approximate methods and present numerical comparisons for model one-dimensional potentials and for accurate three-dimensional vibrational force fields for H2O and SO2
Generalized If ... Then...Else Inference Rules with Linguistic Modifiers for Approximate Reasoning
Le Anh Phuong; Tran Dinh Khang
2012-01-01
In this paper, based on the our previous researchs about generalized modus ponens with linguistic modifiers for If...Then rules, we propose generalized If...Then...Else inference rules with linguistic modifiers in linguistic many-valued logic framework with using hedge moving rules for approximate reasoning.
Research of Approximate Reasoning in Semantic Web%语义Web近似推理研究
廖先旭; 黄佳进
2011-01-01
随着语义Web本体技术的快速发展和近似推理技术的应用，语义Web近似推理满足了快速有效地搜索有用的信息和知识的需求。本文主要从语义Web近似推理的难点介绍了近年来关于语义web近似推理的研究，并在最后对语义web近似推理研究的发展趋势做了总结。%With the fast development of ontology technology for Semantic Web and the application of approximate reasoning, approximate reasoning on the Semantic Web can satisfy the demand of finding useful information and knowledge fast and efficiently. This paper introduces approximate reasoning on the Semantic Web research in recent years from its key problems and the research trends of approximate reasoning on Semantic Web.
Iterative Methods for the Force-based Quasicontinuum Approximation
Dobson, Matthew; Luskin, Mitchell; Ortner, Christoph
2009-01-01
Force-based atomistic-continuum hybrid methods are the only known pointwise consistent methods for coupling a general atomistic model to a finite element continuum model. For this reason, and due to their algorithmic simplicity, force-based coupling methods have become a popular class of atomistic-continuum hybrid models as well as other types of multiphysics models. However, the recently discovered unusual stability properties of the linearized force-based quasicontinuum (QCF) approximation,...
Darby, John L.
2007-03-01
LinguisticBelief is a Java computer code that evaluates combinations of linguistic variables using an approximate reasoning rule base. Each variable is comprised of fuzzy sets, and a rule base describes the reasoning on combinations of variables fuzzy sets. Uncertainty is considered and propagated through the rule base using the belief/plausibility measure. The mathematics of fuzzy sets, approximate reasoning, and belief/ plausibility are complex. Without an automated tool, this complexity precludes their application to all but the simplest of problems. LinguisticBelief automates the use of these techniques, allowing complex problems to be evaluated easily. LinguisticBelief can be used free of charge on any Windows XP machine. This report documents the use and structure of the LinguisticBelief code, and the deployment package for installation client machines.
Reverse triple I method of fuzzy reasoning
宋士吉; 吴澄
2002-01-01
A theory of reverse triple I method with sustention degree is presented by using the implication operator R0 in every step of the fuzzy reasoning. Its computation formulas of supremum for fuzzy modus ponens and infimum for fuzzy modus tollens are given respectively. Moreover, through the generalization of this problem, the corresponding formulas of ?-reverse triple I method with sustention degree are also obtained. In addition, the theory of reverse triple I method with restriction degree is proposed as well by using the operator R0, and the computation formulas of infimum for fuzzy modus ponens and supremum for fuzzy modus tollens are shown.
Approximate syllogistic reasoning: a contribution to inference patterns and use cases
Pereira-Fariña, Martín
2014-01-01
In this thesis two models of syllogistic reasoning for dealing with arguments that involve fuzzy quantified statements and approximate chaining are proposed. The modeling of quantified statements is based on the Theory of Generalized Quantifiers, which allows us to manage different kind of quantifiers simultaneously, and the inference process is interpreted in terms of a mathematical optimization problem, which allows us to deal with more arguments that standard deductive ones. For the case o...
Impulse approximation versus elementary particle method
Calculations are made for radiative muon capture in 3He, both in impulse approximation and with the elementary particle method, and results are compared. It is argued that a diagrammatic method which takes a selected set of Feynman diagrams into account only provides insufficient warrant that effects not included are small. Therefore low-energy theorems are employed, as first given by Adler and Dothan, to determine the amplitude up to and including all terms linear in photon momentum and momentum transfer at the weak vertex. This amplitude is applied to radiative muon capture with the elementary particle method (EPM). The various form factors needed are discussed. It is shown that the results are particularly sensitive to the π-3He-3H coupling constant of which many contradictory determinations have been described in the literature. The classification of the nuclear wave function employed in the impulse approximation (IA) is summarized. The ν-decay of 3H and (radiative muon capture in 3He is treated and numerical results are given. Next, pion photoproduction and radiative pion capture are considered. IA and EPM for radiative muon capture are compared more closely. It is concluded that two-step processes are inherently difficult; the elementary particle method has convergence problems, and unknown parameters are present. In the impulse approximation, which is perhaps conceptually more difficult, the two-step interaction for the nucleon is considered as effectively point-like with small non-local corrections. (Auth.)
An approximate method for classical scattering problems
An approximate method of calculating scattering cross sections is presented. Newton's second law and the conservation of energy are used to relate the scattering angle to the impulse delivered to the projectile by the scatterer. In order to calculate the impulse, it is necessary to know the time dependence of the trajectory. We assume that the projectile travels the two asymptotes to the actual trajectory with constant velocity
Study of quarkonium spectroscopy through the approximated variational method
The spectroscopy of the qq sup(-) bound states in a non-relativistic approximation using a approximate variational method is studied. Because of its similarity to positronium, a wave function of the hidrogen atom, is used. The 'coulomb-logaritmic-linear' was the potential used to described it. The fitting is done, and relevant coupling constant due to a logaritmic piece is found. All states described in this way furnishes v2 3P are reasonably explained and it no occurs with the mass diference between psi and eta sub(c). (Author)
Approximations in the PE-method
Arranz, Marta Galindo
Two differenct sources of errors may occur in the implementation of the PE methods; a phase error introduced in the approximation of a pseudo-differential operator and an amplitude error generated from the starting field. First, the inherent phase errors introduced in the solution are analyzed for...... a case where the normal mode solution to the wave equation is valid, when the sound is propagated in a downward refracting atmosphere. The angular limitations for the different parabolic approximations are deduced, and calculations showing shifts in the starter as the second source of error is...... investigated. Numerical and analytical starters are compared for source locations close to the ground. The spectral properties of several starters are presented....
Hoebel, Louis J.
1993-01-01
The problem of plan generation (PG) and the problem of plan execution monitoring (PEM), including updating, queries, and resource-bounded replanning, have different reasoning and representation requirements. PEM requires the integration of qualitative and quantitative information. PEM is the receiving of data about the world in which a plan or agent is executing. The problem is to quickly determine the relevance of the data, the consistency of the data with respect to the expected effects, and if execution should continue. Only spatial and temporal aspects of the plan are addressed for relevance in this work. Current temporal reasoning systems are deficient in computational aspects or expressiveness. This work presents a hybrid qualitative and quantitative system that is fully expressive in its assertion language while offering certain computational efficiencies. In order to proceed, methods incorporating approximate reasoning using hierarchies, notions of locality, constraint expansion, and absolute parameters need be used and are shown to be useful for the anytime nature of PEM.
A Method for Approximate Reasoning in Exploratory Data Analysis
Holeňa, Martin
Wien : Austrian Society for Cybernetic Studies, 1996, s. 329-334. ISBN 3-85206-133-4. [European Meeting on Cybernetics and Systems Research /13./. Vienna (AT), 09.04.1996-12.04.1996] Grant ostatní: COPERNICUS(XE) MUM-10053
Sparse Approximation via Penalty Decomposition Methods
Lu, Zhaosong
2012-01-01
In this paper we consider sparse approximation problems, that is, general $l_0$ minimization problems with the $l_0$-"norm" of a vector being a part of constraints or objective function. In particular, we first study the first-order optimality conditions for these problems. We then propose penalty decomposition (PD) methods for solving them in which a sequence of penalty subproblems are solved by a block coordinate descent (BCD) method. Under some suitable assumptions, we establish that any accumulation point of the sequence generated by the PD methods satisfies the first-order optimality conditions of the problems. Furthermore, for the problems in which the $l_0$ part is the only nonconvex part, we show that such an accumulation point is a local minimizer of the problems. In addition, we show that any accumulation point of the sequence generated by the BCD method is a saddle point of the penalty subproblem. Moreover, for the problems in which the $l_0$ part is the only nonconvex part, we establish that such ...
Outdoor sensor-based operation of autonomous robots has revealed to be an extremely challenging problem, mainly because of the difficulties encountered when attempting to represent the many uncertainties which are always present in the real world. These uncertainties are primarily due to sensor imprecisions and unpredictability of the environment, i.e., lack of full knowledge of the environment characteristics and dynamics. Two basic principles, or philosophies, and their associated methodologies are proposed in an attempt to remedy some of these difficulties. The first principle is based on the concept of ''minimal model'' for accomplishing given tasks and proposes to utilize only the minimum level of information and precision necessary to accomplish elemental functions of complex tasks. This approach diverges completely from the direction taken by most artificial vision studies which conventionally call for crisp and detailed analysis of every available component in the perception data. The paper will first review the basic concepts of this approach and will discuss its pragmatic feasibility when embodied in a behaviorist framework. The second principle which is proposed deals with implicit representation of uncertainties using Fuzzy Set Theory-based approximations and approximate reasoning, rather than explicit (crisp) representation through calculation and conventional propagation techniques. A framework which merges these principles and approaches is presented, and its application to the problem of sensor-based outdoor navigation of a mobile robot is discussed. Results of navigation experiments with a real car in actual outdoor environments are also discussed to illustrate the feasibility of the overall concept
Pin, F.G.
1993-11-01
Outdoor sensor-based operation of autonomous robots has revealed to be an extremely challenging problem, mainly because of the difficulties encountered when attempting to represent the many uncertainties which are always present in the real world. These uncertainties are primarily due to sensor imprecisions and unpredictability of the environment, i.e., lack of full knowledge of the environment characteristics and dynamics. Two basic principles, or philosophies, and their associated methodologies are proposed in an attempt to remedy some of these difficulties. The first principle is based on the concept of ``minimal model`` for accomplishing given tasks and proposes to utilize only the minimum level of information and precision necessary to accomplish elemental functions of complex tasks. This approach diverges completely from the direction taken by most artificial vision studies which conventionally call for crisp and detailed analysis of every available component in the perception data. The paper will first review the basic concepts of this approach and will discuss its pragmatic feasibility when embodied in a behaviorist framework. The second principle which is proposed deals with implicit representation of uncertainties using Fuzzy Set Theory-based approximations and approximate reasoning, rather than explicit (crisp) representation through calculation and conventional propagation techniques. A framework which merges these principles and approaches is presented, and its application to the problem of sensor-based outdoor navigation of a mobile robot is discussed. Results of navigation experiments with a real car in actual outdoor environments are also discussed to illustrate the feasibility of the overall concept.
Methods of Fourier analysis and approximation theory
Tikhonov, Sergey
2016-01-01
Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.
Reasons and Methods to Learn the Management
Li, Hongxin; Ding, Mengchun
2010-01-01
Reasons for learning the management include (1) perfecting the knowledge structure, (2) the management is the base of all organizations, (3) one person may be the manager or the managed person, (4) the management is absolutely not simple knowledge, and (5) the learning of the theoretical knowledge of the management can not be replaced by the…
An Analysis of General Fuzzy Logic and Fuzzy Reasoning Method
Il, Kwak Son
2016-01-01
In this article, we describe the fuzzy logic, fuzzy language and algorithms as the basis of fuzzy reasoning, one of the intelligent information processing method, and then describe the general fuzzy reasoning method.
Evaluating methods for approximating stochastic differential equations
Brown, Scott D; RATCLIFF, ROGER; Smith, Philip L.
2006-01-01
Models of decision making and response time (RT) are often formulated using stochastic differential equations (SDEs). Researchers often investigate these models using a simple Monte Carlo method based on Euler’s method for solving ordinary differential equations. The accuracy of Euler’s method is investigated and compared to the performance of more complex simulation methods. The more complex methods for solving SDEs yielded no improvement in accuracy over the Euler method. However, the matri...
PERSONNEL DEMOTIVATING: THE REASONS, FACTORS, ELIMINATION METHODS
Kuznetsova Ekaterina Andreevna
2012-01-01
The motivation of the personnel in any economic conditions remains a leading link in an enterprise control system. At creation of system of motivation tracking of extent of its impact on productivity of work of the personnel is important. The boomerang effect which is shown in a demotivating of separate groups of the personnel is often observed. In article features of manifestation of demotivating factors at various stages of work of the personnel are analyzed, the circle of the reasons bring...
Shape theory categorical methods of approximation
Cordier, J M
2008-01-01
This in-depth treatment uses shape theory as a ""case study"" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. It offers students a unified and consolidated presentation of extensive research from category theory, shape theory, and the study of topological algebras.A short introduction to geometric shape explains specifics of the construction of the shape category and relates it to an abstract definition of shape theory. Upon returning to the geometric base, the text considers simplical complexes and
Augmenting Ordinal Methods of Attribute Weight Approximation
Daneilson, Mats; Ekenberg, Love; He, Ying
2014-01-01
Multicriteria decision aid (MCDA) methods have been around for quite some time. However, the elicitation of preference information in MCDA processes and the lack of supporting practical means are problematic in real-life applications. Various proposals have been made for how to eliminate some...... of the obstacles and methods for introducing so-called surrogate weights have proliferated in the form of ordinal ranking methods for criteria weights. Considering the decision quality, one main problem is that the input information allowed in ordinal methods is sometimes too restricted. At the same time, decision...... makers often possess more background information, for example, regarding the relative strengths of the criteria, and might want to use that. We propose combined methods for facilitating the elicitation process and show how this provides a way to use partial information from the strength of preference...
WANG Guojun; CHIN K. S.; DANG C.Y.
2005-01-01
The concepts of metric R0-algebra and Hilbert cube of type R0 are introduced.A unified approximate reasoning theory in propositional caculus system L* and predicate calculus system K* is established semantically as well as syntactically, and a unified complete theorem is obtained.
Approximating Mathematical Semantic Web Services Using Approximation Formulas and Numerical Methods
Mogos, Andrei-Horia
2009-01-01
Mathematical semantic web services are very useful in practice, but only a small number of research results are reported in this area. In this paper we present a method of obtaining an approximation of a mathematical semantic web service, from its semantic description, using existing mathematical semantic web services, approximation formulas, and numerical methods techniques. We also give a method for automatic comparison of two complexity functions. In addition, we present a method for classifying the numerical methods mathematical semantic web services from a library.
High order source approximation for the EFEN method
The flat source approximation in one dimensional Exponential Function Expansion Nodal (EFEN) method is extended to a high order polynomial approximation while maintaining the simplicity of the nodal response matrix. By applying the new method to a one dimensional PWR pin-by-pin problem, it has been observed that quadratic source approximation is good enough for PWR pin-by-pin calculation, while the flat source approximation causes about 5% of relative error to the thermal flux. By applying the new method to a one dimensional assembly homogenized problem, it has been found that the EFEN method with cubic source approximation can be employed to handle PWR core diffusion problems. Numerical results suggest the optimization of source approximation order for different energy groups and different spacial locations to achieve more accurate results with less computing effort. (author)
Approximations of continuous Newton's method: An extension of Cayley's problem
Jon Jacobsen
2007-02-01
Full Text Available Continuous Newton's Method refers to a certain dynamical system whose associated flow generically tends to the roots of a given polynomial. An Euler approximation of this system, with step size $h=1$, yields the discrete Newton's method algorithm for finding roots. In this note we contrast Euler approximations with several different approximations of the continuous ODE system and, using computer experiments, consider their impact on the associated fractal basin boundaries of the roots.
A Semantic Retrieval Method Based on the Fuzzy Reasoning
无
2002-01-01
This paper gives a semantic fuzzy retrieval method of multimedia object,discusses the principle of fuzzy semantic retrieval technique,presents a fuzzy reasoning mechanism based on the knowledge base,and designs the relevant reasoning algorithms.Researchful results have innovative significance.
Nonlinear ordinary differential equations analytical approximation and numerical methods
Hermann, Martin
2016-01-01
The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...
Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems
Benzi, M. [Universita di Bologna (Italy); Tuma, M. [Inst. of Computer Sciences, Prague (Czech Republic)
1996-12-31
A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods.
Approximate Method for Solving the Linear Fuzzy Delay Differential Equations
S. Narayanamoorthy
2015-01-01
Full Text Available We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.
An approximate methods approach to probabilistic structural analysis
Mcclung, R. C.; Millwater, H. R.; Wu, Y.-T.; Thacker, B. H.; Burnside, O. H.
1989-01-01
A major research and technology program in Probabilistic Structural Analysis Methods (PSAM) is currently being sponsored by the NASA Lewis Research Center with Southwest Research Institute as the prime contractor. This program is motivated by the need to accurately predict structural response in an environment where the loadings, the material properties, and even the structure may be considered random. The heart of PSAM is a software package which combines advanced structural analysis codes with a fast probability integration (FPI) algorithm for the efficient calculation of stochastic structural response. The basic idea of PAAM is simple: make an approximate calculation of system response, including calculation of the associated probabilities, with minimal computation time and cost, based on a simplified representation of the geometry, loads, and material. The deterministic solution resulting should give a reasonable and realistic description of performance-limiting system responses, although some error will be inevitable. If the simple model has correctly captured the basic mechanics of the system, however, including the proper functional dependence of stress, frequency, etc. on design parameters, then the response sensitivities calculated may be of significantly higher accuracy.
Energy of Bardeen Model Using Approximate Symmetry Method
Sharif, M.; Waheed, Saira
2010-01-01
In this paper, we investigate the energy problem in general relativity using approximate Lie symmetry methods for differential equations. This procedure is applied to Bardeen model (the regular black hole solution). Here we are forced to evaluate the third-order approximate symmetries of the orbital and geodesic equations. It is shown that energy must be re-scaled by some factor in the third-order approximation. We discuss the insights of this re-scaling factor.
Approximate analytical methods for solving ordinary differential equations
Radhika, TSL; Rani, T Raja
2015-01-01
Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles. It covers both well-established techniques and recently developed procedures, including the classical series solution method, diverse perturbation methods, pioneering asymptotic methods, and the latest homotopy methods.The book is suitable not only for mathematicians and engineers but also for biologists, physicists, and economists. It gives a complete descripti
Numerical Stability and Convergence of Approximate Methods for Conservation Laws
Galkin, V. A.
We present the new approach to background of approximate methods convergence based on functional solutions theory for conservation laws. The applications to physical kinetics, gas and fluid dynamics are considered.
A double power series method for approximating cosmological perturbations
Wren, Andrew J
2016-01-01
We introduce a double power series method for finding approximate analytical solutions for systems of differential equations commonly found in cosmological perturbation theory. The method was set out, in a non-cosmological context, by Feshchenko, Shkil' and Nikolenko (FSN) in 1966, and is applicable to cases where perturbations are on sub-horizon scales. The FSN method is essentially an extension of the well known Wentzel-Kramers-Brillouin (WKB) method for finding approximate analytical solutions for ordinary differential equations. The FSN method is well suited for solving systems of linear second order ordinary differential equations, that also depend on a small parameter, which here we take to be the inverse wave-number. We use the FSN method to find new approximate oscillating solutions in linear order cosmological perturbation theory for a flat radiation-matter universe. Together with this model's well known growing and decaying M\\'esz\\'aros solutions, these oscillating modes provide a complete set of su...
Children's Expression of Negative Affect: Reasons and Methods.
Zeman, Janice; Shipman, Kimberly
1996-01-01
Examines the influence of socialization figures (parents, friends), emotion type (anger, sadness, physical pain), age, and gender on 66 second-grade and 71 fifth-grade children's reasons for and methods of affect expression. Found that girls reported using verbal means to communicate emotion, whereas boys cited mildly aggressive methods. (MDM)
An approximate method to acoustic radiation problems: element radiation superposition method
wANG Bin; TANG weilin; FAN Jun
2008-01-01
An approximate method is brought forward to predict the acoustic pressure based on the surface velocity.It is named Element Radiation Superposition Method(ERSM).The study finds that each element in Acoustic Transfer Vector(ATV)equals the acoustic pressure radiated by the corresponding surface element vibrating in unit velocity and other surface elements keep still.that is the acoustic pressure radiated by the corresponding baffled pistonvibrating in unit velocity.So,it utilizes the acoustic pressure radiated by a baffled piston to establish the transfer relationship between the surfaEe velocity and the acoustic pressure.The total acoustic pressure is obtained through summing up the products of the surface velocity and the transfer quantity.It adopts the regular baffle to fit the actual baffle in order to calculate the acoustic pressure radiated by the baffled piston.This approximate method has larger advantage in calculating speed and memory space than Boundary Element Method.Numerical simulations show that this approximate method is reasonable and feasible.
Dual methods and approximation concepts in structural synthesis
Fleury, C.; Schmit, L. A., Jr.
1980-01-01
Approximation concepts and dual method algorithms are combined to create a method for minimum weight design of structural systems. Approximation concepts convert the basic mathematical programming statement of the structural synthesis problem into a sequence of explicit primal problems of separable form. These problems are solved by constructing explicit dual functions, which are maximized subject to nonnegativity constraints on the dual variables. It is shown that the joining together of approximation concepts and dual methods can be viewed as a generalized optimality criteria approach. The dual method is successfully extended to deal with pure discrete and mixed continuous-discrete design variable problems. The power of the method presented is illustrated with numerical results for example problems, including a metallic swept wing and a thin delta wing with fiber composite skins.
Approximating methods for intractable probabilistic models: Applications in neuroscience
Højen-Sørensen, Pedro; Hansen, Lars Kai; Rasmussen, Carl Edward; Larsen, Jan
2002-01-01
This thesis investigates various methods for carrying out approximate inference in intractable probabilistic models. By capturing the relationships between random variables, the framework of graphical models hints at which sets of random variables pose a problem to the inferential step. The approximating techniques used in this thesis originate from the field of statistical physics which for decades has been facing the same type of intractable computations when analyzing large systems of inte...
A further development of the flux polynomial approximations method
In this paper two of the transport problems were treated: the energy independent particle transport in spherical geometry and the energy dependent neutron transport in plane hydrogen media. Using the asymptotic behaviours in space and lethargy of the known analytical solutions of these problems (given by the singular eigenfunction method and by the 'Marshak approximation') some significant improvements in the synthesis of an elementary function method and the bi-orthogonal polynomial flux approximations method were done. The computed values were compared to the referent data and agreement was achieved. (author)
Intermediate boundary conditions for LOD, ADI and approximate factorization methods
Leveque, R. J.
1985-01-01
A general approach to determining the correct intermediate boundary conditions for dimensional splitting methods is presented. The intermediate solution U is viewed as a second order accurate approximation to a modified equation. Deriving the modified equation and using the relationship between this equation and the original equation allows us to determine the correct boundary conditions for U*. This technique is illustrated by applying it to locally one dimensional (LOD) and alternating direction implicit (ADI) methods for the heat equation in two and three space dimensions. The approximate factorization method is considered in slightly more generality.
Approximate methods in gamma-ray skyshine calculations
An approximate computational method for gamma-ray skyshine calculations is described. The method is suitable for a source collimated uniformly about the vertical and accounts for uniform overhead concrete shielding above the source. Results of calculations are compared to measurements as well as results of other calculations
Analytical Evaluation of Beam Deformation Problem Using Approximate Methods
Barari, Amin; Kimiaeifar, A.; Domairry, G.
2010-01-01
, and this process produces noise in the obtained answers. This paper deals with the solution of second order of differential equation governing beam deformation using four analytical approximate methods, namely the Perturbation, Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM) and......The beam deformation equation has very wide applications in structural engineering. As a differential equation, it has its own problem concerning existence, uniqueness and methods of solutions. Often, original forms of governing differential equations used in engineering problems are simplified...... Variational Iteration Method (VIM). The comparisons of the results reveal that these methods are very effective, convenient and quite accurate for systems of non-linear differential equation....
A working-set framework for sequential convex approximation methods
Stolpe, Mathias
2008-01-01
to guarantee global convergence of the method. The algorithm works directly on the nonlinear constraints in the convex sub-problems and solves a sequence of relaxations of the current sub-problem. The algorithm terminates with the optimal solution to the sub-problem after solving a finite number of relaxations.......We present an active-set algorithmic framework intended as an extension to existing implementations of sequential convex approximation methods for solving nonlinear inequality constrained programs. The framework is independent of the choice of approximations and the stabilization technique used...
Higher-order Chebyshev rational approximation method (CRAM)
The burnup equations can in principle be solved by computing the exponential of the burnup matrix. However, due to the difficult numerical characteristics of burnup matrices, the problem is extremely stiff, and the matrix exponential solution was long considered infeasible for an entire burnup system containing over a thousand nuclides. After discovering that the eigenvalues of burnup matrices are generally confined to a region near the negative real axis, the Chebyshev rational approximation method (CRAM) was introduced as a novel method to solve the burnup equations. It can be characterized as the best rational function on the negative real axis and it has been shown to be capable of simultaneously solving an entire burnup system both accurately and efficiently. The main difficulty in using CRAM for computing the matrix exponential is determining the coefficients of the rational function for a given approximation order. Some polynomial CRAM coefficients have been published in 1984, and based on these literature values, CRAM approximations up to the order 16 have been thus far applied in burnup calculations. The topic of this paper is the computation of CRAM approximations and their application to burnup equations. A Remez-type method utilizing the equioscillation property of best approximations is used to construct the CRAM approximants for approximation orders 1,. . . , 50. Numerical results are presented for a large burnup system and for a decay system. It is demonstrated that higher-order CRAM can be used to accurately solve the burnup equations even with time steps of the order of millions of years. (author)
Metamorphic computer virus detection by Case- Based Reasoning (CBR) methods
Abdellatif Berkat
2011-01-01
Metamorphic virus employs code obfuscation techniques to mutate itself. It absconds from signaturebaseddetection system by modifying internal structure without compromising original functionality.In this paper, we propose a new method, for detecting metamorphic computer viruses, that is based on thetechnique of Case-Based Reasoning (CBR). In this method:-Can detect similar viruses with high probability.- The updating of the virus database is done automatically without connecting to the Intern...
Approximating methods for intractable probabilistic models: Applications in neuroscience
Højen-Sørensen, Pedro
2002-01-01
This thesis investigates various methods for carrying out approximate inference in intractable probabilistic models. By capturing the relationships between random variables, the framework of graphical models hints at which sets of random variables pose a problem to the inferential step. The appro...
Approximate iterative operator method for potential-field downward continuation
Tai, Zhenhua; Zhang, Fengxu; Zhang, Fengqin; Hao, Mengcheng
2016-05-01
An approximate iterative operator method in wavenumber domain was proposed to improve the stability and accuracy of downward continuation of potential fields measured from the ground surface, marine or airborne. Firstly, the generalized iterative formula of downward continuation is derived in wavenumber domain; then, the transformational relationship between horizontal second-order partial derivatives and continuation is derived based on the Taylor series and Laplace equation, to obtain an approximate operator. By introducing this operator to the generalized iterative formula, a rapid algorithm is developed for downward continuation. The filtering and convergence characteristics of this method are analyzed for the purpose of estimating the optimal interval of number of iterations. We demonstrate the proposed method on synthetic data, and the results validate the flexibility of the proposed method. At last, we apply the proposed method to real data, and the results show the proposed method can enhance gravity anomalies generated by concealed orebodies. And in the contour obtained by making our proposed method results continue upward to measured level, the numerical results have approximate distribution and amplitude with original anomalies.
Complex method for approximated solutions to Born-Infeld equation
Ferraro, Rafael
2015-01-01
We display the method to solve the Born-Infeld equation in the complex plane. As the exact solution is obtained in an implicit form, we turn it into an explicit form by means of a perturbative procedure which takes care of secular behaviors common to this kind of approximations. We apply the method to build solutions to Born-Infeld electrodynamics. In particular, we study BI electromagnetic waves at interfaces, with the aim of searching for effects susceptible of experimental detection.
Error Estimates for Approximate Optimization by the Extended Ritz Method
Kůrková, Věra; Sanguineti, M.
2005-01-01
Roč. 15, č. 2 (2005), s. 461-487. ISSN 1052-6234 R&D Projects: GA ČR GA201/02/0428 Institutional research plan: CEZ:AV0Z10300504 Keywords : functional optimization * rates of convergence of suboptimal solutions * (extended) Ritz method * curse of dimensionality * convex best approximation problems * learning from data by kernel methods Subject RIV: BA - General Mathematics Impact factor: 1.238, year: 2005
An approximation concepts method for space frame synthesis
Mills-Curran, W. C.; Lust, R. V.; Schmit, L. A.
1982-01-01
A method is presented for the minimum mass design of three dimensional space frames constructed of thin walled rectangular cross-section members. Constraints on nodal displacements and rotations, material stress, local buckling, and cross sectional dimensions are included. A high quality separable approximate problem is formed in terms of the reciprocals of the four section properties of the frame element cross section, replacing all implicit functions with simplified explicit relations. The cross sectional dimensions are efficiently calculated without using multilevel techniques. Several test problems are solved, demonstrating that a series of approximate problem solutions converge rapidly to an optimal design.
Multiuser detection and channel estimation: Exact and approximate methods
Fabricius, Thomas
2003-01-01
This dissertation deals with optimal and close to optimal multiuser detection in Code Division Multiple Access. We derive optimal detection strategies in the sense of minimum expected probability of bit error, sequence error, and mean square error. These are implemented efficiently by the use of...... the Junction Tree Algorithm, which is a generalisation of Pearl's Belief Propagation, the BCJR, sum product, min/max sum, and Viterbi's algorithm. Although efficient algoithms, they have an inherent exponential complexity in the number of users when applied to CDMA multiuser detection. For this reason...... subtractive interference cancellation with hyperbolic tangent tentative decision device, in statistical mechanics and machine learning called the naive mean field approach. The differences between the proposed algorithms lie in how the bias is estimated/approximated. We propose approaches based on a second...
Space-angle approximations in the variational nodal method
The variational nodal method is formulated such that the angular and spatial approximations maybe examined separately. Spherical harmonic, simplified spherical harmonic, and discrete ordinate approximations are coupled to the primal hybrid finite element treatment of the spatial variables. Within this framework, two classes of spatial trial functions are presented: (1) orthogonal polynomials for the treatment of homogeneous nodes and (2) bilinear finite subelement trial functions for the treatment of fuel assembly sized nodes in which fuel-pin cell cross sections are represented explicitly. Polynomial and subelement trial functions are applied to benchmark water-reactor problems containing MOX fuel using spherical harmonic and simplified spherical harmonic approximations. The resulting accuracy and computing costs are compared
Approximation methods for the partition functions of anharmonic systems
The analytical approximations for the classical, quantum mechanical and reduced partition functions of the diatomic molecule oscillating internally under the influence of the Morse potential have been derived and their convergences have been tested numerically. This successful analytical method is used in the treatment of anharmonic systems. Using Schwinger perturbation method in the framework of second quantization formulism, the reduced partition function of polyatomic systems can be put into an expression which consists separately of contributions from the harmonic terms, Morse potential correction terms and interaction terms due to the off-diagonal potential coefficients. The calculated results of the reduced partition function from the approximation method on the 2-D and 3-D model systems agree well with the numerical exact calculations
Interfacing Relativistic and Nonrelativistic Methods: A Systematic Sequence of Approximations
Dyall, Ken; Langhoff, Stephen R. (Technical Monitor)
1997-01-01
A systematic sequence of approximations for the introduction of relativistic effects into nonrelativistic molecular finite-basis set calculations is described. The theoretical basis for the approximations is the normalized elimination of the small component (ESC) within the matrix representation of the modified Dirac equation. The key features of the normalized method are the retention of the relativistic metric and the ability to define a single matrix U relating the pseudo-large and large component coefficient matrices. This matrix is used to define a modified set of one- and two-electron integrals which have the same appearance as the integrals of the Breit-Pauli Hamiltonian. The first approximation fixes the ratios of the large and pseudo-large components to their atomic values, producing an expansion in atomic 4-spinors. The second approximation defines a local fine-structure constant on each atomic centre, which has the physical value for centres considered to be relativistic and zero for nonrelativistic centres. In the latter case, the 4-spinors are the positive-energy kinetic al ly-balanced solutions of the Levy-Leblond equation, and the integrals involving pseudo-large component basis functions on these centres, are set to zero. Some results are presented for test systems to illustrate the various approximations.
Approximation methods for efficient learning of Bayesian networks
Riggelsen, C
2008-01-01
This publication offers and investigates efficient Monte Carlo simulation methods in order to realize a Bayesian approach to approximate learning of Bayesian networks from both complete and incomplete data. For large amounts of incomplete data when Monte Carlo methods are inefficient, approximations are implemented, such that learning remains feasible, albeit non-Bayesian. The topics discussed are: basic concepts about probabilities, graph theory and conditional independence; Bayesian network learning from data; Monte Carlo simulation techniques; and, the concept of incomplete data. In order to provide a coherent treatment of matters, thereby helping the reader to gain a thorough understanding of the whole concept of learning Bayesian networks from (in)complete data, this publication combines in a clarifying way all the issues presented in the papers with previously unpublished work.
Parallel iterative solvers and preconditioners using approximate hierarchical methods
Grama, A.; Kumar, V.; Sameh, A. [Univ. of Minnesota, Minneapolis, MN (United States)
1996-12-31
In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES solver for Boundary Element Methods. The solver uses a hierarchical approximate matrix-vector product based on a hybrid Barnes-Hut / Fast Multipole Method. We study the impact of various accuracy parameters on the convergence and show that with minimal loss in accuracy, our solver yields significant speedups. We demonstrate the excellent parallel efficiency and scalability of our solver. The combined speedups from approximation and parallelism represent an improvement of several orders in solution time. We also develop fast and paralellizable preconditioners for this problem. We report on the performance of an inner-outer scheme and a preconditioner based on truncated Green`s function. Experimental results on a 256 processor Cray T3D are presented.
How the great scientists reasoned the scientific method in action
Tibbetts, Gary G
2012-01-01
The scientific method is one of the most basic and essential concepts across the sciences, ensuring that investigations are carried out with precision and thoroughness. The scientific method is typically taught as a step-by-step approach, but real examples from history are not always given. This book teaches the basic modes of scientific thought, not by philosophical generalizations, but by illustrating in detail how great scientists from across the sciences solved problems using scientific reason. Examples include Christopher Columbus, Joseph Priestly, Antoine Lavoisier, Michael Faraday, W
A multiscale two-point flux-approximation method
A large number of multiscale finite-volume methods have been developed over the past decade to compute conservative approximations to multiphase flow problems in heterogeneous porous media. In particular, several iterative and algebraic multiscale frameworks that seek to reduce the fine-scale residual towards machine precision have been presented. Common for all such methods is that they rely on a compatible primal–dual coarse partition, which makes it challenging to extend them to stratigraphic and unstructured grids. Herein, we propose a general idea for how one can formulate multiscale finite-volume methods using only a primal coarse partition. To this end, we use two key ingredients that are computed numerically: (i) elementary functions that correspond to flow solutions used in transmissibility upscaling, and (ii) partition-of-unity functions used to combine elementary functions into basis functions. We exemplify the idea by deriving a multiscale two-point flux-approximation (MsTPFA) method, which is robust with regards to strong heterogeneities in the permeability field and can easily handle general grids with unstructured fine- and coarse-scale connections. The method can easily be adapted to arbitrary levels of coarsening, and can be used both as a standalone solver and as a preconditioner. Several numerical experiments are presented to demonstrate that the MsTPFA method can be used to solve elliptic pressure problems on a wide variety of geological models in a robust and efficient manner
Optimization in engineering sciences approximate and metaheuristic methods
Stefanoiu, Dan; Popescu, Dumitru; Filip, Florin Gheorghe; El Kamel, Abdelkader
2014-01-01
The purpose of this book is to present the main metaheuristics and approximate and stochastic methods for optimization of complex systems in Engineering Sciences. It has been written within the framework of the European Union project ERRIC (Empowering Romanian Research on Intelligent Information Technologies), which is funded by the EU's FP7 Research Potential program and has been developed in co-operation between French and Romanian teaching researchers. Through the principles of various proposed algorithms (with additional references) this book allows the reader to explore various methods o
Generation method of educational materials using qualitative reasoning
Central Research Institute of Electric Power Industry has developed a nuclear power plant educational system in which educational materials for several events are included. The system effectively teaches operators by tailoring the event explanations to their knowledge levels of understanding. The preparation of the educational materials, however, is laborious and this becomes one of the problems in the practical use of the system. Discussed in the present paper is a basic explanation generation method using qualitative reasoning. This has been developed to solve the problem. Qualitative equations describing a recirculation pumps trip were transformed into production rules. These were stored in the knowledge base of an event explanation generation system together with explanation sentences. When an operator selects a certain variable's time-interval in which he wants to know the reasons for a variable change, the inference engine searches for the rule which satisfies both the qualitative value and qualitative differential value concerned with this time-interval. Then the event explanation generation section provides explanations by combining the explanation sentences attached to the rules. This paper demonstrates that it is possible to apply qualitative reasoning to such complex reactor systems, and also that explanations can be generated using the simulation results from a transient analysis code. (author)
Simple Methods to Approximate CPC Shape to Preserve Collection Efficiency
David Jafrancesco
2012-01-01
Full Text Available The compound parabolic concentrator (CPC is the most efficient reflective geometry to collect light to an exit port. Anyway, to allow its actual use in solar plants or photovoltaic concentration systems, a tradeoff between system efficiency and cost reduction, the two key issues for sunlight exploitation, must be found. In this work, we analyze various methods to model an approximated CPC aimed to be simpler and more cost-effective than the ideal one, as well as to preserve the system efficiency. The manufacturing easiness arises from the use of truncated conic surfaces only, which can be realized by cheap machining techniques. We compare different configurations on the basis of their collection efficiency, evaluated by means of nonsequential ray-tracing software. Moreover, due to the fact that some configurations are beam dependent and for a closer approximation of a real case, the input beam is simulated as nonsymmetric, with a nonconstant irradiance on the CPC internal surface.
A Surface Approximation Method for Image and Video Correspondences.
Huang, Jingwei; Wang, Bin; Wang, Wenping; Sen, Pradeep
2015-12-01
Although finding correspondences between similar images is an important problem in image processing, the existing algorithms cannot find accurate and dense correspondences in images with significant changes in lighting/transformation or with the non-rigid objects. This paper proposes a novel method for finding accurate and dense correspondences between images even in these difficult situations. Starting with the non-rigid dense correspondence algorithm [1] to generate an initial correspondence map, we propose a new geometric filter that uses cubic B-Spline surfaces to approximate the correspondence mapping functions for shared objects in both images, thereby eliminating outliers and noise. We then propose an iterative algorithm which enlarges the region containing valid correspondences. Compared with the existing methods, our method is more robust to significant changes in lighting, color, or viewpoint. Furthermore, we demonstrate how to extend our surface approximation method to video editing by first generating a reliable correspondence map between a given source frame and each frame of a video. The user can then edit the source frame, and the changes are automatically propagated through the entire video using the correspondence map. To evaluate our approach, we examine applications of unsupervised image recognition and video texture editing, and show that our algorithm produces better results than those from state-of-the-art approaches. PMID:26241974
An Approximate Analytical Method of the Nonlinear Vibroacoustic Coupling System
Qizheng Zhou
2014-01-01
Full Text Available An approximate analytical method of the nonlinear vibroacoustic coupling system is proposed for the first time. Taking the Duffing oscillator-plate-medium system as an example, the nonlinear vibroacoustic coupling equations are developed using variational principle. The two major difficulties which lie in solving the coupling equations are the uncertain motion of the oscillator and the surface acoustic pressure on the plate, a system for which the fluid-structure coupling cannot be neglected. Based on the incremental harmonic balance (IHB method, the motion of the oscillator is expressed in the form of the Fourier series, and then the modal expression method and the incoherent assumption are employed to discretize the displacement and the surface pressure of the plate. Then the approximate analytical solution is given by the IHB method. The characteristics of acoustic radiation and surface quadratic velocity of the plate, the nonlinear characteristics of oscillator, and the influence of the excitation frequency and the nonlinear stiffness on the results are investigated by the numerical simulation. The results show that the excitation at the frequency close to the natural frequency of the oscillator can produce a significant response of the third-harmonic generation which determines the vibroacoustic characteristics of the plate.
Approximate method for controlling solid elastic waves by transformation media
Hu, Jin; Chang, Zheng; Hu, Gengkai
2011-11-01
By idealizing a general mapping as a series of local affine ones, we derive approximately transformed material parameters necessary to control solid elastic waves within classical elasticity theory. The transformed elastic moduli are symmetric, and can be used with Navier's equation to manipulate elastic waves. It is shown numerically that the method can provide a powerful tool to control elastic waves in solids in case of high frequency or small material gradient. Potential applications can be anticipated in nondestructive testing, structure impact protection, petroleum exploration, and seismology.
Approximate design calculation methods for radiation streaming in shield irregularities
Investigation and assessment are made for approximate design calculation methods of radiation streaming in shield irregularities. Investigation is made for (1) source, (2) definition of streaming radiation components, (3) calculation methods of streaming radiation, (4) streaming formulas for each irregularity, (5) difficulties in application of streaming formulas, etc. Furthermore, investigation is made for simple calculation codes and albedo data. As a result, it is clarified that streaming calculation formulas are not enough to cover various irregularities and their accuracy or application limit is not sufficiently clear. Accurate treatment is not made in the formulas with respect to the radiation behavior for slant incidence, bend part, offset etc., that results in too much safety factors in the design calculation and distrust of the streaming calculation. To overcome the state and improve the accuracy of the design calculation for shield irregularities, it is emphasized to assess existing formulas and develop better formulas based on systematic experimental studies. (author)
Parabolic approximation method for the mode conversion-tunneling equation
The derivation of the wave equation which governs ICRF wave propagation, absorption, and mode conversion within the kinetic layer in tokamaks has been extended to include diffraction and focussing effects associated with the finite transverse dimensions of the incident wavefronts. The kinetic layer considered consists of a uniform density, uniform temperature slab model in which the equilibrium magnetic field is oriented in the z-direction and varies linearly in the x-direction. An equivalent dielectric tensor as well as a two-dimensional energy conservation equation are derived from the linearized Vlasov-Maxwell system of equations. The generalized form of the mode conversion-tunneling equation is then extracted from the Maxwell equations, using the parabolic approximation method in which transverse variations of the wave fields are assumed to be weak in comparison to the variations in the primary direction of propagation. Methods of solving the generalized wave equation are discussed. 16 refs
Discrete Dipole Approximation Aided Design Method for Nanostructure Arrays
ZHU Shao-Li; LUO Xian-Gang; DU Chun-Lei
2007-01-01
A discrete dipole approximation (DDA) aided design method is proposed to determine the parameters of nanostructure arrays. The relationship between the thickness, period and extinction efficiency of nanostructure arrays for the given shape can be calculated using the DDA. Based on the calculated curves, the main parameters of the nanostructure arrays such as thickness and period can be determined. Using this aided method, a rhombic sliver nanostructure array is designed with the determinant parameters of thickness (40 nm) and period (440 nm).We further fabricate the rhombic sliver nanostructure arrays and testify the character of the extinction spectra.The obtained extinction spectra is within the visible range and the full width at half maximum is 99nm, as is expected.
The method of approximate inverse theory and applications
Schuster, Thomas
2007-01-01
Inverse problems arise whenever one tries to calculate a required quantity from given measurements of a second quantity that is associated to the first one. Besides medical imaging and non-destructive testing, inverse problems also play an increasing role in other disciplines such as industrial and financial mathematics. Hence, there is a need for stable and efficient solvers. The book is concerned with the method of approximate inverse which is a regularization technique for stably solving inverse problems in various settings such as L2-spaces, Hilbert spaces or spaces of distributions. The performance and functionality of the method is demonstrated on several examples from medical imaging and non-destructive testing such as computerized tomography, Doppler tomography, SONAR, X-ray diffractometry and thermoacoustic computerized tomography. The book addresses graduate students and researchers interested in the numerical analysis of inverse problems and regularization techniques or in efficient solvers for the...
Back-transformation of treatment differences - an approximate method
Laursen, Rikke Pilmann; Dalskov, Stine-Mathilde; Damsgaard, Camilla Trab; Ritz, Christian
2014-01-01
-transformed estimated differences, and corresponding standard errors and 95% confidence intervals.Subjects/Methods:Based on data from two randomized controlled studies and an exemplary data set that had all previously been published, we evaluated our approximate procedure by comparing results for different approaches......Background/Objectives:Transformation of outcomes is frequently used in the analysis of studies in clinical nutrition. However, back-transformation of estimated treatment means and differences is complicated by the nonlinear nature of the transformations. It is not straightforward to obtain an...... estimated treatment difference that can be interpreted without any reference to the additional predictors included in the statistical model; and moreover, standard errors are not easily available. The aim of this work was to provide a generally applicable, yet operational procedure for obtaining back...
On rational approximation methods for inverse source problems
Rundell, William
2011-02-01
The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Such is the ubiquity of these problems, the underlying model can lead to a partial differential equation of any of the major types, but here we focus on the case of steady-state electrostatic or thermal imaging and consider boundary value problems for Laplace\\'s equation. Our inclusions are interior forces with compact support and our data consists of a single measurement of (say) voltage/current or temperature/heat flux on the external boundary. We propose an algorithm that under certain assumptions allows for the determination of the support set of these forces by solving a simpler "equivalent point source" problem, and which uses a Newton scheme to improve the corresponding initial approximation. © 2011 American Institute of Mathematical Sciences.
Methods of Approximation Theory in Complex Analysis and Mathematical Physics
Saff, Edward
1993-01-01
The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. ...
Portable Rule Extraction Method for Neural Network Decisions Reasoning
Darius PLIKYNAS
2005-08-01
Full Text Available Neural network (NN methods are sometimes useless in practical applications, because they are not properly tailored to the particular market's needs. We focus thereinafter specifically on financial market applications. NNs have not gained full acceptance here yet. One of the main reasons is the "Black Box" problem (lack of the NN decisions explanatory power. There are though some NN decisions rule extraction methods like decompositional, pedagogical or eclectic, but they suffer from low portability of the rule extraction technique across various neural net architectures, high level of granularity, algorithmic sophistication of the rule extraction technique etc. The authors propose to eliminate some known drawbacks using an innovative extension of the pedagogical approach. The idea is exposed by the use of a widespread MLP neural net (as a common tool in the financial problems' domain and SOM (input data space clusterization. The feedback of both nets' performance is related and targeted through the iteration cycle by achievement of the best matching between the decision space fragments and input data space clusters. Three sets of rules are generated algorithmically or by fuzzy membership functions. Empirical validation of the common financial benchmark problems is conducted with an appropriately prepared software solution.
P K Bera
2012-01-01
The approximate analytical bound-state solutions of the Schrödinger equation for the Wei Hua oscillator are carried out in N-dimensional space by taking Pekeris approximation scheme to the orbital centrifugal term. Solutions of the corresponding hyper-radial equation are obtained using the conventional Nikiforov–Uvarov (NU) method.
Approximation by randomly weighting method in censored regression model
无
2009-01-01
Censored regression ("Tobit") models have been in common use, and their linear hypothesis testings have been widely studied. However, the critical values of these tests are usually related to quantities of an unknown error distribution and estimators of nuisance parameters. In this paper, we propose a randomly weighting test statistic and take its conditional distribution as an approximation to null distribution of the test statistic. It is shown that, under both the null and local alternative hypotheses, conditionally asymptotic distribution of the randomly weighting test statistic is the same as the null distribution of the test statistic. Therefore, the critical values of the test statistic can be obtained by randomly weighting method without estimating the nuisance parameters. At the same time, we also achieve the weak consistency and asymptotic normality of the randomly weighting least absolute deviation estimate in censored regression model. Simulation studies illustrate that the per-formance of our proposed resampling test method is better than that of central chi-square distribution under the null hypothesis.
Approximation by randomly weighting method in censored regression model
WANG ZhanFeng; WU YaoHua; ZHAO LinCheng
2009-01-01
Censored regression ("Tobit") models have been in common use,and their linear hypothesis testings have been widely studied.However,the critical values of these tests are usually related to quantities of an unknown error distribution and estimators of nuisance parameters.In this paper,we propose a randomly weighting test statistic and take its conditional distribution as an approximation to null distribution of the test statistic.It is shown that,under both the null and local alternative hypotheses,conditionally asymptotic distribution of the randomly weighting test statistic is the same as the null distribution of the test statistic.Therefore,the critical values of the test statistic can be obtained by randomly weighting method without estimating the nuisance parameters.At the same time,we also achieve the weak consistency and asymptotic normality of the randomly weighting least absolute deviation estimate in censored regression model.Simulation studies illustrate that the performance of our proposed resampling test method is better than that of central chi-square distribution under the null hypothesis.
Conditioning Methods for Exact and Approximate Inference in Causal Networks
Darwiche, Adnan
2013-01-01
We present two algorithms for exact and approximate inference in causal networks. The first algorithm, dynamic conditioning, is a refinement of cutset conditioning that has linear complexity on some networks for which cutset conditioning is exponential. The second algorithm, B-conditioning, is an algorithm for approximate inference that allows one to trade-off the quality of approximations with the computation time. We also present some experimental results illustrating the properties of the ...
OWL-based reasoning methods for validating archetypes.
Menárguez-Tortosa, Marcos; Fernández-Breis, Jesualdo Tomás
2013-04-01
Some modern Electronic Healthcare Record (EHR) architectures and standards are based on the dual model-based architecture, which defines two conceptual levels: reference model and archetype model. Such architectures represent EHR domain knowledge by means of archetypes, which are considered by many researchers to play a fundamental role for the achievement of semantic interoperability in healthcare. Consequently, formal methods for validating archetypes are necessary. In recent years, there has been an increasing interest in exploring how semantic web technologies in general, and ontologies in particular, can facilitate the representation and management of archetypes, including binding to terminologies, but no solution based on such technologies has been provided to date to validate archetypes. Our approach represents archetypes by means of OWL ontologies. This permits to combine the two levels of the dual model-based architecture in one modeling framework which can also integrate terminologies available in OWL format. The validation method consists of reasoning on those ontologies to find modeling errors in archetypes: incorrect restrictions over the reference model, non-conformant archetype specializations and inconsistent terminological bindings. The archetypes available in the repositories supported by the openEHR Foundation and the NHS Connecting for Health Program, which are the two largest publicly available ones, have been analyzed with our validation method. For such purpose, we have implemented a software tool called Archeck. Our results show that around 1/5 of archetype specializations contain modeling errors, the most common mistakes being related to coded terms and terminological bindings. The analysis of each repository reveals that different patterns of errors are found in both repositories. This result reinforces the need for making serious efforts in improving archetype design processes. PMID:23246613
The generalized Mayer theorem in the approximating hamiltonian method
With the help of the generalized Mayer theorem we obtain the improved inequality for free energies of model and approximating systems, where only ''connected parts'' over the approximating hamiltonian are taken into account. For the concrete system we discuss the problem of convergency of appropriate series of ''connected parts''. (author)
Yang, Z
1994-09-01
Two approximate methods are proposed for maximum likelihood phylogenetic estimation, which allow variable rates of substitution across nucleotide sites. Three data sets with quite different characteristics were analyzed to examine empirically the performance of these methods. The first, called the "discrete gamma model," uses several categories of rates to approximate the gamma distribution, with equal probability for each category. The mean of each category is used to represent all the rates falling in the category. The performance of this method is found to be quite good, and four such categories appear to be sufficient to produce both an optimum, or near-optimum fit by the model to the data, and also an acceptable approximation to the continuous distribution. The second method, called "fixed-rates model", classifies sites into several classes according to their rates predicted assuming the star tree. Sites in different classes are then assumed to be evolving at these fixed rates when other tree topologies are evaluated. Analyses of the data sets suggest that this method can produce reasonable results, but it seems to share some properties of a least-squares pairwise comparison; for example, interior branch lengths in nonbest trees are often found to be zero. The computational requirements of the two methods are comparable to that of Felsenstein's (1981, J Mol Evol 17:368-376) model, which assumes a single rate for all the sites. PMID:7932792
Communication: Improved pair approximations in local coupled-cluster methods
In local coupled cluster treatments the electron pairs can be classified according to the magnitude of their energy contributions or distances into strong, close, weak, and distant pairs. Different approximations are introduced for the latter three classes. In this communication, an improved simplified treatment of close and weak pairs is proposed, which is based on long-range cancellations of individually slowly decaying contributions in the amplitude equations. Benchmark calculations for correlation, reaction, and activation energies demonstrate that these approximations work extremely well, while pair approximations based on local second-order Møller-Plesset theory can lead to errors that are 1-2 orders of magnitude larger
Mobile Monitoring and Reasoning Methods to Prevent Cardiovascular Diseases
Diego López-de-Ipiña
2013-05-01
Full Text Available With the recent technological advances, it is possible to monitor vital signs using Bluetooth-enabled biometric mobile devices such as smartphones, tablets or electric wristbands. In this manuscript, we present a system to estimate the risk of cardiovascular diseases in Ambient Assisted Living environments. Cardiovascular disease risk is obtained from the monitoring of the blood pressure by means of mobile devices in combination with other clinical factors, and applying reasoning techniques based on the Systematic Coronary Risk Evaluation Project charts. We have developed an end-to-end software application for patients and physicians and a rule-based reasoning engine. We have also proposed a conceptual module to integrate recommendations to patients in their daily activities based on information proactively inferred through reasoning techniques and context-awareness. To evaluate the platform, we carried out usability experiments and performance benchmarks.
Kuwahara, Hiroyuki; Myers, Chris J
2008-09-01
Given the substantial computational requirements of stochastic simulation, approximation is essential for efficient analysis of any realistic biochemical system. This paper introduces a new approximation method to reduce the computational cost of stochastic simulations of an enzymatic reaction scheme which in biochemical systems often includes rapidly changing fast reactions with enzyme and enzyme-substrate complex molecules present in very small counts. Our new method removes the substrate dissociation reaction by approximating the passage time of the formation of each enzyme-substrate complex molecule which is destined to a production reaction. This approach skips the firings of unimportant yet expensive reaction events, resulting in a substantial acceleration in the stochastic simulations of enzymatic reactions. Additionally, since all the parameters used in our new approach can be derived by the Michaelis-Menten parameters which can actually be measured from experimental data, applications of this approximation can be practical even without having full knowledge of the underlying enzymatic reaction. Here, we apply this new method to various enzymatic reaction systems, resulting in a speedup of orders of magnitude in temporal behavior analysis without any significant loss in accuracy. Furthermore, we show that our new method can perform better than some of the best existing approximation methods for enzymatic reactions in terms of accuracy and efficiency. PMID:18662102
An approximation method for diffusion based leaching models
In connection with the fixation of nuclear waste in a glassy matrix equations have been derived for leaching models based on a uniform concentration gradient approximation, and hence a uniform flux, therefore requiring the use of only Fick's first law. In this paper we improve on the uniform flux approximation, developing and justifying the approach. The resulting set of equations are solved to a satisfactory approximation for a matrix dissolving at a constant rate in a finite volume of leachant to give analytical expressions for the time dependence of the thickness of the leached layer, the diffusional and dissolutional contribution to the flux, and the leachant composition. Families of curves are presented which cover the full range of all the physical parameters for this system. The same procedure can be readily extended to more complex systems. (author)
Sherlock Holmes's Methods of Deductive Reasoning Applied to Medical Diagnostics
Miller, Larry
1985-01-01
Having patterned the character of Sherlock Holmes after one of his professors, Sir Arthur Conan Doyle, himself a physician, incorporated many of the didactic qualities of the 19th century medical diagnostician into the character of Holmes. In this paper I explore Holmes's techniques of deductive reasoning and their basis in 19th and 20th century medical diagnostics.
Sherlock Holmes's Methods of Deductive Reasoning Applied to Medical Diagnostics
Miller, Larry
1985-01-01
Having patterned the character of Sherlock Holmes after one of his professors, Sir Arthur Conan Doyle, himself a physician, incorporated many of the didactic qualities of the 19th century medical diagnostician into the character of Holmes. In this paper I explore Holmes's techniques of deductive reasoning and their basis in 19th and 20th century medical diagnostics. PMID:3887762
Sherlock Holmes' methods of deductive reasoning applied to medical diagnostics.
Miller, L
1985-03-01
Having patterned the character of Sherlock Holmes after one of his professors, Sir Arthur Conan Doyle, himself a physician, incorporated many of the didactic qualities of the 19th century medical diagnostician into the character of Holmes. In this paper I explore Holmes's techniques of deductive reasoning and their basis in 19th and 20th century medical diagnostics. PMID:3887762
α-Automated Reasoning Method Based on Lattice-Valued Propositional Logic LP(X)
王伟; 徐扬; 王学芳
2002-01-01
This paper is focused on automated reasoning based on classical propositional logic and lattice-valued propositional logic LP(X). A new method of automated reasoning is given, and the soundness and completeness theorems of this method are proved.
Stochastic Approximation Methods for Latent Regression Item Response Models
von Davier, Matthias; Sinharay, Sandip
2010-01-01
This article presents an application of a stochastic approximation expectation maximization (EM) algorithm using a Metropolis-Hastings (MH) sampler to estimate the parameters of an item response latent regression model. Latent regression item response models are extensions of item response theory (IRT) to a latent variable model with covariates…
Importance sampling approach for the nonstationary approximation error method
The approximation error approach has previously been proposed to handle modelling, numerical and computational errors. This approach has been developed both for stationary and nonstationary inverse problems (Kalman filtering). The key idea of the approach is to compute the approximate statistics of the errors over the distribution of all unknowns and uncertainties and carry out approximative marginalization with respect to these errors. In nonstationary problems, however, information is accumulated over time, and the initial uncertainties may turn out to have been exaggerated. In this paper, we propose an algorithm with which the approximation error statistics can be updated during the accumulation of measurement information. The proposed algorithm is based on importance sampling. The recursions that are proposed here are, however, based on the (extended) Kalman filter and therefore do not employ the often exceedingly heavy computational load of particle filtering. As a computational example, we study an estimation problem that is related to a convection–diffusion problem in which the velocity field is not accurately specified
A method of approximating range size of small mammals
Stickel, L.F.
1965-01-01
In summary, trap success trends appear to provide a useful approximation to range size of easily trapped small mammals such as Peromyscus. The scale of measurement can be adjusted as desired. Further explorations of the usefulness of the plan should be made and modifications possibly developed before adoption.
26 CFR 1.412(c)(3)-1 - Reasonable funding methods.
2010-04-01
... 26 Internal Revenue 5 2010-04-01 2010-04-01 false Reasonable funding methods. 1.412(c)(3)-1... Reasonable funding methods. (a) Introduction—(1) In general. This section prescribes rules for determining whether or not, in the case of an ongoing plan, a funding method is reasonable for purposes of section...
Fuzzy Reasoning Methods by Choosing Different Fuzzy Counters and Analysis of Effect
无
2001-01-01
Different fuzzy reasoning methods were gave by choosing different fuzzy counters. This article generally introduced the basic structure of fuzzy controller,and compared and analysised the reasoning effect of fuzzy reasoning methods and the effect of computer simulating control basicly on different fuzzy counters.
Berezkin, V. E.; Lotov, A. V.; Lotova, E. A.
2014-06-01
Methods for approximating the Edgeworth-Pareto hull (EPH) of the set of feasible criteria vectors in nonlinear multicriteria optimization problems are examined. The relative efficiency of two EPH approximation methods based on classical methods of searching for local extrema of convolutions of criteria is experimentally studied for a large-scale applied problem (with several hundred variables). A hybrid EPH approximation method combining classical and genetic approximation methods is considered.
Topological approximation methods for evolutionary problem of nonlinear hydrodynamics
Zvyagin, Victor
2008-01-01
The authors present functional analytical methods for solving a class of partial differential equations. The results have important applications to the numerical treatment of rheology (specific examples are the behaviour of blood or print colours) and to other applications in fluid mechanics. A class of methods for solving problems in hydrodynamics is presented.
Automated Reasoning and Equation Solving with the Characteristic Set Method
Wen-Tsun Wu; Xiao-Shan Gao
2006-01-01
A brief introduction to the characteristic set method is given for solving algebraic equation systems and then the method is extended to algebraic difference systems. The method can be used to decompose the zero set for a difference polynomial set in general form to the union of difference polynomial sets in triangular form. Based on the characteristic set method, a decision procedure for the first order theory over an algebraically closed field and a procedure to prove certain difference identities are proposed.
Monaco, Pierluigi
2016-01-01
Precision cosmology has recently triggered new attention on the topic of approximate methods for the clustering of matter on large scales, whose foundations date back to the period from late '60s to early '90s. Indeed, although the prospect of reaching sub-percent accuracy in the measurement of clustering poses a challenge even to full N-body simulations, an accurate estimation of the covariance matrix of clustering statistics requires usage of a large number (hundreds in the most favourable cases) of simulated (mock) galaxy catalogs. Combination of few N-body simulations with a large number of realizations performed with approximate methods, combined with the shrinkage technique or a similar tool, gives the most promising approach to solve this problem with a reasonable amount of resources. In this paper I review this topic, starting from the foundations of the methods, then going through the pioneering efforts of the '90s, and finally presenting the latest extensions and a few codes that are now being used ...
Reverse triple I method of restriction for fuzzy reasoning
无
2002-01-01
A theory of reverse triple I method of restriction for implication operator R0 is proposed.And the general computation formulas of infimum for fuzzy modus ponens and supremum for fuzzy modus tollens of a-reverse triple I method of restriction are obtained respectively.
Elastic wave scattering calculations and the matrix variational Pade approximant method
The matrix variational Pade approximant and its generalization to elastic wave scattering are discussed. Predictions of the method for the scattering of a longitudinal plane wave are compared with the exact scattering from spherical voids and inclusions. Its predictions are also compared to those of the first and second Born approximations and to the standard matrix Pade approximant based on these Born approximations
A method to reduce ambiguities of qualitative reasoning for conceptual design applications
D' Amelio, V.; Chmarra, M.K.; Tomiyama, T
2013-01-01
Qualitative reasoning can generate ambiguous behaviors due to the lack of quantitative information. Despite many different research results focusing on ambiguities reduction, fundamentally it is impossible to totally remove ambiguities with only qualitative methods and to guarantee the consistency of results. This prevents the wide use of qualitative reasoning techniques in practical situations, particularly in conceptual design, where qualitative reasoning is considered intrinsically useful....
SET: A Pupil Detection Method Using Sinusoidal Approximation
Amir-Homayoun eJavadi
2015-04-01
Full Text Available Mobile eye-tracking in external environments remains challenging, despite recent advances in eye-tracking software and hardware engineering. Many current methods fail to deal with the vast range of outdoor lighting conditions and the speed at which these can change. This confines experiments to artificial environments where conditions must be tightly controlled. Additionally, the emergence of low-cost eye tracking devices calls for the development of analysis tools that enable non-technical researchers to process the output of their images. We have developed a fast and accurate method (known as ‘SET’ that is suitable even for natural environments with uncontrolled, dynamic and even extreme lighting conditions. We compared the performance of SET with that of two open-source alternatives by processing two collections of eye images: images of natural outdoor scenes with extreme lighting variations (‘Natural’; and images of less challenging indoor scenes (‘CASIA-Iris-Thousand’. We show that SET excelled in outdoor conditions and was faster, without significant loss of accuracy, indoors. SET offers a low cost eye-tracking solution, delivering high performance even in challenging outdoor environments. It is offered through an open-source MATLAB toolkit as well as a dynamic-link library (‘DLL’, which can be imported into many programming languages including C# and Visual Basic in Windows OS (www.eyegoeyetracker.co.uk.
SET: a pupil detection method using sinusoidal approximation.
Javadi, Amir-Homayoun; Hakimi, Zahra; Barati, Morteza; Walsh, Vincent; Tcheang, Lili
2015-01-01
Mobile eye-tracking in external environments remains challenging, despite recent advances in eye-tracking software and hardware engineering. Many current methods fail to deal with the vast range of outdoor lighting conditions and the speed at which these can change. This confines experiments to artificial environments where conditions must be tightly controlled. Additionally, the emergence of low-cost eye tracking devices calls for the development of analysis tools that enable non-technical researchers to process the output of their images. We have developed a fast and accurate method (known as "SET") that is suitable even for natural environments with uncontrolled, dynamic and even extreme lighting conditions. We compared the performance of SET with that of two open-source alternatives by processing two collections of eye images: images of natural outdoor scenes with extreme lighting variations ("Natural"); and images of less challenging indoor scenes ("CASIA-Iris-Thousand"). We show that SET excelled in outdoor conditions and was faster, without significant loss of accuracy, indoors. SET offers a low cost eye-tracking solution, delivering high performance even in challenging outdoor environments. It is offered through an open-source MATLAB toolkit as well as a dynamic-link library ("DLL"), which can be imported into many programming languages including C# and Visual Basic in Windows OS (www.eyegoeyetracker.co.uk). PMID:25914641
Efficient Path Query and Reasoning Method Based on Rare Axis
姜洋; 冯志勇; 王鑫马晓宁
2015-01-01
A new concept of rare axis based on statistical facts is proposed, and an evaluation algorithm is designed thereafter. For the nested regular expressions containing rare axes, the proposed algorithm can reduce its evaluation complexity from polynomial time to nearly linear time. The distributed technique is also employed to construct the navigation axis indexes for resource description framework (RDF) graph data. Experiment results in DrugBank and BioGRID show that this method can improve the query efficiency significantly while ensuring the accuracy and meet the query requirements on Web-scale RDF graph data.
A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations
Zhang Zhi-Yong; Yong Xue-Lin; Chen Yu-Fu
2009-01-01
A novel method for obtaining the approximate symmetry of a partial differential equation with a small parameter is introduced. By expanding the independent variable and the dependent variable in the small parameter series, we obtain more affluent approximate symmetries. The method is applied to two perturbed nonlinear partial differential equations and new approximate solutions are derived.
Reason and Condition for Mode Kissing in MASW Method
Gao, Lingli; Xia, Jianghai; Pan, Yudi; Xu, Yixian
2016-05-01
Identifying correct modes of surface waves and picking accurate phase velocities are critical for obtaining an accurate S-wave velocity in MASW method. In most cases, inversion is easily conducted by picking the dispersion curves corresponding to different surface-wave modes individually. Neighboring surface-wave modes, however, will nearly meet (kiss) at some frequencies for some models. Around the frequencies, they have very close roots and energy peak shifts from one mode to another. At current dispersion image resolution, it is difficult to distinguish different modes when mode-kissing occurs, which is commonly seen in near-surface earth models. It will cause mode misidentification, and as a result, lead to a larger overestimation of S-wave velocity and error on depth. We newly defined two mode types based on the characteristics of the vertical eigendisplacements calculated by generalized reflection and transmission coefficient method. Rayleigh-wave mode near the kissing points (osculation points) change its type, that is to say, one Rayleigh-wave mode will contain different mode types. This mode type conversion will cause the mode-kissing phenomenon in dispersion images. Numerical tests indicate that the mode-kissing phenomenon is model dependent and that the existence of strong S-wave velocity contrasts increases the possibility of mode-kissing. The real-world data shows mode misidentification caused by mode-kissing phenomenon will result in higher S-wave velocity of bedrock. It reminds us to pay attention to this phenomenon when some of the underground information is known.
Convergence of hausdorff approximation methods for the Edgeworth-Pareto hull of a compact set
Efremov, R. V.
2015-11-01
The Hausdorff methods comprise an important class of polyhedral approximation methods for convex compact bodies, since they have an optimal convergence rate and possess other useful properties. The concept of Hausdorff methods is extended to a problem arising in multicriteria optimization, namely, to the polyhedral approximation of the Edgeworth-Pareto hull (EPH) of a convex compact set. It is shown that the sequences of polyhedral sets generated by Hausdorff methods converge to the EPH to be approximated. It is shown that the Estimate Refinement method, which is most frequently used to approximate the EPH of convex compact sets, is a Hausdorff method and, hence, generates sequences of sets converging to the EPH.
Lawrenz, Frances
1985-01-01
Determined: (1) if elementary education majors (N=91) from different levels of reasoning ability learned more science concepts under different grouping methods in an inquiry/learning cycle-based physical science class; and (2) if these students became able to reason more effectively under the different grouping methods. (JN)
Afanas'ev, A. P.; Dzyuba, S. M.
2015-10-01
A method for constructing approximate analytic solutions of systems of ordinary differential equations with a polynomial right-hand side is proposed. The implementation of the method is based on the Picard method of successive approximations and a procedure of continuation of local solutions. As an application, the problem of constructing the minimal sets of the Lorenz system is considered.
Method for disclosing the reasoning behind computer-aided diagnosis of pulmonary nodules
This paper proposes a method for disclosing the reasoning behind computer-aided diagnosis (CADx) based on a Bayesian network. The purpose of this method is to promote the acceptance of CADx by physicians by providing the reasoning behind the inferences. The proposed method first calculates the influence ratio to the inference result for each subset of input information. It then selects some subsets that have large influence ratios and shows them as the reasoning or grounds for the inference. In experiments using artificial data with known classification rules, the proposed method detected correct rules for about 90% of the data. With regard to clinical data, the average value for the effectiveness of reasoning as judged by two physicians was 3.4. This value is greater than '3', which is considered a reasonable grade. (author)
Beam propagation method using a [(p- 1)/ p] Padé approximant of the propagator.
Lu, Ya Yan; Ho, Pui Lin
2002-05-01
A new beam propagation method (BPM) is developed based on a direct approximation to the propagator by its [(p-1)/p] Padé approximant. The approximant is simple to construct and has the desired damping effect for the evanescent modes. The method is applied to a tapered waveguide for TM-polarized waves, based on the energy-conserving improvement of the one-way Helmholtz equation. Numerical results are compared with those obtained with other variants of the BPM. PMID:18007898
A Conflict Context Reasoning Method Based on Dempster-Shafer Theory in Ubiquitous Computing
Xinkai Yang
2013-08-01
Full Text Available In this paper, one conflict context reasoning method based on Dempster-Shafer theory is proposed. Firstly the context conflict problems are illustrated and partitioned based on theory of evidence. Then the context model combined with Dempster-Shafer theory is presented and applied to the reasoning method based on Dempster rule of combination. The effectiveness of this method is verified with a RFID application example.
A Conflict Context Reasoning Method Based on Dempster-Shafer Theory in Ubiquitous Computing
Xinkai Yang
2013-01-01
In this paper, one conflict context reasoning method based on Dempster-Shafer theory is proposed. Firstly the context conflict problems are illustrated and partitioned based on theory of evidence. Then the context model combined with Dempster-Shafer theory is presented and applied to the reasoning method based on Dempster rule of combination. The effectiveness of this method is verified with a RFID application example.
无
1990-01-01
Fuzzy set systems can be used to solve the problem with uncertain knowledge,and default logic can be used to solve the problem with incomplete knowledge,in some sense.In this paper,based on interval-valued fuzzy sets we introduce a method of inference which combines approximate reasoning an default ogic,and give the procedure of transforming monotonic reasoning into default reasoning.
Yoo, J.; Shin, H. S.; Song, T. Y.; Park, W. S. [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1997-12-31
Previous our numerical results in computing point kinetics equations show a possibility in developing approximations to estimate sensitivity responses of nuclear reactor. We recalculate sensitivity responses by maintaining the corrections with first order of sensitivity parameter. We present a method for computing sensitivity responses of nuclear reactor based on an approximation derived from point kinetics equations. Exploiting this approximation, we found that the first order approximation works to estimate variations in the time to reach peak power because of their linear dependence on a sensitivity parameter, and that there are errors in estimating the peak power in the first order approximation for larger sensitivity parameters. To confirm legitimacy of out approximation, these approximate results are compared with exact results obtained from out previous numerical study. 4 refs., 2 figs., 3 tabs. (Author)
First and second order approximate reliability analysis methods using evidence theory
The first order approximate reliability method (FARM) and second order approximate reliability method (SARM) are formulated based on evidence theory in this paper. The proposed methods can significantly improve the computational efficiency for evidence-theory-based reliability analysis, while generally provide sufficient precision. First, the most probable focal element (MPFE), an important concept as the most probable point (MPP) in probability-theory-based reliability analysis, is searched using a uniformity approach. Subsequently, FARM approximates the limit-state function around the MPFE using the linear Taylor series, while SARM approximates it using the quadratic Taylor series. With the first and second order approximations, the reliability interval composed of the belief measure and the plausibility measure is efficiently obtained for FARM and SARM, respectively. Two simple problems with explicit expressions and one engineering application of vehicle frontal impact are presented to demonstrate the effectiveness of the proposed methods. - Highlights: • The first order approximate reliability method using evidence theory is proposed. • The second order approximate reliability method using evidence theory is proposed. • The proposed methods can significantly improve the computational efficiency. • The proposed methods can provide sufficient accuracy for general engineering problems
An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method
Belendez, A., E-mail: a.belendez@ua.e [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Mendez, D.I. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Marini, S. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Pascual, I. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2009-08-03
The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the 'cubication' of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used.
An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method
The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the 'cubication' of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used.
Xiao-Ying Qin
2014-01-01
Full Text Available An Adomian decomposition method (ADM is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.
An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue Functions
Wei Wang
2014-01-01
Full Text Available We present an approximate nonsmooth algorithm to solve a minimization problem, in which the objective function is the sum of a maximum eigenvalue function of matrices and a convex function. The essential idea to solve the optimization problem in this paper is similar to the thought of proximal bundle method, but the difference is that we choose approximate subgradient and function value to construct approximate cutting-plane model to solve the above mentioned problem. An important advantage of the approximate cutting-plane model for objective function is that it is more stable than cutting-plane model. In addition, the approximate proximal bundle method algorithm can be given. Furthermore, the sequences generated by the algorithm converge to the optimal solution of the original problem.
On the Influence of New Media and Methods to Achieve Reasonable Spread
胡海燕
2016-01-01
The emergence of new media not only accelerates the spread of information and brings convenience to people, but also subtly changes every aspect of people's life.This paper aims to discuss the influences that the new media bring for people and the methods that can achieve reasonable spread. All of us have the responsibility and obligation to achieve reasonable spread and make the new media serve better for the human progress.
An Iterative Method for the Approximation of Fibers in Slow-Fast Systems
Kristiansen, Kristian Uldall; Brøns, Morten; Starke, Jens
2014-01-01
In this paper we extend a method for iteratively improving slow manifolds so that it also can be used to approximate the fiber directions. The extended method is applied to general finite-dimensional real analytic systems where we obtain exponential estimates of the tangent spaces to the fibers....... The method is demonstrated on the Michaelis--Menten--Henri model and the Lindemann mechanism. The latter example also serves to demonstrate the method on a slow-fast system in nonstandard slow-fast form. Finally, we extend the method further so that it also approximates the curvature of the fibers....
An efficient method of computing higher-order bond price perturbation approximations
Andreasen, Martin; Zabczyk, Pawel
2011-01-01
This paper develops a fast method of computing arbitrary order perturbation approximations to bond prices in DSGE models. The procedure is implemented to third order where it can shorten the approximation process by more than 100 times. In a consumption-based endowment model with habits, it is further shown that a third-order perturbation solution is more accurate than the log-normal method and a procedure using consol bonds.
OPTIMAL ERROR ESTIMATES OF THE PARTITION OF UNITY METHOD WITH LOCAL POLYNOMIAL APPROXIMATION SPACES
Yun-qing Huang; Wei Li; Fang Su
2006-01-01
In this paper, we provide a theoretical analysis of the partition of unity finite element method(PUFEM), which belongs to the family of meshfree methods. The usual error analysis only shows the order of error estimate to the same as the local approximations[12].Using standard linear finite element base functions as partition of unity and polynomials as local approximation space, in 1-d case, we derive optimal order error estimates for PUFEM interpolants. Our analysis show that the error estimate is of one order higher than the local approximations. The interpolation error estimates yield optimal error estimates for PUFEM solutions of elliptic boundary value problems.
Aptitude treatment effects of laboratory grouping method for students of differing reasoning ability
Lawrenz, Frances; Munch, Theodore W.
This study examines aptitude treatment effects in an inquiry/learning cycle based physical science class for elementary education majors. The aptitude was formal reasoning ability and the students were arranged into three groups: high, middle, and low ability reasoners. The treatment was method of forming groups to work in the laboratory. Students in each of three classes were grouped according to reasoning ability. In one class the laboratory groups were homogeneous, i.e., students of similar reasoning ability were grouped together. In the second class the students were grouped heterogeneously, i.e., students of different reasoning ability were grouped together. In the third class, the student choice pattern, the students chose their own partners. The findings were that there were no aptitude treatment interaction for achievement or for gain in formal reasoning ability, that grouping students of similar cognitive ability together for laboratory work in the class was more effective in terms of science achievement than grouping students of differing cognitive ability together or than allowing students to choose their own partners, and that students at different levels of reasoning ability experienced differential gains in that ability over the semester.
A New Inexactness Criterion for Approximate Logarithmic-Quadratic Proximal Methods
无
2006-01-01
Recently, a class of logarithmic-quadratic proximal (LQP) methods was introduced by Auslender, Teboulle and Ben-Tiba. The inexact versions of these methods solve the sub-problems in each iteration approximately. In this paper, we present a practical inexactness criterion for the inexact version of these methods.
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Fran(c)ois Chaplais
2006-01-01
In applications it is useful to compute the local average of a function f(u) of an input u from empirical statistics on u. A very simple relation exists when the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so,it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.
An approximate method for design and analysis of an ALOHA system
Kobayashi, H.; Onozato, Y.; Huynh, D.
1977-01-01
An approximate method for the design and performance prediction of a multiaccess communication system which employs the ALOHA packet-switching technique is developed, based on the use of a diffusion process approximation of an ALOHA-like system (with or without time-slotting). A simple closed-form solution for the variable Q(t), a variant of the number of backlog messages at time t, is given in terms of a few system and user parameters. Final results are expressed in terms of ordinary performance measures such as throughput and average delay. Several numerical examples are given to demonstrate the usefulness of the approximation technique developed.
To calculate total dose effect on semi-conductor devices in satellite for a period of space mission effectively, two approximate calculation models for a comic radiation shielding were proposed. They are a sectoring method and a chord-length distribution method. When an approximate method was applied in this study, complex structure of satellite was described into multiple 1-dimensional slabs, structural materials were converted to reference material(aluminum), and the pre-calculated dose-depth conversion function was introduced to simplify the calculation process. Verification calculation was performed for orbit location and structure geometry of KITSAT-1 and compared with detailed 3-dimensional calculation results and experimental values. The calculation results from approximate method were estimated conservatively with acceptable error. However, results for satellite mission simulation were underestimated in total dose rate compared with experimental values
S. Das
2013-12-01
Full Text Available In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution. Effects of parameters on the convergence of the approximate series solution by minimizing the averaged residual error with the proper choices of parameters are calculated numerically and presented through graphs and tables for different particular cases.
Analytical Approximation Methods for the Stabilizing Solution of the Hamilton–Jacobi Equation
Sakamoto, Noboru; Schaft, Arjan J. van der
2008-01-01
In this paper, two methods for approximating the stabilizing solution of the Hamilton–Jacobi equation are proposed using symplectic geometry and a Hamiltonian perturbation technique as well as stable manifold theory. The first method uses the fact that the Hamiltonian lifted system of an integrable
Analytical Approximation Methods for the Stabilizing Solution of the Hamilton-Jacobi Equation
Sakamoto, Noboru; van der Schaft, Arjan J.
2008-01-01
In this paper, two methods for approximating the stabilizing solution of the Hamilton-Jacobi equation are proposed using symplectic geometry and a Hamiltonian perturbation technique as well as stable manifold theory. The first method uses the fact that the Hamiltonian lifted system of an integrable
Approximate Analytic and Numerical Solutions to Lane-Emden Equation via Fuzzy Modeling Method
De-Gang Wang
2012-01-01
Full Text Available A novel algorithm, called variable weight fuzzy marginal linearization (VWFML method, is proposed. This method can supply approximate analytic and numerical solutions to Lane-Emden equations. And it is easy to be implemented and extended for solving other nonlinear differential equations. Numerical examples are included to demonstrate the validity and applicability of the developed technique.
The Nikiforov-Uvarov method is employed to calculate the Schroedinger equation with a rotation Morse potential. The bound state energy eigenvalues and the corresponding eigenfunction are obtained. All of these calculations present an effective and clear method under a Pekeris approximation to solve a rotation Morse model. Meanwhile the results obtained here are in good agreement with the previous ones. (author)
Numerical solution of 2D-vector tomography problem using the method of approximate inverse
Svetov, Ivan; Maltseva, Svetlana; Polyakova, Anna
2016-08-01
We propose a numerical solution of reconstruction problem of a two-dimensional vector field in a unit disk from the known values of the longitudinal and transverse ray transforms. The algorithm is based on the method of approximate inverse. Numerical simulations confirm that the proposed method yields good results of reconstruction of vector fields.
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无
2009-01-01
An approximate homotopy symmetry method for nonlinear problems is proposed and applied to the sixth-order Boussinesq equation,which arises from fluid dynamics.We summarize the general formulas for similarity reduction solutions and similarity reduction equations of different orders,educing the related homotopy series solutions.Zero-order similarity reduction equations are equivalent to the Painlevé IV type equation or Weierstrass elliptic equation.Higher order similarity solutions can be obtained by solving linear variable coefficients ordinary differential equations.The auxiliary parameter has an effect on the convergence of homotopy series solutions.Series solutions and similarity reduction equations from the approximate symmetry method can be retrieved from the approximate homotopy symmetry method.
Quantum Approximate Methods for the Atomistic Modeling of Multicomponent Alloys. Chapter 7
Bozzolo, Guillermo; Garces, Jorge; Mosca, Hugo; Gargano, pablo; Noebe, Ronald D.; Abel, Phillip
2007-01-01
This chapter describes the role of quantum approximate methods in the understanding of complex multicomponent alloys at the atomic level. The need to accelerate materials design programs based on economical and efficient modeling techniques provides the framework for the introduction of approximations and simplifications in otherwise rigorous theoretical schemes. As a promising example of the role that such approximate methods might have in the development of complex systems, the BFS method for alloys is presented and applied to Ru-rich Ni-base superalloys and also to the NiAI(Ti,Cu) system, highlighting the benefits that can be obtained from introducing simple modeling techniques to the investigation of such complex systems.
GPGCD, an Iterative Method for Calculating Approximate GCD, for Multiple Univariate Polynomials
Terui, Akira
2010-01-01
We present an extension of our GPGCD method, an iterative method for calculating approximate greatest common divisor (GCD) of univariate polynomials, to multiple polynomial inputs. For a given pair of polynomials and a degree, our algorithm finds a pair of polynomials which has a GCD of the given degree and whose coefficients are perturbed from those in the original inputs, making the perturbations as small as possible, along with the GCD. In our GPGCD method, the problem of approximate GCD is transferred to a constrained minimization problem, then solved with the so-called modified Newton method, which is a generalization of the gradient-projection method, by searching the solution iteratively. In this paper, we extend our method to accept more than two polynomials with the real coefficients as an input.
In this paper we describe two analytical numerical methods applied to one-speed slab-geometry deep penetration transport problems. The linear discontinuous (LDN) equations are used to approximate the monoenergetic Boltzmann equation in slab geometry; they are obtained by considering a linear expansion of the angular flux inside each of the N elements of a uniform angular grid. The two analytical numerical methods are referred to as the spectral Green's function (SGF) nodal method and the Laplace transform (LTLDN) method. The SGF nodal method and the LTLDN method generate numerical solutions to the LDN equations that are completely free of spatial approximations, apart from finite arithmetic considerations. Numerical results to typical model problems and suggestions for future work are also presented. (orig.)
Approximate two layer (inviscid/viscous) methods to model aerothermodynamic environments
Dejarnette, Fred R.
1992-01-01
Approximate inviscid and boundary layer techniques for aerodynamic heating calculations are discussed. An inviscid flowfield solution is needed to provide surface pressures and boundary-layer edge properties. Modified Newtonian pressures coupled with an approximate shock shape will suffice for relatively simple shapes like sphere-cones with cone half-angles between 15 and 45 deg. More accurate approximate methods have been developed which make use of modified Maslen techniques. Slender and large angle sphere-cones and more complex shapes generally require an Euler code, like HALIS, to provide that information. The boundary-layer solution is reduced significantly by using the axisymmetric analog and approximate heating relations developed by Zoby, et al. (1981). Analysis is presented for the calculation of inviscid surface streamlines and metrics. Entropy-layer swallowing effects require coupling the inviscid and boundary-layer solutions.
A New Homotopy Analysis Method for Approximating the Analytic Solution of KdV Equation
Vahid Barati
2014-01-01
Full Text Available In this study a new technique of the Homotopy Analysis Method (nHAM is applied to obtain an approximate analytic solution of the well-known Korteweg-de Vries (KdV equation. This method removes the extra terms and decreases the time taken in the original HAM by converting the KdV equation to a system of first order differential equations. The resulted nHAM solution at third order approximation is then compared with that of the exact soliton solution of the KdV equation and found to be in excellent agreement.
Abedini, Mohammad; Nojoumian, Mohammad Ali; Salarieh, Hassan; Meghdari, Ali
2015-08-01
In this paper, model reference control of a fractional order system has been discussed. In order to control the fractional order plant, discrete-time approximation methods have been applied. Plant and reference model are discretized by Grünwald-Letnikov definition of the fractional order derivative using "Short Memory Principle". Unknown parameters of the fractional order system are appeared in the discrete time approximate model as combinations of parameters of the main system. The discrete time MRAC via RLS identification is modified to estimate the parameters and control the fractional order plant. Numerical results show the effectiveness of the proposed method of model reference adaptive control.
Dongyang Shi; Haihong Wang; Yuepeng Du
2009-01-01
An anisotropic nonconforming finite element method is presented for a class of nonlinear Sobolev equations. The optimal error estimates and supercloseness are obtained for both semi-discrete and fully-discrete approximate schemes, which are the same as the traditional finite element methods. In addition, the global superconvergence is derived through the postprocessing technique. Numerical experiments are included to illustrate the feasibility of the proposed method.
A numeric-analytic method for approximating quadratic Riccati differential equation
Belal Batiha
2012-03-01
Full Text Available In this paper, the multistage variational iteration method (MVIM isapplied to the solution of quadratic Riccati differential equations. The solution of quadratic Riccati differential equation obtained using the classical variational iteration method (VIM give good approximationsonly in the neighborhood of the initial position. The solution obtained by MVIM give good approximations for a larger interval. Comparison MVIM solution with classical VIM and exact solution show that the MVIM is a powerful method for the solution of nonlinear equations.
A New Trigonometric Method of Summation and its Application to the Degree of Approximation
G Das; Anasuya Nath; B K Ray
2002-05-01
The object of the present investigation is to introduce a new trigonometric method of summation which is both regular and Fourier effective and determine its status with reference to other methods of summation (see $\\mathcal{x}$2–$\\mathcal{x}$4) and also give an application of this method to determine the degree of approximation in a new Banach space of functions conceived as a generalized Hölder metric (see $\\mathcal{x}$5).
An Approximate Method for the Surge Response of the Tension Leg Platform
Rahim Shoghi; Mohammad Reza Tabeshpour
2014-01-01
The solution for the Duffing equation in a nonlinear vibration problem is studied in this paper. Clearly, in the case of the perturb parameter being a larger value, the traditional perturbation method is no longer valid but the Homotopy Perturbation Method (HPM) is applicable usually. HPM is used to solve the weak and strong nonlinear differential equations for finding the perturbed frequency of the response. The obtained frequencies via HPM and the approximate method have good accordance for weak and strong nonlinear differential equations. Additionally, the calculated responses by use of the approximate method are compared with the responses obtained from the Numerical method in the time history of the response and phase plane. The results represent good accordance between them.
Global collocation methods for approximation and the solution of partial differential equations
Solomonoff, A.; Turkel, E.
1986-01-01
Polynomial interpolation methods are applied both to the approximation of functions and to the numerical solutions of hyperbolic and elliptic partial differential equations. The derivative matrix for a general sequence of the collocation points is constructed. The approximate derivative is then found by a matrix times vector multiply. The effects of several factors on the performance of these methods including the effect of different collocation points are then explored. The resolution of the schemes for both smooth functions and functions with steep gradients or discontinuities in some derivative are also studied. The accuracy when the gradients occur both near the center of the region and in the vicinity of the boundary is investigated. The importance of the aliasing limit on the resolution of the approximation is investigated in detail. Also examined is the effect of boundary treatment on the stability and accuracy of the scheme.
An approximate method to study the one-velocity neutron integral transport equation
An approximate method to study the monokinetic linear transport equation is outlined, starting from its integral form, rather than the integro-differential one. The approximate solution may be deduced either analytically, in simple cases, or numerically by means of typical space discretization techniques, through a system of second-order differential equations, associated with proper boundary conditions. Both the system and the boundary conditions may be matched with the standard neutron diffusion multigroup ones, by means of a proper correspondence of the coefficients and of the unknowns. The slab and the radially-symmetric sphere are then analysed in detail. It is shown how, in the plane case, the present approximation is perfectly equivalent to the well-known discrete ordinate one. For curved geometries no such equivalence exists, and it is in these cases that the application of the method at hand looks promising, in order to avoid complications and numerical problems in practical applications. (author)
The information-based complexity of approximation problem by adaptive Monte Carlo methods
2008-01-01
In this paper, we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MWpr,α(Td), 1 < p < ∞, in the norm of Lq(Td), 1 < q < ∞, by adaptive Monte Carlo methods. Applying the discretization technique and some properties of pseudo-s-scale, we determine the exact asymptotic orders of this problem.
Viscosity Approximation Method for Infinitely Many Asymptotically Nonexpansive Maps in Banach Spaces
Ruo Feng RAO
2011-01-01
In the framework of reflexive Banach spaces satisfying a weakly continuous duality map,the author uses the viscosity approximation method to obtain the strong convergence theorem for iterations with infinitely many asymptotically nonexpansive mappings.The main results obtained in this paper improve and extend some recent results.
A tritium radioactivity source was measured by triple-to-double coincidence ratio (TDCR) equipment of the National Metrology Institute of Japan (NMIJ), and measured data were fitted using polynomial approximation and the Newton–Raphson method, a technique whereby equations are solved numerically by successive approximations. The method used to obtain the activity minimizes the difference between statistically calculated data and experimental data. In the fitting, since calculated statistical efficiency and TDCR values are discrete, the calculated efficiencies are approximated by quadratic functions around experimental values and the Newton–Raphson method is used for convergence at the minimal difference between experimental data and calculated data. In this way, the activity of tritium was successfully obtained. - Highlights: ► The TDCR data were fitted using polynomial approximation and the Newton–Raphson method. ► Activity was then successfully obtained by this fitting. ► The fitting procedure developed in this paper enables kB to be extracted for the scintilltor being used.
Analytical Approximation Method for the Center Manifold in the Nonlinear Output Regulation Problem
Suzuki, H.; Sakamoto, N.; Čelikovský, Sergej
Cancum: IEEE, 2008, s. 1163-1168. ISBN 978-1-4244-3124-3. [47th IEEE Conference on Decision and Control. Cancum (MX), 09.12.2008-11.12.2008] Institutional research plan: CEZ:AV0Z10750506 Keywords : approximate methods * nonlinear systems * output regulation Subject RIV: BC - Control Systems Theory
Astudillo, R.; Van Gijzen, M.B.
2014-01-01
A new algorithm to compute eigenpairs of large unsymmetric matrices is presented. Using the Induced Dimension Reduction method (IDR), which was originally proposed for solving linear systems, we obtain a Hessenberg decomposition from which we approximate the eigen-values and eigenvectors of a matrix
Approximation to the Mean and Variance of Moments Method Estimate Due to Gamma Distribution
In this paper, we shall consider the approximation to the mean and variance of moments method estimators due to gamma distribution by using Taylor series expansion approach.This approach showed that the estimators are asymptotically unbiased with mean square error approach zero as the sample size approach infinity.The theoretical approach assessed practically by using Monte-Carlo simulation
Kuhn, William F.
At the core of what it means to be a scientist or engineer is the ability to think rationally using scientific reasoning methods. Yet, typically if asked, scientist and engineers are hard press for a reply what that means. Some may argue that the meaning of scientific reasoning methods is a topic for the philosophers and psychologist, but this study believes and will prove that the answers lie with the scientists and engineers, for who really know the workings of the scientific reasoning thought process than they. This study will provide evidence to the aims: (a) determine the fundamental characteristics of cognitive reasoning methods exhibited by engineer/scientists working in R&D projects, (b) sample the engineer/scientist community to determine their views as to the importance, frequency, and ranking of each of characteristics towards benefiting their R&D projects, (c) make concluding remarks regarding any identified competency gaps in the exhibited or expected cognitive reasoning methods of engineer/scientists working on R&D projects. To drive these aims are the following three research questions. The first, what are the salient characteristics of cognitive reasoning methods exhibited by engineer/scientists in an R&D environment? The second, what do engineer/scientists consider to be the frequency and importance of the salient cognitive reasoning methods characteristics? And the third, to what extent, if at all, do patent holders and technical fellows differ with regard to their perceptions of the importance and frequency of the salient cognitive reasoning characteristics of engineer/scientists? The methodology and empirical approach utilized and described: (a) literature search, (b) Delphi technique composed of seven highly distinguish engineer/scientists, (c) survey instrument directed to distinguish Technical Fellowship, (d) data collection analysis. The results provide by Delphi Team answered the first research question. The collaborative effort validated
Approximation and inference methods for stochastic biochemical kinetics - a tutorial review
Schnoerr, David; Grima, Ramon
2016-01-01
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the Chemical Master Equation. Despite its simple structure, no analytic solutions to the Chemical Master Equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic models for chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langev...
New finite volume methods for approximating partial differential equations on arbitrary meshes
This dissertation presents some new methods of finite volume type for approximating partial differential equations on arbitrary meshes. The main idea lies in solving twice the problem to be dealt with. One addresses the elliptic equations with variable (anisotropic, antisymmetric, discontinuous) coefficients, the parabolic linear or non linear equations (heat equation, radiative diffusion, magnetic diffusion with Hall effect), the wave type equations (Maxwell, acoustics), the elasticity and Stokes'equations. Numerous numerical experiments show the good behaviour of this type of method. (author)
Debrabant, Kristian; Rößler, Andreas
2013-01-01
In the present paper, a class of stochastic Runge-Kutta methods containing the second order stochastic Runge-Kutta scheme due to E. Platen for the weak approximation of It\\^o stochastic differential equation systems with a multi-dimensional Wiener process is considered. Order one and order two conditions for the coefficients of explicit stochastic Runge-Kutta methods are solved and the solution space of the possible coefficients is analyzed. A full classification of the coefficients for such ...
Alam Khan, Najeeb; Razzaq, Oyoon Abdul
2016-03-01
In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.
On-site approximation for spin-orbit coupling in LCAO density functional methods
Fernandez-Seivane, Lucas; Oliveira, Miguel A; Sanvito, Stefano; Ferrer, Jaime
2006-01-01
We propose a computational method that simplifies drastically the inclusion of spin-orbit interaction in density functional theory implemented on localised atomic orbital basis sets. Our method is based on a well-known procedure for obtaining pseudopotentials from atomic relativistic 'ab initio' calculations and on an on-site approximation for the spin-orbit matrix elements. We have implemented the technique in the SIESTA code, and we show that it provides accurate results for the overall ban...
Modelling CH$_3$OH masers: Sobolev approximation and accelerated lambda iteration method
Nesterenok, Aleksandr
2015-01-01
A simple one-dimensional model of CH$_3$OH maser is considered. Two techniques are used for the calculation of molecule level populations: the accelerated lambda iteration (ALI) method and the large velocity gradient (LVG), or Sobolev, approximation. The LVG approximation gives accurate results provided that the characteristic dimensions of the medium are larger than 5-10 lengths of the resonance region. We presume that this condition can be satisfied only for the largest observed maser spot distributions. Factors controlling the pumping of class I and class II methanol masers are considered.
Adomian Decomposition Method and Padé Approximants for Nonlinear Differential-Difference Equations
LIU Yan-Ming; CHEN Yong
2009-01-01
Combining Adomian decomposition method (ADM) with Padd approximants, we solve two differential-difference equations (DDEs): the relativistic Toda lattice equation and the modified Volterra lattice equation.With the help of symbolic computation Maple, the results obtained by ADM-Padé technique are compared with those obtained by using ADM alone.The numerical results demonstrate that ADM-Padé technique give the approximate solution with faster convergence rate and higher accuracy and relative in larger domain of convergence than using ADM.
M. P. Menguc
2011-09-01
Full Text Available We embark on this preliminary study of the suitability of the discrete dipole approximation with surface interaction (DDA-SI method to model electric field scattering from noble metal nano-structures on dielectric substrates. The refractive index of noble metals, particularly due to their high imaginary components, require smaller lattice spacings and are especially sensitive to the shape integrity and the volume of the dipole model. The results of DDA-SI method are validated against those of the well-established finite element method (FEM and the finite difference time domain (FDTD method.
Transportation problem by Monalisha\\'s approximation method for optimal solution (mamos
Monalisha Pattnaik
2015-09-01
Full Text Available Background: This paper finds initial basic feasible solution and optimal solution to the transportation problem by using MAM's (Monalisha's Approximation Method. Methods: Using the concept of comparison of the transportation problem by other methods of solution, the paper introduces a very effective method in terms of cost and time for solving these problems. This paper extends transportation problem by using different method of obtaining both initial basic feasible solution and optimal solution simultaneously other than existing methods. Results and conclusions: It is presented a cost saving and less time consuming and accurate method for obtaining the best optimal solution of the transportation problem . With the problem assumptions, the optimal solution can still be theoretically solved using the existing methods. Finally, numerical examples and sensitivity analysis are presented to illustrate the effectiveness of the theoretical results, and to gain additional managerial insights.
A Scalable Method for Solving High-Dimensional Continuous POMDPs Using Local Approximation
Erez, Tom
2012-01-01
Partially-Observable Markov Decision Processes (POMDPs) are typically solved by finding an approximate global solution to a corresponding belief-MDP. In this paper, we offer a new planning algorithm for POMDPs with continuous state, action and observation spaces. Since such domains have an inherent notion of locality, we can find an approximate solution using local optimization methods. We parameterize the belief distribution as a Gaussian mixture, and use the Extended Kalman Filter (EKF) to approximate the belief update. Since the EKF is a first-order filter, we can marginalize over the observations analytically. By using feedback control and state estimation during policy execution, we recover a behavior that is effectively conditioned on incoming observations despite the unconditioned planning. Local optimization provides no guarantees of global optimality, but it allows us to tackle domains that are at least an order of magnitude larger than the current state-of-the-art. We demonstrate the scalability of ...
Parallel Preconditioned Conjugate Gradient Square Method Based on Normalized Approximate Inverses
George A. Gravvanis
2005-01-01
Full Text Available A new class of normalized explicit approximate inverse matrix techniques, based on normalized approximate factorization procedures, for solving sparse linear systems resulting from the finite difference discretization of partial differential equations in three space variables are introduced. A new parallel normalized explicit preconditioned conjugate gradient square method in conjunction with normalized approximate inverse matrix techniques for solving efficiently sparse linear systems on distributed memory systems, using Message Passing Interface (MPI communication library, is also presented along with theoretical estimates on speedups and efficiency. The implementation and performance on a distributed memory MIMD machine, using Message Passing Interface (MPI is also investigated. Applications on characteristic initial/boundary value problems in three dimensions are discussed and numerical results are given.
The Financial Impact of Risk Factors Affecting Project Cost Contingency: Evidential Reasoning Method
Emmanuel Abeere-Inga; Joseph Ignatius Teye Buertey; Theophilus Adjei Kumi
2013-01-01
The process of cost modeling using risk analysis for construction projects is very crucial for the achievement of project success. The purpose of this paper is to present an analysis of the financial impact of risk factors affecting key construction work sections; using a systematic risk methodology based on empirical judgment. The failure mode effect analysis (FMEA) and the evidential reasoning methods are presented as qualitative and quantitative risk tools respectively. Data analysis from ...
Bishop, R. F.; Li, P. H. Y.
2011-04-01
An approximation hierarchy, called the lattice-path-based subsystem (LPSUBm) approximation scheme, is described for the coupled-cluster method (CCM). It is applicable to systems defined on a regular spatial lattice. We then apply it to two well-studied prototypical (spin-(1)/(2) Heisenberg antiferromagnetic) spin-lattice models, namely, the XXZ and the XY models on the square lattice in two dimensions. Results are obtained in each case for the ground-state energy, the ground-state sublattice magnetization, and the quantum critical point. They are all in good agreement with those from such alternative methods as spin-wave theory, series expansions, quantum Monte Carlo methods, and the CCM using the alternative lattice-animal-based subsystem (LSUBm) and the distance-based subsystem (DSUBm) schemes. Each of the three CCM schemes (LSUBm, DSUBm, and LPSUBm) for use with systems defined on a regular spatial lattice is shown to have its own advantages in particular applications.
An approximation hierarchy, called the lattice-path-based subsystem (LPSUBm) approximation scheme, is described for the coupled-cluster method (CCM). It is applicable to systems defined on a regular spatial lattice. We then apply it to two well-studied prototypical (spin-(1/2) Heisenberg antiferromagnetic) spin-lattice models, namely, the XXZ and the XY models on the square lattice in two dimensions. Results are obtained in each case for the ground-state energy, the ground-state sublattice magnetization, and the quantum critical point. They are all in good agreement with those from such alternative methods as spin-wave theory, series expansions, quantum Monte Carlo methods, and the CCM using the alternative lattice-animal-based subsystem (LSUBm) and the distance-based subsystem (DSUBm) schemes. Each of the three CCM schemes (LSUBm, DSUBm, and LPSUBm) for use with systems defined on a regular spatial lattice is shown to have its own advantages in particular applications.
无
2010-01-01
For structural system with random basic variables as well as fuzzy basic variables,uncertain propagation from two kinds of basic variables to the response of the structure is investigated.A novel algorithm for obtaining membership function of fuzzy reliability is presented with saddlepoint approximation(SA)based line sampling method.In the presented method,the value domain of the fuzzy basic variables under the given membership level is firstly obtained according to their membership functions.In the value domain of the fuzzy basic variables corresponding to the given membership level,bounds of reliability of the structure response satisfying safety requirement are obtained by employing the SA based line sampling method in the reduced space of the random variables.In this way the uncertainty of the basic variables is propagated to the safety measurement of the structure,and the fuzzy membership function of the reliability is obtained.Compared to the direct Monte Carlo method for propagating the uncertainties of the fuzzy and random basic variables,the presented method can considerably improve computational efficiency with acceptable precision.The presented method has wider applicability compared to the transformation method,because it doesn’t limit the distribution of the variable and the explicit expression of performance function, and no approximation is made for the performance function during the computing process.Additionally,the presented method can easily treat the performance function with cross items of the fuzzy variable and the random variable,which isn’t suitably approximated by the existing transformation methods.Several examples are provided to illustrate the advantages of the presented method.
Evaluation of approximate methods for the prediction of noise shielding by airframe components
Ahtye, W. F.; Mcculley, G.
1980-01-01
An evaluation of some approximate methods for the prediction of shielding of monochromatic sound and broadband noise by aircraft components is reported. Anechoic-chamber measurements of the shielding of a point source by various simple geometric shapes were made and the measured values compared with those calculated by the superposition of asymptotic closed-form solutions for the shielding by a semi-infinite plane barrier. The shields used in the measurements consisted of rectangular plates, a circular cylinder, and a rectangular plate attached to the cylinder to simulate a wing-body combination. The normalized frequency, defined as a product of the acoustic wave number and either the plate width or cylinder diameter, ranged from 4.6 to 114. Microphone traverses in front of the rectangular plates and cylinders generally showed a series of diffraction bands that matched those predicted by the approximate methods, except for differences in the magnitudes of the attenuation minima which can be attributed to experimental inaccuracies. The shielding of wing-body combinations was predicted by modifications of the approximations used for rectangular and cylindrical shielding. Although the approximations failed to predict diffraction patterns in certain regions, they did predict the average level of wing-body shielding with an average deviation of less than 3 dB.
The DSUBm approximation scheme for the coupled cluster method and applications to quantum magnets
R.F. Bishop
2009-01-01
Full Text Available A new approximate scheme, DSUBm, is described for the coupled cluster method. We apply it to two well-studied (spin-1/2 Heisenberg antiferromagnet spin-lattice models, namely: the XXZ and the XY models on the square lattice in two dimensions. Results are obtained in each case for the ground-state energy, the sublattice magnetization and the quantum critical point. They are in good agreement with those from such alternative methods as spin-wave theory, series expansions, exact diagonalization techniques, quantum Monte Carlo methods and those from the CCM using the LSUBm scheme.
Born approximation to a perturbative numerical method for the solution of the Schroedinger equation
A step function perturbative numerical method (SF-PN method) is developed for the solution of the Cauchy problem for the second order liniar differential equation in normal form. An important point stressed in the present paper, which seems to have been previously ignored in the literature devoted to the PN methods, is the close connection between the first order perturbation theory of the PN approach and the wellknown Born approximation, and, in general, the connection between the varjous orders of the PN corrections and the Neumann series. (author)
Approximate Explicit Solution of Falkner-Skan Equation by Homotopy Perturbation Method
N. Moallemi
2012-08-01
Full Text Available In this study, by mean`s of He`s Homotopy Perturbation Method (HPM an approximate solution of Falkner-Skan equation obtained. In boundary layer theory, we have seen how similarity methods combine two independent variables into one, and therefore our problems our simplified to ODE Equations. If we use HPM we can deforms a difficult ordinary differential equation into a simple problem which can be easily solved. Comparison is made between the solution of Falkner Skan equation for 4 cases and those in open literature to verify accuracy of this work. Results show that the method is very effective and simple.
Accumulated approximation: A new method for structural optimization by iterative improvement
Rasmussen, John
1990-01-01
A new method for the solution of non-linear mathematical programming problems in the field of structural optimization is presented. It is an iterative scheme which for each iteration refines the approximation of objective and constraint functions by accumulating the function values of previously visited design points. The method has proven to be competitive for a number of well-known examples of which one is presented here. Furthermore because of the accumulation strategy, the method produces convergence even when the sensitivity analysis is inaccurate.
LongShuyao; HuDe'an
2003-01-01
The meshless method is a new numerical technique presented in recent years .It uses the moving least square (MLS) approximation as a shape function . The smoothness of the MLS approximation is determined by that of the basic function and of the weight function, and is mainly determined by that of the weight function. Therefore, the weight function greatly affects the accuracy of results obtained. Different kinds of weight functions, such as the spline function, the Gauss function and so on, are proposed recently by many researchers. In the present work, the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method. The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed. Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and a in Gauss and exponential weight functions are in the range of reasonable values, respectively, and the higher the smoothness of the weight function, the better the features of the solutions.
A New Newton's Method with Diagonal Jacobian Approximation for Systems of Nonlinear Equations
M. Y. Waziri
2010-01-01
Full Text Available Problem statement: The major weaknesses of Newton method for nonlinear equations entail computation of Jacobian matrix and solving systems of n linear equations in each of the iterations. Approach: In some extent function derivatives are quit costly and Jacobian is computationally expensive which requires evaluation (storage of n×n matrix in every iteration. Results: This storage requirement became unrealistic when n becomes large. We proposed a new method that approximates Jacobian into diagonal matrix which aims at reducing the storage requirement, computational cost and CPU time, as well as avoiding solving n linear equations in each iterations. Conclusion/Recommendations: The proposed method is significantly cheaper than Newtons method and very much faster than fixed Newtons method also suitable for small, medium and large scale nonlinear systems with dense or sparse Jacobian. Numerical experiments were carried out which shows that, the proposed method is very encouraging.
An atmospheric backscatter model on wind measurements using far-field approximation method
SHU Weiping; ZHAO Zhengyu
2007-01-01
A backscatter model was developed for measuring wind field with the far-field approximation method.The theoretical computation and computer simulations with one spatial dimension show that this model can realistically describe the physical meaning and process of the three methods in wind measurements including the spaced antenna (SA) method,Doppler beam swing (DBS) method,and spaced interferometry (SI).The computational difficulties of the traditional theoretical model cannot only be smoothed away,but common characteristics and differences of the three methods can be compared deeply.The comparison of the numerical results between the Wuhan medium frequency (MF) radar (30° N,114° E) observation and the computer simulation of the full correlation analysis (FCA) of the SA method indicates that the two results agree very well and this model has practical application.
A Resampling-Based Stochastic Approximation Method for Analysis of Large Geostatistical Data
Liang, Faming
2013-03-01
The Gaussian geostatistical model has been widely used in modeling of spatial data. However, it is challenging to computationally implement this method because it requires the inversion of a large covariance matrix, particularly when there is a large number of observations. This article proposes a resampling-based stochastic approximation method to address this challenge. At each iteration of the proposed method, a small subsample is drawn from the full dataset, and then the current estimate of the parameters is updated accordingly under the framework of stochastic approximation. Since the proposed method makes use of only a small proportion of the data at each iteration, it avoids inverting large covariance matrices and thus is scalable to large datasets. The proposed method also leads to a general parameter estimation approach, maximum mean log-likelihood estimation, which includes the popular maximum (log)-likelihood estimation (MLE) approach as a special case and is expected to play an important role in analyzing large datasets. Under mild conditions, it is shown that the estimator resulting from the proposed method converges in probability to a set of parameter values of equivalent Gaussian probability measures, and that the estimator is asymptotically normally distributed. To the best of the authors\\' knowledge, the present study is the first one on asymptotic normality under infill asymptotics for general covariance functions. The proposed method is illustrated with large datasets, both simulated and real. Supplementary materials for this article are available online. © 2013 American Statistical Association.
We describe the generalized perturbation method in the atomic-sphere approximation (ASA) for calculating the effective cluster interactions. Based on our development of Korringa-Kohn-Rostoker coherent-potential approximation in the ASA [Singh et al., Phys. Rev. B 44, 8578 (1991)], the present approach is the next step towards developing a first-principles method that can be easily applied to describe substitutionally disordered alloys based on simple lattice structures as well as complex lattice structures with low symmetry. To test the accuracy of the ASA results, we have calculated the effective pair interactions (EPI) up to fourth-nearest neighbors for the substitutionally disordered Pd0.5V0.5 and Pd0.75Rh0.25 alloys. Our calculated EPI's are in good agreement with the respective muffin-tin results
About the Generalized Reasoning Methods and their Use in Semiotic Systems
Mihaela I. MUNTEAN
2006-01-01
Full Text Available In computational semiotics the problem is to emulate a semiosis cycle within a digital computer. This needs the construction of intelligent systems, able to perform intelligent behavior, such as sensorial perception, world modeling, value judgement and behavior generation. These intelligent systems could be generally implemented through object networks and the basic functions mentioned above could be obtained by generalization of some elementary knowledge operators. Based on the three main reasoning methods, deduction, induction and abduction, well known in the philosophy of science and used in AI systems, there were three knew knowledge operators defined: knowledge extraction, knowledge generation and knowledge generation, operators that could be viewed as generalized interpretations of the standard reasoning procedures. This paper presents these new concepts and their connection, the current understanding of generalized deduction, induction and abduction and also how these operators could serve as the building blocks of universal intelligent systems.
An Improved Approximate-Bayesian Model-choice Method for Estimating Shared Evolutionary History
Oaks, Jamie R.
2014-01-01
Background To understand biological diversification, it is important to account for large-scale processes that affect the evolutionary history of groups of co-distributed populations of organisms. Such events predict temporally clustered divergences times, a pattern that can be estimated using genetic data from co-distributed species. I introduce a new approximate-Bayesian method for comparative phylogeographical model-choice that estimates the temporal distribution of divergences across taxa...
Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods
Nielsen, Søren R.K.; Sørensen, John Dalsgaard
Close approximations to the first passage probability of failure in random vibration can be obtained by integral equation methods. A simple relation exists between the first passage probability density function and the distribution function for the time interval spent below a barrier before outcr...... passage probability density. The results of the theory agree well with simulation results for narrow banded processes dominated by a single frequency, as well as for bimodal processes with 2 dominating frequencies in the structural response....
George Caminha-Maciel; Irineu Figueiredo
2013-01-01
We present an analysis of the error involved in the so-called low induction number approximation in the electromagnetic methods. In particular, we focus on the EM34 equipment settings and field configurations, widely used for geophysical prospecting of laterally electrical conductivity anomalies and shallow targets. We show the theoretical error for the conductivity in both vertical and horizontal dipole coil configurations within the low induction number regime and up to the maximum measurin...
An approximate method for solving a melting problem with periodic boundary conditions
Qu Liang-Hui; Xing Lin; Yu Zhi-Yun; Ling Feng; Xu Jian-Guo
2014-01-01
An effective thermal diffusivity method is used to solve one-dimensional melting problem with periodic boundary conditions in a semi-infinite domain. An approximate analytic solution showing the functional relation between the location of the moving boundary and time is obtained by using Laplace transform. The evolution of the moving boundary and the temperature field in the phase change domain are simulated numerically, and the numerical results are compar...
A nodal method for solving the time-depending diffusion equation in the IQS approximation
The fast and slow variation of the neutron flux shape needed for the dynamical description of nuclear reactor cores can be described advantageously in the Improved Quasistatic (IQS) model where the flux is factorized by a fast changing space-independent amplitude and a slow changing shape function. The basic equations of a time-dependent nodal approximation using the IQS method is presented.The calculational procedure of the response matrices is also described. (R.P.) 2 refs
An approximate method for solving a melting problem with periodic boundary conditions
Qu Liang-Hui
2014-01-01
Full Text Available An effective thermal diffusivity method is used to solve one-dimensional melting problem with periodic boundary conditions in a semi-infinite domain. An approximate analytic solution showing the functional relation between the location of the moving boundary and time is obtained by using Laplace transform. The evolution of the moving boundary and the temperature field in the phase change domain are simulated numerically, and the numerical results are compared with previous results in open literature.
Negara, Ardiansyah
2013-01-01
Anisotropy of hydraulic properties of subsurface geologic formations is an essential feature that has been established as a consequence of the different geologic processes that they undergo during the longer geologic time scale. With respect to petroleum reservoirs, in many cases, anisotropy plays significant role in dictating the direction of flow that becomes no longer dependent only on the pressure gradient direction but also on the principal directions of anisotropy. Furthermore, in complex systems involving the flow of multiphase fluids in which the gravity and the capillarity play an important role, anisotropy can also have important influences. Therefore, there has been great deal of motivation to consider anisotropy when solving the governing conservation laws numerically. Unfortunately, the two-point flux approximation of finite difference approach is not capable of handling full tensor permeability fields. Lately, however, it has been possible to adapt the multipoint flux approximation that can handle anisotropy to the framework of finite difference schemes. In multipoint flux approximation method, the stencil of approximation is more involved, i.e., it requires the involvement of 9-point stencil for the 2-D model and 27-point stencil for the 3-D model. This is apparently challenging and cumbersome when making the global system of equations. In this work, we apply the equation-type approach, which is the experimenting pressure field approach that enables the solution of the global problem breaks into the solution of multitude of local problems that significantly reduce the complexity without affecting the accuracy of numerical solution. This approach also leads in reducing the computational cost during the simulation. We have applied this technique to a variety of anisotropy scenarios of 3-D subsurface flow problems and the numerical results demonstrate that the experimenting pressure field technique fits very well with the multipoint flux approximation
A method for the accurate and smooth approximation of standard thermodynamic functions
Coufal, O.
2013-01-01
A method is proposed for the calculation of approximations of standard thermodynamic functions. The method is consistent with the physical properties of standard thermodynamic functions. This means that the approximation functions are, in contrast to the hitherto used approximations, continuous and smooth in every temperature interval in which no phase transformations take place. The calculation algorithm was implemented by the SmoothSTF program in the C++ language which is part of this paper. Program summaryProgram title:SmoothSTF Catalogue identifier: AENH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3807 No. of bytes in distributed program, including test data, etc.: 131965 Distribution format: tar.gz Programming language: C++. Computer: Any computer with gcc version 4.3.2 compiler. Operating system: Debian GNU Linux 6.0. The program can be run in operating systems in which the gcc compiler can be installed, see http://gcc.gnu.org/install/specific.html. RAM: 256 MB are sufficient for the table of standard thermodynamic functions with 500 lines Classification: 4.9. Nature of problem: Standard thermodynamic functions (STF) of individual substances are given by thermal capacity at constant pressure, entropy and enthalpy. STF are continuous and smooth in every temperature interval in which no phase transformations take place. The temperature dependence of STF as expressed by the table of its values is for further application approximated by temperature functions. In the paper, a method is proposed for calculating approximation functions which, in contrast to the hitherto used approximations, are continuous and smooth in every temperature interval. Solution method: The approximation functions are
The reliability of approximate radiation transport methods for irradiated disk studies
Kuiper, Rolf
2013-01-01
Context: Dynamical studies of irradiated circumstellar disks require an accurate treatment of radiation transport to, for example, properly determine cooling and fragmentation properties. The radiation transport algorithm should be as fast as the (magneto-) hydrodynamics to allow for an efficient usage of computing resources. Methods: We use a setup of a central star and a slightly flared circumstellar disk. We perform simulations for a wide range of optical depths of the disk's midplane from tau(550nm) = 0.1 up to tau(810nm) = 1 million. We check the accuracy of the gray flux-limited diffusion (FLD) approximation and a gray and frequency-dependent ray-tracing plus FLD approximation. Results: 1. For moderate optical depths, a gray approximation of the stellar irradiation yields a slightly hotter inner rim and a slightly cooler midplane of the disk at larger radii, but is otherwise in agreement with the frequency-dependent treatment. 2. The gray FLD approximation fails to compute an appropriate temperature pro...
A recursive model-reduction method for approximate inference in Gaussian Markov random fields.
Johnson, Jason K; Willsky, Alan S
2008-01-01
This paper presents recursive cavity modeling--a principled, tractable approach to approximate, near-optimal inference for large Gauss-Markov random fields. The main idea is to subdivide the random field into smaller subfields, constructing cavity models which approximate these subfields. Each cavity model is a concise, yet faithful, model for the surface of one subfield sufficient for near-optimal inference in adjacent subfields. This basic idea leads to a tree-structured algorithm which recursively builds a hierarchy of cavity models during an "upward pass" and then builds a complementary set of blanket models during a reverse "downward pass." The marginal statistics of individual variables can then be approximated using their blanket models. Model thinning plays an important role, allowing us to develop thinned cavity and blanket models thereby providing tractable approximate inference. We develop a maximum-entropy approach that exploits certain tractable representations of Fisher information on thin chordal graphs. Given the resulting set of thinned cavity models, we also develop a fast preconditioner, which provides a simple iterative method to compute optimal estimates. Thus, our overall approach combines recursive inference, variational learning and iterative estimation. We demonstrate the accuracy and scalability of this approach in several challenging, large-scale remote sensing problems. PMID:18229805
One Fairing Method of Cubic B-spline Curves Based on Weighted Progressive Iterative Approximation
ZHANG Li; YANG Yan; LI Yuan-yuan; TAN Jie-qing
2014-01-01
A new method to the problem of fairing planar cubic B-spline curves is introduced in this paper. The method is based on weighted progressive iterative approximation (WPIA for short) and consists of following steps:finding the bad point which needs to fair, deleting the bad point, re-inserting a new data point to keep the structure of the curve and applying WPIA method with the new set of the data points to obtain the faired curve. The new set of the data points is formed by the rest of the original data points and the new inserted point. The method can be used for shape design and data processing. Numerical examples are provided to demonstrate the effectiveness of the method.
The effect of method and format on the responses of subjects to a Piagetian reasoning problem
Staver, John R.; Pascarella, Ernest T.
Researchers interested in studying the effects of subjects' reasoning levels, as defined by Piaget (Inhelder & Piaget, 1958), on science achievement or other dependent variables face two measurement problems. First, the traditional clinical method is time-consuming and impractical for large numbers of subjects. Second, alternative methods of assessment, although reliable and valid, may over- or underestimate subjects' reasoning levels. The objective of this investigation was to determine the effects of various methods and formats of administering a Piagetian task on subjects' performance. The task chosen for this investigation was the Mr. Short-Mr. Tall problem (Karplus & Lavatelli, 1969; Karplus et al., 1977). The task was presented using four methods: (1) individual clinical interview, (2) group presentation of task followed by paper-and-pencil problem with illustration, (3) group administration of paper-and-pencil instrument with illustration, and (4) group administration of paper-and-pencil instrument without illustration. Each method included four formats: (1) completion answer with essay justification, (2) completion answer with multiple-choice justification, (3) multiple-choice answer with essay justification, and (4) multiple-choice answer with multiple-choice justification. Three hundred seventy-six students who were enrolled in a freshman level biological science class participated in the study. The research design was a 4 × 4 factorial design with method and format of assessment as the main effects. The participants were in 16 distinct laboratory or discussion sections, and each section was randomly assigned to a cell in the research design. Regression analysis with the individual as the unit of analysis showed that neither method nor format of assessment accounted for a significant amount of variance in student performance. The overall interaction remained nonsignificant. Regression analysis with sections as the unit of analysis revealed similar
Halim CEYLAN
2007-02-01
Full Text Available This study develops approximate mathematical expressions for delay components at signalized intersections. Delay components are solved with the coordinate transformation method. The performance indicators for the signalized intersection are determined as an oversaturated and under saturated cases. During the analysis, the steady-state and the deterministic queuing theory are investigated first, and then time-dependent transformation is made. Developed model, called YHM, is applied to an example signalized intersection. Results are compared with the current situation and the Webster method. YHM is improved the intersection performance by about 500 % for this example. Moreover, signal parameters are significantly differs from the current and Webster signal control.
Exact and approximate interior corner problem in neutron diffusion by integral transform methods
Bareiss, E.H.; Chang, K.S.J.; Constatinescu, D.A.
1976-09-01
The mathematical solution of the neutron diffusion equation exhibits singularities in its derivatives at material corners. A mathematical treatment of the nature of these singularities and its impact on coarse network approximation methods in computational work is presented. The mathematical behavior is deduced from Green's functions, based on a generalized theory for two space dimensions, and the resulting systems of integral equations, as well as from the Kontorovich--Lebedev Transform. The effect on numerical calculations is demonstrated for finite difference and finite element methods for a two-region corner problem.
Approximation of magnetic data surface with ANN (artificial neural network) method
Complete text of publication follows. Aero magnetic digital gridded data acquired and processed by US geological survey with Mexican collaborators have been downloaded from internet. The field dataset is a part of the Online Magnetic Dataset for North America, with more than 200,000 data points. Using ANN method a surface has been fitted to the magnetic data. ANN is programmed under Matlab software environment by using Multi Layer Perception (MLP) structure.The ANN model had multilayer perception structure most programmed on there Matlab. The accuracy of surface approximation was tested by 1) comparison with result of other methods contained in Surfer program; 2) Interpolated known data on the surface.
Reliability assessments based on probabilistic fracture mechanics can give insight into the effects of changes in design parameters, operational conditions and maintenance schemes. Although they are often not capable of providing absolute reliability values, these methods at least allow the ranking of different solutions among alternatives. Due to the variety of possible solutions for design, operation and maintenance problems numerous probabilistic reliability assessments have to be carried out. This is a laborous task especially for crack containing welds of nuclear pipes subjected to fatigue. The objective of this paper is to compare the Monte Carlo simulation method and a newly developed approximative approach using the Markov process ansatz for this task
A new method for extraction of approximately vertical lines from natural images
赵建坤; 吴江华; 张田文
2002-01-01
For natural images with complex background and noise, this new approach appears is more effective than other techniques for three key reasons: 1)edge elements treated interdependently to overcome the weakness of standard Hough transform (HT); 2)gradient orientation information taken into account in the process of HT; 3) an effective method used to "merge" the HT result, i.e. many "clustered short lines" into single straight line to represent the edge of object to be recognized. This method consists of three steps are: 1) edge detection; 2)modified Hough transform to extract "clustered short lines"; 3) merging "clustered short lines" into a single line after few modifications. The method presented in this paper could also be used for extraction of non-vertical straight lines.
The approximate inversion as a reconstruction method in X-ray computerized tomography
Dietz, R L
1999-01-01
The mathematical model of the X-ray computerized tomography will be developed in the first chapter, the approximate inversion will be introduced, and the Radon Transform will be used as an example to demonstrate calculation of a reconstruction cone. In the second chapter, a reconstruction method for the parallel geometry is discussed, leading to derivation of the method for a fan-beam geometry. The approximate inversion calculated for the limited-angle case is presented as an example of incomplete data problems. As with complete data problems, numerical examples are given and the method is compared with existing other methods. 3D reconstruction is the topic of the third chapter. Although of no relevance in practice, a parallel geometry will be examined. No problems are encountered in transferring the reconstruction cone to the cone beam geometry, but only for a scanning curve which also is of no relevance in practice. A further reconstruction method is presented for curves fulfilling the so-called Tuy conditi...
New identification method for Hammerstein models based on approximate least absolute deviation
Xu, Bao-Chang; Zhang, Ying-Dan
2016-07-01
Disorder and peak noises or large disturbances can deteriorate the identification effects of Hammerstein non-linear models when using the least-square (LS) method. The least absolute deviation technique can be used to resolve this problem; however, its absolute value cannot meet the need of differentiability required by most algorithms. To improve robustness and resolve the non-differentiable problem, an approximate least absolute deviation (ALAD) objective function is established by introducing a deterministic function that exhibits the characteristics of absolute value under certain situations. A new identification method for Hammerstein models based on ALAD is thus developed in this paper. The basic idea of this method is to apply the stochastic approximation theory in the process of deriving the recursive equations. After identifying the parameter matrix of the Hammerstein model via the new algorithm, the product terms in the matrix are separated by calculating the average values. Finally, algorithm convergence is proven by applying the ordinary differential equation method. The proposed algorithm has a better robustness as compared to other LS methods, particularly when abnormal points exist in the measured data. Furthermore, the proposed algorithm is easier to apply and converges faster. The simulation results demonstrate the efficacy of the proposed algorithm.
Approximation by random weighting method for M-test in linear models
2007-01-01
The M-test has been in common use and widely studied in testing the linear hypotheses in linear models. However, the critical value for the test is usually related to the quantities of the unknown error distribution and the estimate of the nuisance parameters may be rather involved, not only for the M-test method but also for the existing bootstrap methods. In this paper we suggest a random weighting resampling method for approximating the null distribution of the M-test statistic. It is shown that, under both the null and the local alternatives, the random weighting statistic has the same asymptotic distribution as the null distribution of the M-test. The critical values of the M-test can therefore be obtained by the random weighting method without estimating the nuisance parameters. A distinguished feature of the proposed method is that the approximation is valid even the null hypothesis is not true and the power evaluation is possible under the local alternatives.
S-curve networks and an approximate method for estimating degree distributions of complex networks
In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 (Internet Protocol version 4) addresses, this paper proposes a forecasting model by using S curve (logistic curve). The growing trend of IPv4 addresses in China is forecasted. There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6. Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with a bulk growth. The model is said to be an S-curve network. Analysis demonstrates that the analytic method based on uniform distributions (i.e., Barabási-Albert method) is not suitable for the network. It develops an approximate method to predict the growth dynamics of the individual nodes, and uses this to calculate analytically the degree distribution and the scaling exponents. The analytical result agrees with the simulation well, obeying an approximately power-law form. This method can overcome a shortcoming of Barabási-Albert method commonly used in current network research. (general)
Approximation by random weighting method for M-test in linear models
Xiao-yan WU; Ya-ning YANG; Lin-cheng ZHAO
2007-01-01
The M-test has been in common use and widely studied in testing the linear hypotheses in linear models. However, the critical value for the test is usually related to the quantities of the unknown error distribution and the estimate of the nuisance parameters may be rather involved, not only for the M-test method but also for the existing bootstrap methods. In this paper we suggest a random weighting resampling method for approximating the null distribution of the M-test statistic.It is shown that, under both the null and the local alternatives, the random weighting statistic has the same asymptotic distribution as the null distribution of the M-test. The critical values of the M-test can therefore be obtained by the random weighting method without estimating the nuisance parameters. A distinguished feature of the proposed method is that the approximation is valid even the null hypothesis is not true and the power evaluation is possible under the local alternatives.
A general approximate method for the groundwater response problem caused by water level variation
Jiang, Qinghui; Tang, Yuehao
2015-10-01
The Boussinesq equation (BEQ) can be used to describe groundwater flow through an unconfined aquifer. Based on 1D BEQ, we present a general approximate method to predict the water table response in a semi-infinite aquifer system with a vertical or sloping boundary. A decomposition method is adopted by separating the original problem into a linear diffusion equation (DE) and two correction functions. The linear DE satisfies all the initial and boundary conditions, reflecting the basic characteristics of groundwater movement. The correction functions quantitatively measure the errors due to the degeneration from the original BEQ to a linear DE. As the correction functions must be linearized to obtain analytical solution forms, the proposed method is an approximate approach. In the case studies, we apply this method to four different situations of water level variation (i.e., constant, sudden, linear and periodic change) resting on vertical or sloping boundaries. The results are compared against numerical results, field data and other analytical solutions, which demonstrate that the proposed method has a good accuracy and versatility over a wide range of applications.
Patané, G.; Cerri, A.; Skytt, V.; Pittaluga, S.; Biasotti, S.; Sobrero, D.; Dokken, T.; Spagnuolo, M.
2015-08-01
Digital environmental data are becoming commonplace and the amount of information they provide is huge, yet complex to process, due to the size, variety, and dynamic nature of the data captured by the available sensing devices. Making use of the data largely relies on the availability of efficient methods to extract meaningful information, and requires to process the environmental events at the speed data are acquired. This paper focuses on the evaluation of methods to approximate observed rain data, in real conditions of sparsity of the observations. The novelty stands in the selection of a particularly complex area, Liguria region, located in the north-west of Italy, where the orography and the closeness to the sea causes complex hydro-meteorological events. Approximation results are compared on a fine granularity in terms of cumulated rain interval used, gathered from two different rain gauge networks, with different characteristics and spatial distribution. Moreover, beside traditional cross-validation comparison, we provide a qualitative comparison based on the analysis of the number and location of maxima of the approximation. Rain maxima are indeed crucial features of rain fields needed for storm tracking, to support effective monitoring of meteorological events.
Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw
2015-08-18
Highlights: • The complex quantum Hamilton–Jacobi equation is approximately solved in real space. • Equations of motion are derived through use of the derivative propagation method. • Numerically unstable reflected trajectories may pass through the potential barrier. • Transmitted wave packet is obtained by propagating individual Bohmian trajectories. • Excellent transmission probabilities are obtained for both thick and thin barriers. - Abstract: The complex quantum Hamilton–Jacobi equation for the complex action is approximately solved by propagating individual Bohmian trajectories in real space. Equations of motion for the complex action and its spatial derivatives are derived through use of the derivative propagation method. We transform these equations into the arbitrary Lagrangian–Eulerian version with the grid velocity matching the flow velocity of the probability fluid. Setting higher-order derivatives equal to zero, we obtain a truncated system of equations of motion describing the rate of change in the complex action and its spatial derivatives transported along approximate Bohmian trajectories. A set of test trajectories is propagated to determine appropriate initial positions for transmitted trajectories. Computational results for transmitted wave packets and transmission probabilities are presented and analyzed for a one-dimensional Eckart barrier and a two-dimensional system involving either a thick or thin Eckart barrier along the reaction coordinate coupled to a harmonic oscillator.
Highlights: • The complex quantum Hamilton–Jacobi equation is approximately solved in real space. • Equations of motion are derived through use of the derivative propagation method. • Numerically unstable reflected trajectories may pass through the potential barrier. • Transmitted wave packet is obtained by propagating individual Bohmian trajectories. • Excellent transmission probabilities are obtained for both thick and thin barriers. - Abstract: The complex quantum Hamilton–Jacobi equation for the complex action is approximately solved by propagating individual Bohmian trajectories in real space. Equations of motion for the complex action and its spatial derivatives are derived through use of the derivative propagation method. We transform these equations into the arbitrary Lagrangian–Eulerian version with the grid velocity matching the flow velocity of the probability fluid. Setting higher-order derivatives equal to zero, we obtain a truncated system of equations of motion describing the rate of change in the complex action and its spatial derivatives transported along approximate Bohmian trajectories. A set of test trajectories is propagated to determine appropriate initial positions for transmitted trajectories. Computational results for transmitted wave packets and transmission probabilities are presented and analyzed for a one-dimensional Eckart barrier and a two-dimensional system involving either a thick or thin Eckart barrier along the reaction coordinate coupled to a harmonic oscillator
Studying approximating method and numerical computation of heat transfer of a fuel rod in PWR
Based on the differential form of the general heat conduction equation, the approximating expression for a nu clear fuel rod was derived through integral. The fuel rod has asymmetrical heat resource distribution. Bessel function distribution is in radial direction and Cosine function distribution is in axis direction. Also, using the model of the advanced pressure water reactor 600, and taking an iterative calculation between tangential and normal diffusion terms in every control cell, temperature distribution of the fuel rod was computed by the finite volume method (FVM) in the unstructured grids. Comparing the approximate solutions with the numerical results, there was a good agreement between them. On this condition, we derived the location and size of maximum temperature by analysis the temperature distribution and variation. All of these can provide a useful reference for the pressure water reactor thermal design and thermal protection of nuclear engineering. (authors)
Optimal motion planning of an underactuated spacecraft using wavelet approximate method
GE Xinsheng; CHEN Liqun; LIU Yanzhu
2006-01-01
An optimal motion planning scheme using wavelet approximation is proposed for an underactuated spacecraft. The motion planning of an underactuated spacecraft can be formulated as an optimal control of a drift-free system. A cost functional is used to incorporate the control energy and the final state errors. The motion planning is to determine control inputs to minimize the cost functional.Using the method of wavelet, one can transform an infinite-dimensional optimal control problem to a finite-dimensional one and use GaussNewton algorithm to solve it for a feasible trajectory which satisfies nonholonomic constraints. The proposed scheme has been applied to a rigid spacecraft with two momentum wheels. The numerical simulation results indicate that optimal control with wavelet approximation is an effective approach to steering an underactuated spacecraft system from the initial configuration to the final configuration.
Potential function methods for approximately solving linear programming problems theory and practice
Bienstock, Daniel
2002-01-01
Potential Function Methods For Approximately Solving Linear Programming Problems breaks new ground in linear programming theory. The book draws on the research developments in three broad areas: linear and integer programming, numerical analysis, and the computational architectures which enable speedy, high-level algorithm design. During the last ten years, a new body of research within the field of optimization research has emerged, which seeks to develop good approximation algorithms for classes of linear programming problems. This work both has roots in fundamental areas of mathematical programming and is also framed in the context of the modern theory of algorithms. The result of this work, in which Daniel Bienstock has been very much involved, has been a family of algorithms with solid theoretical foundations and with growing experimental success. This book will examine these algorithms, starting with some of the very earliest examples, and through the latest theoretical and computational developments.
The matrix variational Pade approximant and its generalization to elastic wave scattering are discussed. Predictions of the method for the scattering of a longitudinal plane wave are compared with the exact scattering from spherical voids and inclusions. Its predictions are also compared to those of the first four partial sums of the Born Series for the scattered amplitude. Generally, the fourth partial sum and the variational results compare poorly with the exact results for ka less than or equal to 2 if the scatterer is strong, but compare well for ka less than or equal to 10 if the scatterer strength is at best modest. The breakdown of the favorable comparison is traced to the divergence of the Born Series for strong scatterers. It is also demonstrated that by use of the N-point Pade approximant a good comparison with exact results can be obtained for all scatterer strengths
The Wentzel-Kramers-Brillouin approximation method applied to the Wigner function
Tosiek, J.; Cordero, R.; Turrubiates, F. J.
2016-06-01
An adaptation of the Wentzel-Kramers-Brilluoin method in the deformation quantization formalism is presented with the aim to obtain an approximate technique of solving the eigenvalue problem for energy in the phase space quantum approach. A relationship between the phase σ ( r →) of a wave function exp (" separators=" /i ħ σ ( r →)) and its respective Wigner function is derived. Formulas to calculate the Wigner function of a product and of a superposition of wave functions are proposed. Properties of a Wigner function of interfering states are also investigated. Examples of this quasi-classical approximation in deformation quantization are analysed. A strict form of the Wigner function for states represented by tempered generalised functions has been derived. Wigner functions of unbound states in the Poeschl-Teller potential have been found.
Rossi, Mariana; Paesani, Francesco; Bowman, Joel; Ceriotti, Michele
2014-01-01
Including quantum mechanical effects on the dynamics of nuclei in the condensed phase is challenging, because the complexity of exact methods grows exponentially with the number of quantum degrees of freedom. Efforts to circumvent these limitations can be traced down to two approaches: methods that treat a small subset of the degrees of freedom with rigorous quantum mechanics, considering the rest of the system as a static or classical environment, and methods that treat the whole system quantum mechanically, but using approximate dynamics. Here we perform a systematic comparison between these two philosophies for the description of quantum effects in vibrational spectroscopy, taking the Embedded Local Monomer (LMon) model and a mixed quantum-classical (MQC) model as representatives of the first family of methods, and centroid molecular dynamics (CMD) and thermostatted ring polymer molecular dynamics (TRPMD) as examples of the latter. We use as benchmarks D$_2$O doped with HOD and pure H$_2$O at three distinc...
A novel approximation method of CTF amplitude correction for 3D single particle reconstruction
The typical resolution of three-dimensional reconstruction by cryo-EM single particle analysis is now being pushed up to and beyond the nanometer scale. Correction of the contrast transfer function (CTF) of electron microscopic images is essential for achieving such a high resolution. Various correction methods exist and are employed in popular reconstruction software packages. Here, we present a novel approximation method that corrects the amplitude modulation introduced by the contrast transfer function by convoluting the images with a piecewise continuous function. Our new approach can easily be implemented and incorporated into other packages. The implemented method yielded higher resolution reconstructions with data sets from both highly symmetric and asymmetric structures. It is an efficient alternative correction method that allows quick convergence of the 3D reconstruction and has a high tolerance for noisy images, thus easing a bottleneck in practical reconstruction of macromolecules.
Domain decomposition methods for systems of conservation laws: Spectral collocation approximations
Quarteroni, Alfio
1989-01-01
Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.
Wu, Fuke; Tian, Tianhai; Rawlings, James B; Yin, George
2016-05-01
The frequently used reduction technique is based on the chemical master equation for stochastic chemical kinetics with two-time scales, which yields the modified stochastic simulation algorithm (SSA). For the chemical reaction processes involving a large number of molecular species and reactions, the collection of slow reactions may still include a large number of molecular species and reactions. Consequently, the SSA is still computationally expensive. Because the chemical Langevin equations (CLEs) can effectively work for a large number of molecular species and reactions, this paper develops a reduction method based on the CLE by the stochastic averaging principle developed in the work of Khasminskii and Yin [SIAM J. Appl. Math. 56, 1766-1793 (1996); ibid. 56, 1794-1819 (1996)] to average out the fast-reacting variables. This reduction method leads to a limit averaging system, which is an approximation of the slow reactions. Because in the stochastic chemical kinetics, the CLE is seen as the approximation of the SSA, the limit averaging system can be treated as the approximation of the slow reactions. As an application, we examine the reduction of computation complexity for the gene regulatory networks with two-time scales driven by intrinsic noise. For linear and nonlinear protein production functions, the simulations show that the sample average (expectation) of the limit averaging system is close to that of the slow-reaction process based on the SSA. It demonstrates that the limit averaging system is an efficient approximation of the slow-reaction process in the sense of the weak convergence. PMID:27155630
In order to investigate some aspects of the 'Intermediate Resonance Approximation' developed by Goldstein and Cohen, comparative calculations have been made using this method together with more accurate methods. The latter are as follows: a) For homogeneous materials the slowing down equation is solved in the fundamental mode approximation with the computer programme SPENG. All cross sections are given point by point. Because the spectrum can be calculated for at most 2000 energy points, the energy regions where the resonances are accurately described are limited. Isolated resonances in the region 100 to 240 eV are studied for 238U/Fe and 238U/Fe/Na mixtures. In the regions 161 to 251 eV and 701 to 1000 eV, mixtures of 238U and Na are investigated. 239Pu/Na and 239Pu/238U/Na mixtures are studied in the region 161 to 251 eV. b) For heterogeneous compositions in slab geometry the integral transport equation is solved using the FLIS programme in 22 energy groups. Thus, only one resonance can be considered in each calculation. Two resonances are considered, namely those belonging to 238U at 190 and 937 eV. The compositions are lattices of 238U and Fe plates. The computer programme DORIX is used for the calculations using the Intermediate Resonance Approximation. Calculations of reaction rates and effective cross sections are made at 0, 300 and 1100 deg K for homogeneous media and at 300 deg K for heterogeneous media. The results are compared to those obtained by using the programmes SPENG and FLIS and using the narrow resonance approximation
Approximate-model Based Estimation Method for Dynamic Response of Forging Processes
LEI Jie; LU Xinjiang; LI Yibo; HUANG Minghui; ZOU Wei
2015-01-01
Many high-quality forging productions require the large-sized hydraulic press machine (HPM) to have a desirable dynamic response. Since the forging process is complex under the low velocity, its response is difficult to estimate. And this often causes the desirable low-velocity forging condition difficult to obtaln. So far little work has been found to estimate the dynamic response of the forging process under low velocity. In this paper, an approximate-model based estimation method is proposed to estimate the dynamic response of the forging process under low velocity. First, an approximate model is developed to represent the forging process of this complex HPM around the low-velocity working point. Under guaranteeing the modeling performance, the model may greatly ease the complexity of the subsequent estimation of the dynamic response because it has a good linear structure. On this basis, the dynamic response is estimated and the conditions for stability, vibration, and creep are derived according to the solution of the velocity. All these analytical results are further verified by both simulations and experiment. In the simulation verification for modeling, the original movement model and the derived approximate model always have the same dynamic responses with very small approximate error. The simulations and experiment finally demonstrate and test the effectiveness of the derived conditions for stability, vibration, and creep, and these conditions will benefit both the prediction of the dynamic response of the forging process and the design of the controller for the high-quality forging. The proposed method is an effective solution to achieve the desirable low-velocity forging condition.
Marušić, Mirko; Sliško, Josip
2012-01-01
The Lawson Classroom Test of Scientific Reasoning (LCTSR) was used to gauge the relative effectiveness of three different methods of pedagogy, Reading, Presenting, and Questioning (RPQ), Experimenting and Discussion (ED), and Traditional Methods (TM), on increasing students' level of scientific thinking. The data of a one-semester-long senior high-school project indicate that, for the LCTSR: (a) the RPQ group (n = 91) achieved effect-sizes d = 0.30 and (b) the ED group (n = 85) attained effect-sizes d = 0.64. These methods have shown that the Piagetian and Vygotskian visions on learning and teaching can go hand in hand and as such achieve respectable results. To do so, it is important to challenge the students and thus encourage the shift towards higher levels of reasoning. This aim is facilitated through class management which recognizes the importance of collaborative learning. Carrying out Vygotsky's original intention to use teaching to promote cognitive development as well as subject concepts, this research has shown that it is better to have students experience cognitive conflict from directly observed experiments than by reflecting on reported experience from popularization papers or writings found on the internet.