Advanced Concepts and Methods of Approximate Reasoning
1989-12-01
and L. Valverde. On mode and implication in approximate reasoning. In M.M. Gupta, A. Kandel, W. Bandler , J.B. Kiszka, editors, Approximate Reasoning and...190, 1981. [43] E. Trillas and L. Valverde. On mode and implication in approximate reasoning. In M.M. Gupta, A. Kandel, W. Bandler , J.B. Kiszka
Approximate Qualitative Temporal Reasoning
2001-01-01
Bettini, X. Wang, and S. Jajodia. A general framework for time granularity and its application to temporal reasoning. Annals of Mathematics and Artificial...Temporal representation and reasoning in artificial intelligence: Issues and approaches. Annals of Mathematics and Artificial Intelligence, 28, 2000...Quantum mereotopology. Annals of Mathematics and Artificial Intelli- gence, to appear. [42] A. C. Varzi. On the boundary between mereology and topology
Mathematical algorithms for approximate reasoning
Murphy, John H.; Chay, Seung C.; Downs, Mary M.
1988-01-01
Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away
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
Energy Technology Data Exchange (ETDEWEB)
Eisenhawer, S.W.; Bott, T.F.; Smith, R.E.
1998-07-01
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
Energy Technology Data Exchange (ETDEWEB)
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).
Advanced Methods of Approximate Reasoning
1990-11-30
Kyburg, Maria Teresa Lamata, Abe Mamdani, Serafin Moral, Henri Prade. Alessandro Saffiot ti. Glen Shafer, Prakash Shenoy, Philippe Smetb,3 Marcus...Dubois, Francesc Esteva, Oscar Firchein, Marty Fischler, Pascal Fua, Maria Angeles Gil, Luis Godo, Andy Hanson, Jerry Hobbs, David Israel, Joan Jacas, Yvan...Inf. Control, 38:154-169, 1978. [18] L.I. Godo, R. L6pez de Mintaras, C. Sierra , A. Verdaguer. Maiaging linguistically expressed uncertainty in MILORD
A comparison of approximate reasoning results using information uncertainty
Energy Technology Data Exchange (ETDEWEB)
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.
Credibility Discounting in the Theory of Approximate Reasoning
Yager, Ronald R.
2013-01-01
We are concerned with the problem of introducing credibility type information into reasoning systems. The concept of credibility allows us to discount information provided by agents. An important characteristic of this kind of procedure is that a complete lack of credibility rather than resulting in the negation of the information provided results in the nullification of the information provided. We suggest a representational scheme for credibility qualification in the theory of approximate r...
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.
System reliability assessment with an approximate reasoning model
Energy Technology Data Exchange (ETDEWEB)
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.
On the integration of reinforcement learning and approximate reasoning for control
Berenji, Hamid R.
1991-01-01
The author discusses the importance of strengthening the knowledge representation characteristic of reinforcement learning techniques using methods such as approximate reasoning. The ARIC (approximate reasoning-based intelligent control) architecture is an example of such a hybrid approach in which the fuzzy control rules are modified (fine-tuned) using reinforcement learning. ARIC also demonstrates that it is possible to start with an approximately correct control knowledge base and learn to refine this knowledge through further experience. On the other hand, techniques such as the TD (temporal difference) algorithm and Q-learning establish stronger theoretical foundations for their use in adaptive control and also in stability analysis of hybrid reinforcement learning and approximate reasoning-based controllers.
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
Energy Technology Data Exchange (ETDEWEB)
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.
Information processing systems, reasoning modules, and reasoning system design methods
Energy Technology Data Exchange (ETDEWEB)
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.
Evaluation of high-level waste pretreatment processes with an approximate reasoning model
Energy Technology Data Exchange (ETDEWEB)
Bott, T.F.; Eisenhawer, S.W.; Agnew, S.F.
1999-04-01
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 New Method for Reasoning about Action
Institute of Scientific and Technical Information of China (English)
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
DEFF Research Database (Denmark)
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...... 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......’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....
Scientific Facts and Methods in Public Reason
DEFF Research Database (Denmark)
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...... 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 ‘non-controversial’ and more importantly, we are left without a justification for a stricture which excludes certain controversial beliefs and methods of inquiry from the realm of political justification. In this article, we offer what we deem to be the most plausible interpretation of Rawls...
Approximation methods in gravitational-radiation theory
Will, C. M.
1986-02-01
The observation of gravitational-radiation damping in the binary pulsar PSR 1913+16 and the ongoing experimental search for gravitational waves of extraterrestrial origin have made the theory of gravitational radiation an active branch of classical general relativity. In calculations of gravitational radiation, approximation methods play a crucial role. The author summarizes recent developments in two areas in which approximations are important: (1) the quadrupole approximation, which determines the energy flux and the radiation reaction forces in weak-field, slow-motion, source-within-the-near-zone systems such as the binary pulsar; and (2) the normal modes of oscillation of black holes, where the Wentzel-Kramers-Brillouin approximation gives accurate estimates of the complex frequencies of the modes.
Approximations in the PE-method
DEFF Research Database (Denmark)
Arranz, Marta Galindo
1996-01-01
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...
Generalized If ... Then...Else Inference Rules with Linguistic Modifiers for Approximate Reasoning
Directory of Open Access Journals (Sweden)
Le Anh Phuong
2012-11-01
Full Text Available 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.
On the approximate zero of Newton method
Institute of Scientific and Technical Information of China (English)
黄正达
2003-01-01
A judgment criterion to guarantee a point to be a Chen' s approximate zero of Newton method for solving nonlinear equation is sought by dominating sequence techniques. The criterion is based on the fact that the dominating function may have only one simple positive zero, assuming that the operator is weak Lipschitz continuous, which is much more relaxed and can be checked much more easily than Lipschitz continuous in practice. It is demonstrated that a Chen' s approximate zero may not be a Smale' s approximate zero. The error estimate obtained indicated the convergent order when we use |f(x) | < ε to stop computation in software.The result can also be applied for solving partial derivative and integration equations.
On the approximate zero of Newton method
Institute of Scientific and Technical Information of China (English)
黄正达
2003-01-01
A judgment criterion to guarantee a point to be a Chen's approximate zero of Newton method for solving nonlinear equation is sought by dominating sequence techniques. The criterion is based on the fact that the dominating function may have only one simple positive zero, assuming that the operator is weak Lipschitz continuous, which is much more relaxed and can be checked much more easily than Lipschitz continuous in practice. It is demonstrated that a Chen's approximate zero may not be a Smale's approximate zero. The error estimate obtained indicated the convergent order when we use |f(x)|<ε to stop computation in software. The result can also be applied for solving partial derivative and integration equations.
Energy Technology Data Exchange (ETDEWEB)
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.
Second derivatives for approximate spin projection methods.
Thompson, Lee M; Hratchian, Hrant P
2015-02-07
The use of broken-symmetry electronic structure methods is required in order to obtain correct behavior of electronically strained open-shell systems, such as transition states, biradicals, and transition metals. This approach often has issues with spin contamination, which can lead to significant errors in predicted energies, geometries, and properties. Approximate projection schemes are able to correct for spin contamination and can often yield improved results. To fully make use of these methods and to carry out exploration of the potential energy surface, it is desirable to develop an efficient second energy derivative theory. In this paper, we formulate the analytical second derivatives for the Yamaguchi approximate projection scheme, building on recent work that has yielded an efficient implementation of the analytical first derivatives.
Variational Bayesian Approximation methods for inverse problems
Mohammad-Djafari, Ali
2012-09-01
Variational Bayesian Approximation (VBA) methods are recent tools for effective Bayesian computations. In this paper, these tools are used for inverse problems where the prior models include hidden variables and where where the estimation of the hyper parameters has also to be addressed. In particular two specific prior models (Student-t and mixture of Gaussian models) are considered and details of the algorithms are given.
Approximate Methods for State-Space Models
Koyama, Shinsuke; Shalizi, Cosma Rohilla; Kass, Robert E; 10.1198/jasa.2009.tm08326
2010-01-01
State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and computing this expectation is hard when there are nonlinearities. Existing filtering methods, including sequential Monte Carlo, tend to be either inaccurate or slow. In this paper, we study a nonlinear filter for nonlinear/non-Gaussian state-space models, which uses Laplace's method, an asymptotic series expansion, to approximate the state's conditional mean and variance, together with a Gaussian conditional distribution. This {\\em Laplace-Gaussian filter} (LGF) gives fast, recursive, deterministic state estimates, with an error which is set by the stochastic characteristics of the model and is, we show, stable over time. We illustrate the estimation ability of the LGF by applying it to the problem of neural decoding and compare it to sequential Monte Carlo both in simulat...
Reverse triple I method of fuzzy reasoning
Institute of Scientific and Technical Information of China (English)
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.
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.
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.
Approximate reasoning-based learning and control for proximity operations and docking in space
Berenji, Hamid R.; Jani, Yashvant; Lea, Robert N.
1991-01-01
A recently proposed hybrid-neutral-network and fuzzy-logic-control architecture is applied to a fuzzy logic controller developed for attitude control of the Space Shuttle. A model using reinforcement learning and learning from past experience for fine-tuning its knowledge base is proposed. Two main components of this approximate reasoning-based intelligent control (ARIC) model - an action-state evaluation network and action selection network are described as well as the Space Shuttle attitude controller. An ARIC model for the controller is presented, and it is noted that the input layer in each network includes three nodes representing the angle error, angle error rate, and bias node. Preliminary results indicate that the controller can hold the pitch rate within its desired deadband and starts to use the jets at about 500 sec in the run.
Energy Technology Data Exchange (ETDEWEB)
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.
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
Prioritizing the purchase of spare parts using an approximate reasoning models.
Energy Technology Data Exchange (ETDEWEB)
Eisenhawer, S. W. (Stephen W.); Bott, T. F. (Terrence F.); Jackson, J. W. (Joseph W.)
2001-01-01
The complexity of a spare parts prioritization model should be consonant with the amount and quality of data available to populate it. When production processes are new and the reliability database is sparse and represents primarily expert knowledge, an approximate reasoning (AR) based model is appropriate. AR models are designed to emulate the inferential processes used by experts in making judgments. We have designed and tested such a model for the planned component production process for nuclear weapons at Los Alamos National Laboratory. The model successfully represents the experts knowledge concerning the frequency and consequences of a part failure. The use of linguistic variables provides an adaptable format for eliciting this knowledge and providing a consistent brisis for valuing the effect on production of different parts. Ranking the parts for inclusion in a spare parts inventory is a straightforward transformation of the AR output. The basis for this ranking is directly traceable to the elicitation results. AR-based models are well-suited to prioritization problems with these characteristics.
Approximate methods for derivation of covariance data
Energy Technology Data Exchange (ETDEWEB)
Tagesen, S. [Vienna Univ. (Austria). Inst. fuer Radiumforschung und Kernphysik; Larson, D.C. [Oak Ridge National Lab., TN (United States)
1992-12-31
Several approaches for the derivation of covariance information for evaluated nuclear data files (EFF2 and ENDF/B-VI) have been developed and used at IRK and ORNL respectively. Considerations, governing the choice of a distinct method depending on the quantity and quality of available data are presented, advantages/disadvantages are discussed and examples of results are given.
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…
A new approximation method for stress constraints in structural synthesis
Vanderplaats, Garret N.; Salajegheh, Eysa
1987-01-01
A new approximation method for dealing with stress constraints in structural synthesis is presented. The finite element nodal forces are approximated and these are used to create an explicit, but often nonlinear, approximation to the original problem. The principal motivation is to create the best approximation possible, in order to reduce the number of detailed finite element analyses needed to reach the optimum. Examples are offered and compared with published results, to demonstrate the efficiency and reliability of the proposed method.
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...
Institute of Scientific and Technical Information of China (English)
Zhang Zheng-Jie; Wang Ke-Lin; Qin Gan
2005-01-01
By a model of atwo-level particle coupled with boson field, we made it clear that an evolution problem can be solved beyond the rotating wave approximation. We have applied the coherent approximation method, which had been proved to be effective in dealing with stationary state problems of polaron, to the evolution problem of the system mentioned above. The results obtained showed that the coherent approximation method is effective to treat the evolution problem,and, in general cases, the non-rotating wave terms in Hamiltonian should not be ignored. Our results may provide a deep physical insight for further experiments to test the effects of non-rotating wave terms.
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.
Institute of Scientific and Technical Information of China (English)
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.
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
Energy Technology Data Exchange (ETDEWEB)
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
Directory of Open Access Journals (Sweden)
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 Approximation Method of NURBS Curves in NC Machining
Institute of Scientific and Technical Information of China (English)
YUE Ying; HAN Qingyao; WANG Zhangqi
2006-01-01
An algorithm for approximating arbitrary NURBS curve with straight line is presented. Firstly, NURBS curve is acquired according to data points on the curve. Secondly, Approximating arbitrary NURBS curve is based on dichotomy. The resulting straight line approaches to the original curve with relatively fewer segments within the required tolerance. The example shows that the algorithm is simple and its approximation precision is high. The method is most useful in numerical control to drive the cutter along straight line or circular paths.
Calculating resonance positions and widths using the Siegert approximation method
Rapedius, Kevin
2011-01-01
Here we present complex resonance states (or Siegert states), that describe the tunneling decay of a trapped quantum particle, from an intuitive point of view which naturally leads to the easily applicable Siegert approximation method that can be used for analytical and numerical calculations of complex resonances of both the linear and nonlinear Schr\\"odinger equation. Our approach thus complements other treatments of the subject that mostly focus on methods based on continuation in the complex plane or on semiclassical approximations.
An approximate method to acoustic radiation problems: element radiation superposition method
Institute of Scientific and Technical Information of China (English)
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.
A Semantic Retrieval Method Based on the Fuzzy Reasoning
Institute of Scientific and Technical Information of China (English)
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.
Improved stochastic approximation methods for discretized parabolic partial differential equations
Guiaş, Flavius
2016-12-01
We present improvements of the stochastic direct simulation method, a known numerical scheme based on Markov jump processes which is used for approximating solutions of ordinary differential equations. This scheme is suited especially for spatial discretizations of evolution partial differential equations (PDEs). By exploiting the full path simulation of the stochastic method, we use this first approximation as a predictor and construct improved approximations by Picard iterations, Runge-Kutta steps, or a combination. This has as consequence an increased order of convergence. We illustrate the features of the improved method at a standard benchmark problem, a reaction-diffusion equation modeling a combustion process in one space dimension (1D) and two space dimensions (2D).
Triple I method and interval valued fuzzy reasoning
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The aims of this paper are: (i) to show that the CRI method should be improved and remould into the triple I method, (ii) to propose a new type of fuzzy reasoning with multiple rules of which the premise of each rule is an interval valued fuzzy subset, (iii) to establish the "fire one or leave (FOOL)" principle as pretreatment for solving the fuzzy reasoning problem mentioned in (ii), and (iv) to solve the problem mentioned in (ii).
Triple I method and interval valued fuzzy reasoning
Institute of Scientific and Technical Information of China (English)
王国俊
2000-01-01
The aims of this paper are.- (i) to show that the CRI method should be improved and remould into the triple I method, (ii) to propose a new type of fuzzy reasoning with multiple rules of which the premise of each rule is an interval valued fuzzy subset, (iii) to establish the "fire one or leave (FOOL)" principle as pretreatment for solving the fuzzy reasoning problem mentioned in (ii), and (iv) to solve the problem mentioned in (ii).
A working-set framework for sequential convex approximation methods
DEFF Research Database (Denmark)
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...
Multi-level methods and approximating distribution functions
Wilson, D.; Baker, R. E.
2016-07-01
Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie's direct method. These algorithms often come with high computational costs, therefore approximate stochastic simulation algorithms such as the tau-leap method are used. However, in order to minimise the bias in the estimates generated using them, a relatively small value of tau is needed, rendering the computational costs comparable to Gillespie's direct method. The multi-level Monte Carlo method (Anderson and Higham, Multiscale Model. Simul. 10:146-179, 2012) provides a reduction in computational costs whilst minimising or even eliminating the bias in the estimates of system statistics. This is achieved by first crudely approximating required statistics with many sample paths of low accuracy. Then correction terms are added until a required level of accuracy is reached. Recent literature has primarily focussed on implementing the multi-level method efficiently to estimate a single system statistic. However, it is clearly also of interest to be able to approximate entire probability distributions of species counts. We present two novel methods that combine known techniques for distribution reconstruction with the multi-level method. We demonstrate the potential of our methods using a number of examples.
Using Propensity Score Methods to Approximate Factorial Experimental Designs
Dong, Nianbo
2011-01-01
The purpose of this study is through Monte Carlo simulation to compare several propensity score methods in approximating factorial experimental design and identify best approaches in reducing bias and mean square error of parameter estimates of the main and interaction effects of two factors. Previous studies focused more on unbiased estimates of…
Approximating methods for intractable probabilistic models: Applications in neuroscience
DEFF Research Database (Denmark)
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...
Calculating Resonance Positions and Widths Using the Siegert Approximation Method
Rapedius, Kevin
2011-01-01
Here, we present complex resonance states (or Siegert states) that describe the tunnelling decay of a trapped quantum particle from an intuitive point of view that naturally leads to the easily applicable Siegert approximation method. This can be used for analytical and numerical calculations of complex resonances of both the linear and nonlinear…
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.
Approximation methods for the partition functions of anharmonic systems
Energy Technology Data Exchange (ETDEWEB)
Lew, P.; Ishida, T.
1979-07-01
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.
Epistemological Development and Judgments and Reasoning about Teaching Methods
Spence, Sarah; Helwig, Charles C.
2013-01-01
Children's, adolescents', and adults' (N = 96 7-8, 10-11, and 13-14-year-olds and university students) epistemological development and its relation to judgments and reasoning about teaching methods was examined. The domain (scientific or moral), nature of the topic (controversial or noncontroversial), and teaching method (direct…
Epistemological Development and Judgments and Reasoning about Teaching Methods
Spence, Sarah; Helwig, Charles C.
2013-01-01
Children's, adolescents', and adults' (N = 96 7-8, 10-11, and 13-14-year-olds and university students) epistemological development and its relation to judgments and reasoning about teaching methods was examined. The domain (scientific or moral), nature of the topic (controversial or noncontroversial), and teaching method (direct instruction by…
Parallel iterative solvers and preconditioners using approximate hierarchical methods
Energy Technology Data Exchange (ETDEWEB)
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.
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.
Novel determination of differential-equation solutions: universal approximation method
Leephakpreeda, Thananchai
2002-09-01
In a conventional approach to numerical computation, finite difference and finite element methods are usually implemented to determine the solution of a set of differential equations (DEs). This paper presents a novel approach to solve DEs by applying the universal approximation method through an artificial intelligence utility in a simple way. In this proposed method, neural network model (NNM) and fuzzy linguistic model (FLM) are applied as universal approximators for any nonlinear continuous functions. With this outstanding capability, the solutions of DEs can be approximated by the appropriate NNM or FLM within an arbitrary accuracy. The adjustable parameters of such NNM and FLM are determined by implementing the optimization algorithm. This systematic search yields sub-optimal adjustable parameters of NNM and FLM with the satisfactory conditions and with the minimum residual errors of the governing equations subject to the constraints of boundary conditions of DEs. The simulation results are investigated for the viability of efficiently determining the solutions of the ordinary and partial nonlinear DEs.
A multiscale two-point flux-approximation method
Møyner, Olav; Lie, Knut-Andreas
2014-10-01
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
Simple Methods to Approximate CPC Shape to Preserve Collection Efficiency
Directory of Open Access Journals (Sweden)
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.
On the construction of a new solvable model and validity of many-body approximation methods
Zettili, Nouredine; Villars, Felix M. H.
1987-07-01
This work deals both with the construction of a new analytically solvable model and with the quantitative test of the time-dependent Hartree-Fock (TDHF) method. First, we construct a new analytically solvable model, which serves as a testing ground for the various many-body approximation methods. The construction is based on two vector operators that are the generators of a Lie algebra. The model consists of a one-dimensional system of two distinguishable sets of fermions interacting via a schematic two-body force. The model has a simple analytic energy spectrum. Second, we use this model to test the validity of the TDHF approximation. Exact eigenvalues are compared with the corresponding solutions of the TDHF method. The TDHF approximation is shown to be reasonably accurate in the description of the system's eigenstates.
On the construction of a new solvable model and validity of many-body approximation methods
Energy Technology Data Exchange (ETDEWEB)
Zettili, N.; Villars, F.M.H.
1987-07-20
This work deals both with the construction of a new analytically solvable model and with the quantitative test of the time-dependent Hartree-Fock (TDHF) method. First, we construct a new analytically solvable model, which serves as a testing ground for the various many-body approximation methods. The construction is based on two vector operators that are the generators of a Lie algebra. The model consists of a one-dimensional system of two distinguishable sets of fermions interacting via a schematic two-body force. The model has a simple analytic energy spectrum. Second, we use this model to test the validity of the TDHF approximation. Exact eigenvalues are compared with the corresponding solutions of the TDHF method. The TDHF approximation is shown to be reasonably accurate in the description of the system's eigenstates.
Multiuser detection and channel estimation: Exact and approximate methods
DEFF Research Database (Denmark)
Fabricius, Thomas
2003-01-01
. We also derive optimal detectors when nuisance parameters such as the channel and noise level are unknown, and show how well the proposed methods fit into this framework via the Generalised Expectation Maximisation algorithm. Our numerical evaluation show that naive mean field annealing and adaptive...... order Plefka expansion, adaptive TAP, and large system limit self-averaging behaviours, and a method based on Kikuchi and Bethe free energy approximations, which we denote the Generalised Graph Expansion. Since all these methods are improvements of the naive mean field approach we make a thorough...... analysis of the convexity and bifurcations of the naive mean field free energy and optima. This proves that we can avoid local minima by tracking a global convex solution into the non-convex region, effectively avoiding error propagation. This method is in statistical physics denoted mean field annealing...
Network Forensics Method Based on Evidence Graph and Vulnerability Reasoning
Directory of Open Access Journals (Sweden)
Jingsha He
2016-11-01
Full Text Available As the Internet becomes larger in scale, more complex in structure and more diversified in traffic, the number of crimes that utilize computer technologies is also increasing at a phenomenal rate. To react to the increasing number of computer crimes, the field of computer and network forensics has emerged. The general purpose of network forensics is to find malicious users or activities by gathering and dissecting firm evidences about computer crimes, e.g., hacking. However, due to the large volume of Internet traffic, not all the traffic captured and analyzed is valuable for investigation or confirmation. After analyzing some existing network forensics methods to identify common shortcomings, we propose in this paper a new network forensics method that uses a combination of network vulnerability and network evidence graph. In our proposed method, we use vulnerability evidence and reasoning algorithm to reconstruct attack scenarios and then backtrack the network packets to find the original evidences. Our proposed method can reconstruct attack scenarios effectively and then identify multi-staged attacks through evidential reasoning. Results of experiments show that the evidence graph constructed using our method is more complete and credible while possessing the reasoning capability.
Approximate design calculation methods for radiation streaming in shield irregularities
Energy Technology Data Exchange (ETDEWEB)
Miura, Toshimasa; Hirao, Yoshihiro [Ship Research Inst., Mitaka, Tokyo (Japan); Yoritsune, Tsutomu
1997-10-01
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)
An improved multidisciplinary feasible method using DACE approximation approach
Institute of Scientific and Technical Information of China (English)
Su Zijian; Xiao Renbin; Zhong Yifang
2005-01-01
Multidisciplinary feasible method (MDF) is conventional method to multidisciplinary optimization (MDO) and well-understood by users. It reduces the dimensions of the multidisciplinary optimization problem by using the design variables as independent optimization variables. However, at each iteration of the conventional optimization procedure,multidisciplinary analysis (MDA) is numerously performed that results in extreme expense and low optimization efficiency. The intrinsic weakness of MDF is due to the times that it loop fixed-point iterations in MDA, which drive us to improve MDF by building inexpensive approximations as surrogates for expensive MDA. An simple example is presented to demonstrate the usefulness of the improved MDF. Results show that a significant reduction in the number of multidisciplinary analysis required for optimization is obtained as compared with original MDF and the efficiency of optimization is increased.
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...
Discrete Dipole Approximation Aided Design Method for Nanostructure Arrays
Institute of Scientific and Technical Information of China (English)
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.
Approximation method to compute domain related integrals in structural studies
Oanta, E.; Panait, C.; Raicu, A.; Barhalescu, M.; Axinte, T.
2015-11-01
Various engineering calculi use integral calculus in theoretical models, i.e. analytical and numerical models. For usual problems, integrals have mathematical exact solutions. If the domain of integration is complicated, there may be used several methods to calculate the integral. The first idea is to divide the domain in smaller sub-domains for which there are direct calculus relations, i.e. in strength of materials the bending moment may be computed in some discrete points using the graphical integration of the shear force diagram, which usually has a simple shape. Another example is in mathematics, where the surface of a subgraph may be approximated by a set of rectangles or trapezoids used to calculate the definite integral. The goal of the work is to introduce our studies about the calculus of the integrals in the transverse section domains, computer aided solutions and a generalizing method. The aim of our research is to create general computer based methods to execute the calculi in structural studies. Thus, we define a Boolean algebra which operates with ‘simple’ shape domains. This algebraic standpoint uses addition and subtraction, conditioned by the sign of every ‘simple’ shape (-1 for the shapes to be subtracted). By ‘simple’ shape or ‘basic’ shape we define either shapes for which there are direct calculus relations, or domains for which their frontiers are approximated by known functions and the according calculus is carried out using an algorithm. The ‘basic’ shapes are linked to the calculus of the most significant stresses in the section, refined aspect which needs special attention. Starting from this idea, in the libraries of ‘basic’ shapes, there were included rectangles, ellipses and domains whose frontiers are approximated by spline functions. The domain triangularization methods suggested that another ‘basic’ shape to be considered is the triangle. The subsequent phase was to deduce the exact relations for the
A study on degree of approximation by Karamata summability method
Directory of Open Access Journals (Sweden)
Nigam Hare
2011-01-01
Full Text Available Abstract Vuĉkoviĉ [Maths. Zeitchr. 89, 192 (1965] and Kathal [Riv. Math. Univ. Parma, Italy 10, 33-38 (1969] have studied summability of Fourier series by Karamata (K λ summability method. In present paper, for the first time, we study the degree of approximation of function f ∈ Lip (α,r and f ∈ W(L r ,ξ(t by K λ-summability means of its Fourier series and conjugate of function f ̃ ∈ Lip ( α , r and f ̃ ∈ W ( L r , ξ ( t by K λ-summability means of its conjugate Fourier series and establish four quite new theorems. MSC: primary 42B05; 42B08; 42A42; 42A30; 42A50.
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.
Efficient Method to Approximately Solve Retrial Systems with Impatience
Directory of Open Access Journals (Sweden)
Jose Manuel Gimenez-Guzman
2012-01-01
Full Text Available We present a novel technique to solve multiserver retrial systems with impatience. Unfortunately these systems do not present an exact analytic solution, so it is mandatory to resort to approximate techniques. This novel technique does not rely on the numerical solution of the steady-state Kolmogorov equations of the Continuous Time Markov Chain as it is common for this kind of systems but it considers the system in its Markov Decision Process setting. This technique, known as value extrapolation, truncates the infinite state space using a polynomial extrapolation method to approach the states outside the truncated state space. A numerical evaluation is carried out to evaluate this technique and to compare its performance with previous techniques. The obtained results show that value extrapolation greatly outperforms the previous approaches appeared in the literature not only in terms of accuracy but also in terms of computational cost.
Decoherence of Entangled States Calculated by a Systematic Approximate Method
Institute of Scientific and Technical Information of China (English)
LIU Tao; FAN Yun-Xia; HUANG Shu-Weng; WANG Ke-Lin; WANG Yi
2007-01-01
In this paper the coherent-state approximation (CA) method is used to deal with the problem of the decoherence of the entangled states of two two-state systems. As the base of the discussion, the dissipation of one two-state system has been investigated at first. The improved results calculated by CA are given in the paper. It is shown that the right approaching behavior and scaling law have been obtained when CA is applied to the problem of dissipation of two two-state systems coupled with environment. The whole evolution process and calculated results of the decoherence of the entangled states show also the scaling law, right approaching behavior, and rich phenomenon.
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
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. ...
Indian Academy of Sciences (India)
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
Institute of Scientific and Technical Information of China (English)
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
Institute of Scientific and Technical Information of China (English)
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.
Epistemological development and judgments and reasoning about teaching methods.
Spence, Sarah; Helwig, Charles C
2013-01-01
Children's, adolescents', and adults' (N = 96 7-8, 10-11, and 13-14-year-olds and university students) epistemological development and its relation to judgments and reasoning about teaching methods was examined. The domain (scientific or moral), nature of the topic (controversial or noncontroversial), and teaching method (direct instruction by lectures versus class discussions) were systematically varied. Epistemological development was assessed in the aesthetics, values, and physical truth domains. All participants took the domain, nature of the topic, and teaching method into consideration in ways that showed age-related variations. Epistemological development in the value domain alone was predictive of preferences for class discussions and a critical perspective on teacher-centered direct instruction, even when age was controlled in the analysis.
Approximate Bayesian methods for kernel-based object tracking
Zivkovic, Z.; Cemgil, A.T.; Kröse, B.
2009-01-01
A framework for real-time tracking of complex non-rigid objects is presented. The object shape is approximated by an ellipse and its appearance by histogram based features derived from local image properties. An efficient search procedure is used to find the image region with a histogram most simila
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…
Viscosity Approximation Methods for Two Accretive Operators in Banach Spaces
Directory of Open Access Journals (Sweden)
Jun-Min Chen
2013-01-01
Full Text Available We introduced a viscosity iterative scheme for approximating the common zero of two accretive operators in a strictly convex Banach space which has a uniformly Gâteaux differentiable norm. Some strong convergence theorems are proved, which improve and extend the results of Ceng et al. (2009 and some others.
Portable Rule Extraction Method for Neural Network Decisions Reasoning
Directory of Open Access Journals (Sweden)
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.
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.
Structured matrix based methods for approximate polynomial GCD
Boito, Paola
2011-01-01
Defining and computing a greatest common divisor of two polynomials with inexact coefficients is a classical problem in symbolic-numeric computation. The first part of this book reviews the main results that have been proposed so far in the literature. As usual with polynomial computations, the polynomial GCD problem can be expressed in matrix form: the second part of the book focuses on this point of view and analyses the structure of the relevant matrices, such as Toeplitz, Toepliz-block and displacement structures. New algorithms for the computation of approximate polynomial GCD are presented, along with extensive numerical tests. The use of matrix structure allows, in particular, to lower the asymptotic computational cost from cubic to quadratic order with respect to polynomial degree. .
The method of secondary quantization in the strong bond approximation
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O.A. Anikeenok
2015-12-01
Full Text Available Expressions for the calculation of the Fourier transform of the direct Coulomb interaction of electrons have been derived in the method of strong bond. It was shown that in the elaborated method it is not necessary to spread out nuclear charges over the crystal as it is done in the case of delocalized electrons.
Analytical Evaluation of Beam Deformation Problem Using Approximate Methods
DEFF Research Database (Denmark)
Barari, Amin; Kimiaeifar, A.; Domairry, G.
2010-01-01
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...
Directory of Open Access Journals (Sweden)
Pierluigi Monaco
2016-10-01
Full Text Available 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 the late 1960s to early 1990s. 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, not to mention the sampling of parameter space, 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 gives the most promising approach to solve these problems 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 1990s, and finally presenting the latest extensions and a few codes that are now being used in present-generation surveys and thoroughly tested to assess their performance in the context of future surveys.
APPROXIMATE SOLUTION USING A PERTURBATION METHOD FOR DETENTION POND DESIGN
Institute of Scientific and Technical Information of China (English)
Jen-Yan CHEN; Yao-Ming HONG
2002-01-01
It is a common practice to use a hydrological continuity equation as the governing equation in detention pond design. Although the detention volume can be evaluated using a numerical method and computer program,they are not available for engineers to use because of the difficulty involved in the numerical evaluation or the computer program may not be ready for engineers. This study intends to provide a formula for calculating the volume of a detention pond. A nonlinear continuity equation for detention pond design is obtained by applying a triangular/trapezoidal inflow hydrograph and spillway or orifice for the outflow device. This perturbation method is employed to resolve the equation. After discussing the omission and curve fitting methods,a formula for detention pond design is proposed.Several examples are displayed and a high agreement with the numerical result is obtained.
Effective moduli of particulate solids: Lubrication approximation method
Qi, F.; Phan-Thien, N.; X. J. Fan
To efficiently calculate the effective properties of a composite, which consists of rigid spherical inclusions not necessarily of the same sizes in a homogeneous isotropic elastic matrix, a method based on the lubrication forces between neighbouring particles has been developed. The method is used to evaluate the effective Lamé moduli and the Poisson's ratio of the composite, for the particles in random configurations and in cubic lattices. A good agreement with experimental results given by Smith (1975) for particles in random configurations is observed, and also the numerical results on the effective moduli agree well with the results given by Nunan & Keller (1984) for particles in cubic lattices.
An approximate method for determining of investment risk
Slavkova, Maria; Tzenova, Zlatina
2016-12-01
In this work a method for determining of investment risk during all economic states is considered. It is connected to matrix games with two players. A definition for risk in a matrix game is introduced. Three properties are proven. It is considered an appropriate example.
α-Automated Reasoning Method Based on Lattice-Valued Propositional Logic LP(X)
Institute of Scientific and Technical Information of China (English)
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.
Sherlock Holmes's Methods of Deductive Reasoning Applied to Medical Diagnostics
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' 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.
SET: A Pupil Detection Method Using Sinusoidal Approximation
Directory of Open Access Journals (Sweden)
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.
Lubrication approximation in completed double layer boundary element method
Nasseri, S.; Phan-Thien, N.; Fan, X.-J.
This paper reports on the results of the numerical simulation of the motion of solid spherical particles in shear Stokes flows. Using the completed double layer boundary element method (CDLBEM) via distributed computing under Parallel Virtual Machine (PVM), the effective viscosity of suspension has been calculated for a finite number of spheres in a cubic array, or in a random configuration. In the simulation presented here, the short range interactions via lubrication forces are also taken into account, via the range completer in the formulation, whenever the gap between two neighbouring particles is closer than a critical gap. The results for particles in a simple cubic array agree with the results of Nunan and Keller (1984) and Stoksian Dynamics of Brady etal. (1988). To evaluate the lubrication forces between particles in a random configuration, a critical gap of 0.2 of particle's radius is suggested and the results are tested against the experimental data of Thomas (1965) and empirical equation of Krieger-Dougherty (Krieger, 1972). Finally, the quasi-steady trajectories are obtained for time-varying configuration of 125 particles.
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S. Amir ali akbari
2005-01-01
Full Text Available Background and purpose : Withdrawal method is one of the most common contraceptive ways (% 23 nationwide. With regard to its relatively high failure rate (% 4-23 with unwanted pregnancies as well as resulted complications, this descriptive study was conducted to find out the reasons for not applying safe contraceptive methods.Materials and methods: Subject population consisted of 379 married women between 15 and 45 living in Amol city and using withdrawal method. The subjects were selected through different stages with final randomization Data were collected by a questionnaire in which personal, social, and obstetrical history, and reasons for using withdrawal method as well as for not applying other methods were documented. The validity and reliability of the tool were determined by content validity and test-re test method respectively. Pearson coefficient of correlation as well as t-test and ANOVA were used for quantitative and qualitative variables respectively.Results : Findings showed that the mean age of subjects was 28.1 ± 6.4, who had used withdrawal method at least for 3 months. Mean duration in using withdrawal method was 53.6 ± 6.6 months. Health care workers were considered the most frequent source of information (%26.6 and the main reasons for not applying safe contraceptive methods included fear of side effects (% 28.2, husband opposition (% 28.2, contraindication (% 9 Lactation (% 8.7 and indifference to conception (% 7.7. The most common reasons for applying withdrawal method were husband preference (% 25.1, having less complications (% 20.3, availability (% 19.5 and being safer than other methods (% 12.7.Conclusion : It can be concluded that much more efforts should be made to devise and perform family planning programs correctly, and training health care workers continuously and finally educating people either by mass media or by professionals to encourage applying safe contraceptive methods.
A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations
Institute of Scientific and Technical Information of China (English)
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.
Fuzzy Reasoning Methods by Choosing Different Fuzzy Counters and Analysis of Effect
Institute of Scientific and Technical Information of China (English)
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.
Directory of Open Access Journals (Sweden)
Wu Soon-Yi
2009-01-01
Full Text Available We introduce a new approximation scheme combining the viscosity method with extragradient method for finding a common element of the set of solutions of a mixed equilibrium problem and the set of fixed points of a finite family of nonexpansive mappings and the set of the variational inequality for a monotone, Lipschitz continuous mapping. We obtain a strong convergence theorem for the sequences generated by these processes in Hilbert spaces. Based on this result, we also get some new and interesting results. The results in this paper generalize, extend, and improve some well-known results in the literature.
Automated Reasoning and Equation Solving with the Characteristic Set Method
Institute of Scientific and Technical Information of China (English)
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.
Pospelov, A. I.
2016-08-01
Adaptive methods for the polyhedral approximation of the convex Edgeworth-Pareto hull in multiobjective monotone integer optimization problems are proposed and studied. For these methods, theoretical convergence rate estimates with respect to the number of vertices are obtained. The estimates coincide in order with those for filling and augmentation H-methods intended for the approximation of nonsmooth convex compact bodies.
Reducible or irreducible? Mathematical reasoning and the ontological method.
Fisher, William P
2010-01-01
Science is often described as nothing but the practice of measurement. This perspective follows from longstanding respect for the roles mathematics and quantification have played as media through which alternative hypotheses are evaluated and experience becomes better managed. Many figures in the history of science and psychology have contributed to what has been called the "quantitative imperative," the demand that fields of study employ number and mathematics even when they do not constitute the language in which investigators think together. But what makes an area of study scientific is, of course, not the mere use of number, but communities of investigators who share common mathematical languages for exchanging quantitative and quantitative value. Such languages require rigorous theoretical underpinning, a basis in data sufficient to the task, and instruments traceable to reference standard quantitative metrics. The values shared and exchanged by such communities typically involve the application of mathematical models that specify the sufficient and invariant relationships necessary for rigorous theorizing and instrument equating. The mathematical metaphysics of science are explored with the aim of connecting principles of quantitative measurement with the structures of sufficient reason.
Reverse triple I method of restriction for fuzzy reasoning
Institute of Scientific and Technical Information of China (English)
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.
Preferences of Teaching Methods and Techniques in Mathematics with Reasons
Ünal, Menderes
2017-01-01
In this descriptive study, the goal was to determine teachers' preferred pedagogical methods and techniques in mathematics. Qualitative research methods were employed, primarily case studies. 40 teachers were randomly chosen from various secondary schools in Kirsehir during the 2015-2016 educational terms, and data were gathered via…
The Financial Impact of Risk Factors Affecting Project Cost Contingency: Evidential Reasoning Method
Directory of Open Access Journals (Sweden)
Emmanuel Abeere-Inga
2013-07-01
Full Text Available 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 structured questionnaires revealed that four work sections are prone to high scope changes contemporaneous with seven risk factors. Contrary to the usual 10% contingency estimate allowed for construction projects in Ghana, an approximate overall physical contingency range of between 13.36% and 17.88% was determined using evidential reasoning methods. The likely impact of the integrated work sections and risk factors provide a clue to estimators on how to estimate and account for project cost contingency. The research concludes by recommending a framework for improving the estimation process of cost contingency through the integration of efficient risk management strategies, cost estimation and design management process.
Excitation energy transfer rates: comparison of approximate methods to the exact solution
Jesenko, Simon
2014-01-01
We have evaluated excitation energy transfer rates in photosyntetic complexes using the exact HEOM method and various approximate methods frequently used in the literature, namely, the F\\"orster method, the Redfield method, the modified Redfield method and the variational master equation. The rates are evaluated for the case of a simple dimer and a trimer photosynthetic complex, with vibrational environment characterized by the Drude-Lorentz spectral density. Comparing approximate rates to the exact ones, we have confirmed the validity of approximate methods within appropriate limits, however these limits are often well outside parameter ranges that are relevant for the dynamics in real photosynthetic complexes.
Sabatier, Romuald; Fossati, Caroline; Bourennane, Salah; Di Giacomo, Antonio
2008-10-01
Model Based Optical Proximity Correction (MBOPC) is since a decade a widely used technique that permits to achieve resolutions on silicon layout smaller than the wave-length which is used in commercially-available photolithography tools. This is an important point, because masks dimensions are continuously shrinking. As for the current masks, several billions of segments have to be moved, and also, several iterations are needed to reach convergence. Therefore, fast and accurate algorithms are mandatory to perform OPC on a mask in a reasonably short time for industrial purposes. As imaging with an optical lithography system is similar to microscopy, the theory used in MBOPC is drawn from the works originally conducted for the theory of microscopy. Fourier Optics was first developed by Abbe to describe the image formed by a microscope and is often referred to as Abbe formulation. This is one of the best methods for optimizing illumination and is used in most of the commercially available lithography simulation packages. Hopkins method, developed later in 1951, is the best method for mask optimization. Consequently, Hopkins formulation, widely used for partially coherent illumination, and thus for lithography, is present in most of the commercially available OPC tools. This formulation has the advantage of a four-way transmission function independent of the mask layout. The values of this function, called Transfer Cross Coefficients (TCC), describe the illumination and projection pupils. Commonly-used algorithms, involving TCC of Hopkins formulation to compute aerial images during MBOPC treatment, are based on TCC decomposition into its eigenvectors using matricization and the well-known Singular Value Decomposition (SVD) tool. These techniques that use numerical approximation and empirical determination of the number of eigenvectors taken into account, could not match reality and lead to an information loss. They also remain highly runtime consuming. We propose an
A NEW TWO-POINT ADAPTIVENONLINEAR APPROXIMATION METHOD FOR RELIABILITY ANALYSIS
Institute of Scientific and Technical Information of China (English)
LiuShutian
2004-01-01
A two-point adaptive nonlinear approximation (referred to as TANA4) suitable for reliability analysis is proposed. Transformed and normalized random variables in probabilistic analysis could become negative and pose a challenge to the earlier developed two-point approximations; thus a suitable method that can address this issue is needed. In the method proposed, the nonlinearity indices of intervening variables are limited to integers. Then, on the basis of the present method, an improved sequential approximation of the limit state surface for reliability analysis is presented. With the gradient projection method, the data points for the limit state surface approximation are selected on the original limit state surface, which effectively represents the nature of the original response function. On the basis of this new approximation, the reliability is estimated using a first-order second-moment method. Various examples, including both structural and non-structural ones, are presented to show the effectiveness of the method proposed.
A new embedded-atom method approach based on the pth moment approximation
Wang, Kun; Zhu, Wenjun; Xiao, Shifang; Chen, Jun; Hu, Wangyu
2016-12-01
Large scale atomistic simulations with suitable interatomic potentials are widely employed by scientists or engineers of different areas. The quick generation of high-quality interatomic potentials is urgently needed. This largely relies on the developments of potential construction methods and algorithms in this area. Quantities of interatomic potential models have been proposed and parameterized with various methods, such as the analytic method, the force-matching approach and multi-object optimization method, in order to make the potentials more transferable. Without apparently lowering the precision for describing the target system, potentials of fewer fitting parameters (FPs) are somewhat more physically reasonable. Thus, studying methods to reduce the FP number is helpful in understanding the underlying physics of simulated systems and improving the precision of potential models. In this work, we propose an embedded-atom method (EAM) potential model consisting of a new manybody term based on the pth moment approximation to the tight binding theory and the general transformation invariance of EAM potentials, and an energy modification term represented by pairwise interactions. The pairwise interactions are evaluated by an analytic-numerical scheme without the need to know their functional forms a priori. By constructing three potentials of aluminum and comparing them with a commonly used EAM potential model, several wonderful results are obtained. First, without losing the precision of potentials, our potential of aluminum has fewer potential parameters and a smaller cutoff distance when compared with some constantly-used potentials of aluminum. This is because several physical quantities, usually serving as target quantities to match in other potentials, seem to be uniquely dependent on quantities contained in our basic reference database within the new potential model. Second, a key empirical parameter in the embedding term of the commonly used EAM model is
A Method to Improve First Order Approximation of Smoothed Particle Hydrodynamics
Institute of Scientific and Technical Information of China (English)
CHEN Si; ZHOU Dai; BAO Yan; DONG Shi-lin
2008-01-01
Smoothed particle hydrodynamics (SPH) is a useful meshless method. The first and second ordersare the most popular derivatives of the field function in the mechanical governing equations. New methodswere proposed to improve accuracy of SPH approximation by the lemma proved. The lemma describes therelationship of functions and their SPH approximation. Finally, the error comparison of SPH method with orwithout our improvement was carried out.
On the interpretation of large gravimagnetic data by the modified method of S-approximations
Stepanova, I. E.; Raevskiy, D. N.; Shchepetilov, A. V.
2017-01-01
The modified method of S-approximations applied for processing large and superlarge gravity and magnetic prospecting data is considered. The modified S-approximations of the elements of gravitational field are obtained due to the efficient block methods for solving the system of linear algebraic equations (SLAEs) to which the geophysically meaningful problem is reduced. The results of the mathematical experiment are presented.
Nguyen, Nhan T.; Hornby, Gregory; Ishihara, Abe
2013-01-01
This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.
Efficient Path Query and Reasoning Method Based on Rare Axis
Institute of Scientific and Technical Information of China (English)
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.
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.
Energy Technology Data Exchange (ETDEWEB)
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)
Energy Technology Data Exchange (ETDEWEB)
Zhang, Zhenyue [Zhejiang Univ., Hangzhou (People' s Republic of China); Zha, Hongyuan [Pennsylvania State Univ., University Park, PA (United States); Simon, Horst [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2006-07-31
In this paper, we developed numerical algorithms for computing sparse low-rank approximations of matrices, and we also provided a detailed error analysis of the proposed algorithms together with some numerical experiments. The low-rank approximations are constructed in a certain factored form with the degree of sparsity of the factors controlled by some user-specified parameters. In this paper, we cast the sparse low-rank approximation problem in the framework of penalized optimization problems. We discuss various approximation schemes for the penalized optimization problem which are more amenable to numerical computations. We also include some analysis to show the relations between the original optimization problem and the reduced one. We then develop a globally convergent discrete Newton-like iterative method for solving the approximate penalized optimization problems. We also compare the reconstruction errors of the sparse low-rank approximations computed by our new methods with those obtained using the methods in the earlier paper and several other existing methods for computing sparse low-rank approximations. Numerical examples show that the penalized methods are more robust and produce approximations with factors which have fewer columns and are sparser.
An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method
Energy Technology Data Exchange (ETDEWEB)
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.
A NEW SMOOTHING APPROXIMATION METHOD FOR SOLVING BOX CONSTRAINED VARIATIONAL INEQUALITIES
Institute of Scientific and Technical Information of China (English)
Chang-feng Ma; Guo-ping Liang; Shao-peng Liu
2002-01-01
In this paper, we first give a smoothing approximation function of nonsmooth system based on box constrained variational inequalities and then present a new smoothing approximation algorithm. Under suitable conditions,we show that the method is globally and superlinearly convergent. A few numerical results are also reported in the paper.
La Budde, R. A.
1972-01-01
Sampling techniques have been used previously to evaluate Jacobian determinants that occur in classical mechanical descriptions of molecular scattering. These determinants also occur in the quasiclassical approximation. A new technique is described which can be used to evaluate Jacobian determinants which occur in either description. This method is expected to be valuable in the study of reactive scattering using the quasiclassical approximation.
An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue Functions
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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.
A Novel Method in Food Safety Management by Using Case Base Reasoning Method
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S. Saqaeeyan
2015-09-01
Full Text Available Today’s Food Industry has responsibility to provide most consuming food for people. These foods are consumed by large area of society. So they are important source of causes of diseases and food poisoning. Monitoring system have been created to control these diseases and they are used in duration of production step of food supply chain. Hazard Assurance Critical Control Point (HACCP is regarded as best method in safety system. Necessity to create integrated HACCP system forced factories to use intelligent methods to build HACCP for every production. This paper proposes Case-Based Reasoning (CBR technique and use of paired comparisons tables and similarity equations to create HACCP for food system of Sabz Nam Company. Our system is an intelligent system has based on RFID and it works as consulter by generating five proper safety suggestion to food expert. Finally we assess accuracy and efficiency of proposed system on real data of Sabz Nam Company.
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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.
Efficiency of the estimate refinement method for polyhedral approximation of multidimensional balls
Kamenev, G. K.
2016-05-01
The estimate refinement method for the polyhedral approximation of convex compact bodies is analyzed. When applied to convex bodies with a smooth boundary, this method is known to generate polytopes with an optimal order of growth of the number of vertices and facets depending on the approximation error. In previous studies, for the approximation of a multidimensional ball, the convergence rates of the method were estimated in terms of the number of faces of all dimensions and the cardinality of the facial structure (the norm of the f-vector) of the constructed polytope was shown to have an optimal rate of growth. In this paper, the asymptotic convergence rate of the method with respect to faces of all dimensions is compared with the convergence rate of best approximation polytopes. Explicit expressions are obtained for the asymptotic efficiency, including the case of low dimensions. Theoretical estimates are compared with numerical results.
Approximation analytical solutions for a unified plasma sheath model by double decomposition method
Institute of Scientific and Technical Information of China (English)
FangJin－Qing
1998-01-01
A unified plasma sheath model and its potential equation are proposed.Any higher-order approximation analytical solutions for the unified plasma sheath potential equation are derived by double decomposition method.
Duan, Beiping; Zheng, Zhoushun; Cao, Wen
2016-08-01
In this paper, we revisit two spectral approximations, including truncated approximation and interpolation for Caputo fractional derivative. The two approaches have been studied to approximate Riemann-Liouville (R-L) fractional derivative by Chen et al. and Zayernouri et al. respectively in their most recent work. For truncated approximation the reconsideration partly arises from the difference between fractional derivative in R-L sense and Caputo sense: Caputo fractional derivative requires higher regularity of the unknown than R-L version. Another reason for the reconsideration is that we distinguish the differential order of the unknown with the index of Jacobi polynomials, which is not presented in the previous work. Also we provide a way to choose the index when facing multi-order problems. By using generalized Hardy's inequality, the gap between the weighted Sobolev space involving Caputo fractional derivative and the classical weighted space is bridged, then the optimal projection error is derived in the non-uniformly Jacobi-weighted Sobolev space and the maximum absolute error is presented as well. For the interpolation, analysis of interpolation error was not given in their work. In this paper we build the interpolation error in non-uniformly Jacobi-weighted Sobolev space by constructing fractional inverse inequality. With combining collocation method, the approximation technique is applied to solve fractional initial-value problems (FIVPs). Numerical examples are also provided to illustrate the effectiveness of this algorithm.
Approximation and inference methods for stochastic biochemical kinetics—a tutorial review
Schnoerr, David; Sanguinetti, Guido; Grima, Ramon
2017-03-01
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 methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics.
Evaluation of the successive approximations method for acoustic streaming numerical simulations.
Catarino, S O; Minas, G; Miranda, J M
2016-05-01
This work evaluates the successive approximations method commonly used to predict acoustic streaming by comparing it with a direct method. The successive approximations method solves both the acoustic wave propagation and acoustic streaming by solving the first and second order Navier-Stokes equations, ignoring the first order convective effects. This method was applied to acoustic streaming in a 2D domain and the results were compared with results from the direct simulation of the Navier-Stokes equations. The velocity results showed qualitative agreement between both methods, which indicates that the successive approximations method can describe the formation of flows with recirculation. However, a large quantitative deviation was observed between the two methods. Further analysis showed that the successive approximation method solution is sensitive to the initial flow field. The direct method showed that the instantaneous flow field changes significantly due to reflections and wave interference. It was also found that convective effects contribute significantly to the wave propagation pattern. These effects must be taken into account when solving the acoustic streaming problems, since it affects the global flow. By adequately calculating the initial condition for first order step, the acoustic streaming prediction by the successive approximations method can be improved significantly.
OPTIMAL ERROR ESTIMATES OF THE PARTITION OF UNITY METHOD WITH LOCAL POLYNOMIAL APPROXIMATION SPACES
Institute of Scientific and Technical Information of China (English)
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.
Directory of Open Access Journals (Sweden)
Constantin Bota
2014-01-01
Full Text Available The paper presents the optimal homotopy perturbation method, which is a new method to find approximate analytical solutions for nonlinear partial differential equations. Based on the well-known homotopy perturbation method, the optimal homotopy perturbation method presents an accelerated convergence compared to the regular homotopy perturbation method. The applications presented emphasize the high accuracy of the method by means of a comparison with previous results.
Cao, Zhanli; Wang, Fan; Yang, Mingli
2016-10-01
Various approximate approaches to calculate cluster amplitudes in equation-of-motion coupled-cluster (EOM-CC) approaches for ionization potentials (IP) and electron affinities (EA) with spin-orbit coupling (SOC) included in post self-consistent field (SCF) calculations are proposed to reduce computational effort. Our results indicate that EOM-CC based on cluster amplitudes from the approximate method CCSD-1, where the singles equation is the same as that in CCSD and the doubles amplitudes are approximated with MP2, is able to provide reasonable IPs and EAs when SOC is not present compared with CCSD results. It is an economical approach for calculating IPs and EAs and is not as sensitive to strong correlation as CC2. When SOC is included, the approximate method CCSD-3, where the same singles equation as that in SOC-CCSD is used and the doubles equation of scalar-relativistic CCSD is employed, gives rise to IPs and EAs that are in closest agreement with those of CCSD. However, SO splitting with EOM-CC from CC2 generally agrees best with that with CCSD, while that of CCSD-1 and CCSD-3 is less accurate. This indicates that a balanced treatment of SOC effects on both single and double excitation amplitudes is required to achieve reliable SO splitting.
A new approximation method for time-dependent problems in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima (Mexico)]. E-mail: paolo@ucol.mx; Aranda, Alfredo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima (Mexico)]. E-mail: fefo@ucol.mx; Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Diag. 113 y 64 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)]. E-mail: fernande@quimica.unlp.edu.ar; Jones, Hugh [Department of Physics, Imperial College, London SW7 2AZ (United Kingdom)]. E-mail: h.f.jones@imperial.ac.uk
2005-06-06
We propose an approximate solution of the time-dependent Schroedinger equation using the method of stationary states combined with a variational matrix method for finding the energies and eigenstates. We illustrate the effectiveness of the method by applying it to the time development of the wave-function in the quantum-mechanical version of the inflationary slow-roll transition.
Bota, C.; Cǎruntu, B.; Bundǎu, O.
2013-10-01
In this paper we applied the Squared Remainder Minimization Method (SRMM) to find analytic approximate polynomial solutions for Riccati differential equations. Two examples are included to demonstrated the validity and applicability of the method. The results are compared to those obtained by other methods.
ON THE CONVERGENCE OF AN APPROXIMATE PROXIMAL METHOD FOR DC FUNCTIONS
Institute of Scientific and Technical Information of China (English)
A. Moudafi; P-E. Maingé
2006-01-01
In this paper we prove the convergence of the approximate proximal method for DC functions proposed by Sun et al [6]. Our analysis also permits to treat the exact method.We then propose an interesting result in the case where the second component of the DC function is differentiable and provide some computational experiences which proved the efficiency of our method.
A New Inexactness Criterion for Approximate Logarithmic-Quadratic Proximal Methods
Institute of Scientific and Technical Information of China (English)
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.
Institute of Scientific and Technical Information of China (English)
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.
Institute of Scientific and Technical Information of China (English)
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.
Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems
Directory of Open Access Journals (Sweden)
Daniel Olvera
2014-01-01
Full Text Available We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM that is based on the homotopy perturbation method (HPM and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameter h by following the homotopy analysis method (HAM. At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge-Kutta method via the amplitude-time response curves.
Analytical approximate solution of the cooling problem by Adomian decomposition method
Alizadeh, Ebrahim; Sedighi, Kurosh; Farhadi, Mousa; Ebrahimi-Kebria, H. R.
2009-02-01
The Adomian decomposition method (ADM) can provide analytical approximation or approximated solution to a rather wide class of nonlinear (and stochastic) equations without linearization, perturbation, closure approximation, or discretization methods. In the present work, ADM is employed to solve the momentum and energy equations for laminar boundary layer flow over flat plate at zero incidences with neglecting the frictional heating. A trial and error strategy has been used to obtain the constant coefficient in the approximated solution. ADM provides an analytical solution in the form of an infinite power series. The effect of Adomian polynomial terms is considered and shows that the accuracy of results is increased with the increasing of Adomian polynomial terms. The velocity and thermal profiles on the boundary layer are calculated. Also the effect of the Prandtl number on the thermal boundary layer is obtained. Results show ADM can solve the nonlinear differential equations with negligible error compared to the exact solution.
Directory of Open Access Journals (Sweden)
Suxiang He
2014-01-01
Full Text Available An implementable nonlinear Lagrange algorithm for stochastic minimax problems is presented based on sample average approximation method in this paper, in which the second step minimizes a nonlinear Lagrange function with sample average approximation functions of original functions and the sample average approximation of the Lagrange multiplier is adopted. Under a set of mild assumptions, it is proven that the sequences of solution and multiplier obtained by the proposed algorithm converge to the Kuhn-Tucker pair of the original problem with probability one as the sample size increases. At last, the numerical experiments for five test examples are performed and the numerical results indicate that the algorithm is promising.
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 o
Directory of Open Access Journals (Sweden)
Birol İbiş
2014-01-01
Full Text Available This paper aims to obtain the approximate solution of time-fractional advection-dispersion equation (FADE involving Jumarie’s modification of Riemann-Liouville derivative by the fractional variational iteration method (FVIM. FVIM provides an analytical approximate solution in the form of a convergent series. Some examples are given and the results indicate that the FVIM is of high accuracy, more efficient, and more convenient for solving time FADEs.
L0-based sparse approximation: two alternative methods and some applications
Portilla, Javier; Mancera, Luis
2007-09-01
We propose two methods for sparse approximation of images under l II error metric. First one performs an approximation error minimization given a l p-norm of the representation through alternated orthogonal projections onto two sets. We study the cases p = 0 (sub-optimal) and p = 1 (optimal), and find that the l 0-AP method is neatly superior, for typical images and overcomplete oriented pyramids. Given that l I-AP is optimal, this shows that it is not equivalent in practical image processing conditions to minimize one or the other norm, contrarily to what is often assumed. The second method is more powerful, and it performs gradient descent onto decreasingly smoothed versions of the sparse approximation cost function, yielding a method previously proposed as a heuristic. We adapt these techniques for being applied to image restoration, with very positive results.
Energy Technology Data Exchange (ETDEWEB)
Sin, M. W.; Kim, M. H. [Kyunghee Univ., Yongin (Korea, Republic of)
2002-10-01
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.
Energy Technology Data Exchange (ETDEWEB)
Araki, Fujio; Kumagai, Kozo; Iseri, Takumi; Kawano, Tsutomu (National Hospital of Kumamoto (Japan))
1991-04-01
Dose calculation of irregularly shaped fields can be made by the Clarkson technique, which however requires considerable time and is thus not practical. We investigated a simple approximation method for determining field factors (F{sub A}) and tissue-peak ratios (TPRs) for irregularly shaped fields. By this method, we approximated scatter dose by the ratio of area for an irregularly shaped field to that for the overall field (without blocking). Maximum error of equivalent square fields as determined by this method for irregularly shaped fields was -1.3% for field factors, +2.1% for TPRs and +1.4% for the F{sub A} x TPRs. (author).
Directory of Open Access Journals (Sweden)
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.
Approximate Analytic and Numerical Solutions to Lane-Emden Equation via Fuzzy Modeling Method
Directory of Open Access Journals (Sweden)
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.
Institute of Scientific and Technical Information of China (English)
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.
Simulation of mass transfer during osmotic dehydration of apple: a power law approximation method
Abbasi Souraki, B.; Tondro, H.; Ghavami, M.
2014-10-01
In this study, unsteady one-dimensional mass transfer during osmotic dehydration of apple was modeled using an approximate mathematical model. The mathematical model has been developed based on a power law profile approximation for moisture and solute concentrations in the spatial direction. The proposed model was validated by the experimental water loss and solute gain data, obtained from osmotic dehydration of infinite slab and cylindrical shape samples of apple in sucrose solutions (30, 40 and 50 % w/w), at different temperatures (30, 40 and 50 °C). The proposed model's predictions were also compared with the exact analytical and also a parabolic approximation model's predictions. The values of mean relative errors respect to the experimental data were estimated between 4.5 and 8.1 %, 6.5 and 10.2 %, and 15.0 and 19.1 %, for exact analytical, power law and parabolic approximation methods, respectively. Although the parabolic approximation leads to simpler relations, the power law approximation method results in higher accuracy of average concentrations over the whole domain of dehydration time. Considering both simplicity and precision of the mathematical models, the power law model for short dehydration times and the simplified exact analytical model for long dehydration times could be used for explanation of the variations of the average water loss and solute gain in the whole domain of dimensionless times.
Incomplete Phase Space Reconstruction Method Based on Subspace Adaptive Evolution Approximation
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Tai-fu Li
2013-01-01
Full Text Available The chaotic time series can be expanded to the multidimensional space by phase space reconstruction, in order to reconstruct the dynamic characteristics of the original system. It is difficult to obtain complete phase space for chaotic time series, as a result of the inconsistency of phase space reconstruction. This paper presents an idea of subspace approximation. The chaotic time series prediction based on the phase space reconstruction can be considered as the subspace approximation problem in different neighborhood at different time. The common static neural network approximation is suitable for a trained neighborhood, but it cannot ensure its generalization performance in other untrained neighborhood. The subspace approximation of neural network based on the nonlinear extended Kalman filtering (EKF is a dynamic evolution approximation from one neighborhood to another. Therefore, in view of incomplete phase space, due to the chaos phase space reconstruction, we put forward subspace adaptive evolution approximation method based on nonlinear Kalman filtering. This method is verified by multiple sets of wind speed prediction experiments in Wulong city, and the results demonstrate that it possesses higher chaotic prediction accuracy.
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 polynomials with the complex coefficients. 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 transfered to a constrained minimization problem, then solved with a so-called modified Newton method, which is a generalization of the gradient-projection method, by searching the solution iteratively. While our original method is designed for polynomials with the real coefficients, we extend it to accept polynomials with the complex coefficients in this paper.
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.
GPGCD, an Iterative Method for Calculating Approximate GCD, for Multiple Univariate Polynomials
Terui, Akira
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.
Children's discomfort in assessments using different methods for approximal caries detection
Directory of Open Access Journals (Sweden)
Tatiane Fernandes Novaes
2012-04-01
Full Text Available Because discomfort caused by different approximal caries detection methods can influence their performance, the assessment of this discomfort is important. Thus, this study aimed to evaluate the discomfort reported by children after the use of different diagnostic methods to detect approximal caries lesions in primary teeth: visual inspection, bitewing radiography, laser fluorescence (DIAGNOdent pen - LFpen and temporary separation with orthodontic rubbers. Seventy-six children aged 4 to 12 years were examined using these methods. Their discomfort was assessed using the Wong-Baker scale and compared among the methods. Visual inspection caused less discomfort than did other methods. Radiography and the LFpen presented similar levels of discomfort. Older children reported higher discomfort using temporary separation, whereas younger children reported less discomfort with the LFpen. In conclusion, radiographic, temporary separation and LFpen methods provoke higher discomfort than visual inspection.
A New Homotopy Analysis Method for Approximating the Analytic Solution of KdV Equation
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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.
Laplace transform homotopy perturbation method for the approximation of variational problems.
Filobello-Nino, U; Vazquez-Leal, H; Rashidi, M M; Sedighi, H M; Perez-Sesma, A; Sandoval-Hernandez, M; Sarmiento-Reyes, A; Contreras-Hernandez, A D; Pereyra-Diaz, D; Hoyos-Reyes, C; Jimenez-Fernandez, V M; Huerta-Chua, J; Castro-Gonzalez, F; Laguna-Camacho, J R
2016-01-01
This article proposes the application of Laplace Transform-Homotopy Perturbation Method and some of its modifications in order to find analytical approximate solutions for the linear and nonlinear differential equations which arise from some variational problems. As case study we will solve four ordinary differential equations, and we will show that the proposed solutions have good accuracy, even we will obtain an exact solution. In the sequel, we will see that the square residual error for the approximate solutions, belongs to the interval [0.001918936920, 0.06334882582], which confirms the accuracy of the proposed methods, taking into account the complexity and difficulty of variational problems.
A New Trigonometric Method of Summation and its Application to the Degree of Approximation
Indian Academy of Sciences (India)
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).
A New General Algebraic Method and Its Application to Shallow Long Wave Approximate Equations
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations (NLEEs). For illustration, we apply the new method to shallow long wave approximate equations and successfully obtain abundant new exact solutions, which include rational solitary wave solutions and rational triangular periodic wave solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.
Institute of Scientific and Technical Information of China (English)
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.
Institute of Scientific and Technical Information of China (English)
李大鸣; 张红萍; 高永祥
2002-01-01
A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.
Christian, Karen Jeanne
2011-12-01
Students often use study groups to prepare for class or exams; yet to date, we know very little about how these groups actually function. This study looked at the ways in which undergraduate organic chemistry students prepared for exams through self-initiated study groups. We sought to characterize the methods of social regulation, levels of content processing, and types of reasoning processes used by students within their groups. Our analysis showed that groups engaged in predominantly three types of interactions when discussing chemistry content: co-construction, teaching, and tutoring. Although each group engaged in each of these types of interactions at some point, their prevalence varied between groups and group members. Our analysis suggests that the types of interactions that were most common depended on the relative content knowledge of the group members as well as on the difficulty of the tasks in which they were engaged. Additionally, we were interested in characterizing the reasoning methods used by students within their study groups. We found that students used a combination of three content-relevant methods of reasoning: model-based reasoning, case-based reasoning, or rule-based reasoning, in conjunction with one chemically-irrelevant method of reasoning: symbol-based reasoning. The most common way for groups to reason was to use rules, whereas the least common way was for students to work from a model. In general, student reasoning correlated strongly to the subject matter to which students were paying attention, and was only weakly related to student interactions. Overall, results from this study may help instructors to construct appropriate tasks to guide what and how students study outside of the classroom. We found that students had a decidedly strategic approach in their study groups, relying heavily on material provided by their instructors, and using the reasoning strategies that resulted in the lowest levels of content processing. We suggest
On the Influence of New Media and Methods to Achieve Reasonable Spread
Institute of Scientific and Technical Information of China (English)
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.
Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method
Energy Technology Data Exchange (ETDEWEB)
Belendez, A; Pascual, C; Alvarez, M L; Mendez, D I; Yebra, M S; Hernandez, A [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2009-01-15
A modified He's homotopy perturbation method is used to calculate the periodic solutions of a nonlinear pendulum. The method has been modified by truncating the infinite series corresponding to the first-order approximate solution and substituting a finite number of terms in the second-order linear differential equation. As can be seen, the modified homotopy perturbation method works very well for high values of the initial amplitude. Excellent agreement of the analytical approximate period with the exact period has been demonstrated not only for small but also for large amplitudes A (the relative error is less than 1% for A < 152 deg.). Comparison of the result obtained using this method with the exact ones reveals that this modified method is very effective and convenient.
A decision method based on uncertainty reasoning of linguistic truth-valued concept lattice
Yang, Li; Xu, Yang
2010-04-01
Decision making with linguistic information is a research hotspot now. This paper begins by establishing the theory basis for linguistic information processing and constructs the linguistic truth-valued concept lattice for a decision information system, and further utilises uncertainty reasoning to make the decision. That is, we first utilise the linguistic truth-valued lattice implication algebra to unify the different kinds of linguistic expressions; second, we construct the linguistic truth-valued concept lattice and decision concept lattice according to the concrete decision information system and third, we establish the internal and external uncertainty reasoning methods and talk about the rationality of them. We apply these uncertainty reasoning methods into decision making and present some generation methods of decision rules. In the end, we give an application of this decision method by an example.
On the Method of Multiplier-enlargement and Approximation of Unbounded Continuous Functions
Institute of Scientific and Technical Information of China (English)
ZHENG Cheng-De; WANG Ren-Hong
2001-01-01
By combining the classical appropriate functions “1, x, x2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite-Fejéinterpolation polynomial operators are analysed and studied, and a general conclusion is obtained.
The information-based complexity of approximation problem by adaptive Monte Carlo methods
Institute of Scientific and Technical Information of China (English)
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
Institute of Scientific and Technical Information of China (English)
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.
An approximate method for solution to variable moment of inertia problems
Beans, E. W.
1981-01-01
An approximation method is presented for reducing a nonlinear differential equation (for the 'weather vaning' motion of a wind turbine) to an equivalent constant moment of inertia problem. The integrated average of the moment of inertia is determined. Cycle time was found to be the equivalent cycle time if the rotating speed is 4 times greater than the system's minimum natural frequency.
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...
12 CFR 334.25 - Reasonable and simple methods of opting out.
2010-01-01
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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.
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.
On approximation of nonlinear boundary integral equations for the combined method
Energy Technology Data Exchange (ETDEWEB)
Gregus, M.; Khoromsky, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.
1989-09-22
The nonlinear boundary integral equations that arise in research of nonlinear magnetostatic problems are investigated in combined formulation on an unbounded domain. Approximations of the derived operator equations are studied based on the Galerkin method. The investigated boundary operators are strongly monotone, Lipschitz-continuous, potential and have a symmetrical Gateaux derivative. The error estimates of the Galerkin's approximation in Sobolev spaces of fractional powers are obtained using the above-mentioned properties of the operators, too. The problem has been studied on surfaces in two and three-dimensional spaces. We answer also some questions on convergence connected with the discretized systems of equations. 21 refs.
Approximate Dual Averaging Method for Multiagent Saddle-Point Problems with Stochastic Subgradients
Directory of Open Access Journals (Sweden)
Deming Yuan
2014-01-01
Full Text Available This paper considers the problem of solving the saddle-point problem over a network, which consists of multiple interacting agents. The global objective function of the problem is a combination of local convex-concave functions, each of which is only available to one agent. Our main focus is on the case where the projection steps are calculated approximately and the subgradients are corrupted by some stochastic noises. We propose an approximate version of the standard dual averaging method and show that the standard convergence rate is preserved, provided that the projection errors decrease at some appropriate rate and the noises are zero-mean and have bounded variance.
Directory of Open Access Journals (Sweden)
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.
Adomian decomposition method and Padè approximants for solving the Blaszak-Marciniak lattice
Institute of Scientific and Technical Information of China (English)
YangPei; Chen Yong; Li Zhi-Bin
2008-01-01
The Adomian decomposition method (ADM) and Padè approximants are combined to solve the well-known Blaszak-Marciniak lattice,which has rich mathematical structures and many important applications in physics and mathematics.In some cases,the truncated series solution of ADM is adequate only in a small region when the exact solution is not reached.To overcome the drawback,the Padè approximants,which have the advantage in turning the polynomials approximation into a rational function,are applied to the series solution to improve the accuracy and enlarge the convergence domain.By using the ADM-Padè technique,the soliton solutions of the Blaszak-Marciniak lattice are constructed with better accuracy and better convergence than by using the ADM alone.Numerical and figurative illustrations show that it is a promising tool for solving nonlinear problems.
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
Directory of Open Access Journals (Sweden)
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.
Nonlinear approximation method in Lagrangian relaxation-based algorithms for hydrothermal scheduling
Energy Technology Data Exchange (ETDEWEB)
Guan, X. [Pacific Gas and Electric, San Francisco, CA (United States); Luh, P.B.; Zhang, L. [Univ. of Connecticut, Storrs, CT (United States). Dept. of Electrical and Systems Engineering
1995-05-01
When the Lagrangian relaxation technique is used to solve hydrothermal scheduling problems, many subproblems have linear stage-wise cost functions. A well recognized difficulty is that the solutions to these subproblems may oscillate between maximum and minimum generations with slight changes of the multipliers. Furthermore, the subproblem solutions may become singular, i.e., they are un-determined when the linear coefficients become zero. This may result in large differences between subproblem solutions and the optimal primal schedule. In this paper, a nonlinear approximation method is presented which utilizes nonlinear functions, quadratic in this case, to approximate relevant linear cost functions. The analysis shows that the difficulty associated with solution oscillation is reduced, and singularity is avoided. Extensive testing based on Northeast Utilities data indicates that the method consistently generates better schedules than the standard Lagrangian relaxation method.
Institute of Scientific and Technical Information of China (English)
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.
Kolesnikov, V. I.; Yakovlev, V. B.; Bardushkin, V. V.; Lavrov, I. V.; Sychev, A. P.; Yakovleva, E. N.
2013-09-01
Various methods for evaluation of the effective permittivity of heterogeneous media, namely, the effective medium approximation (Bruggeman's approximation), the Maxwell-Garnett approximation, Wiener's bounds, and the Hashin-Shtrikman variational bounds (for effective static characteristics) are combined on the basis of a generalized singular approximation.
Simple and fast cosine approximation method for computer-generated hologram calculation.
Nishitsuji, Takashi; Shimobaba, Tomoyoshi; Kakue, Takashi; Arai, Daisuke; Ito, Tomoyoshi
2015-12-14
The cosine function is a heavy computational operation in computer-generated hologram (CGH) calculation; therefore, it is implemented by substitution methods such as a look-up table. However, the computational load and required memory space of such methods are still large. In this study, we propose a simple and fast cosine function approximation method for CGH calculation. As a result, we succeeded in creating CGH with sufficient quality and made the calculation time 1.6 times as fast at maximum compared to using the look-up table of the cosine function on CPU implementation.
The DSUBm approximation scheme for the coupled cluster method and applications to quantum magnets
Directory of Open Access Journals (Sweden)
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.
Directory of Open Access Journals (Sweden)
Shaheed N. Huseen
2013-01-01
Full Text Available A modified q-homotopy analysis method (mq-HAM was proposed for solving nth-order nonlinear differential equations. This method improves the convergence of the series solution in the nHAM which was proposed in (see Hassan and El-Tawil 2011, 2012. The proposed method provides an approximate solution by rewriting the nth-order nonlinear differential equation in the form of n first-order differential equations. The solution of these n differential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed.
Institute of Scientific and Technical Information of China (English)
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.
Approximated l-states of the Manning-Rosen potential by Nikiforov-Uvarov method
Ikhdair, Sameer M
2011-01-01
The approximately analytical bound state solutions of the l-wave Schr\\"odinger equation for the Manning-Rosen (MR) potential are carried out by a proper approximation to the centrifugal term. The energy spectrum formula and normalized wave functions expressed in terms of the Jacobi polynomials are both obtained for the application of the Nikiforov-Uvarov (NU) method to the Manning-Rosen potential. To show the accuracy of our results, we calculate the eigenvalues numerically for arbitrary quantum numbers n and l with two different values of the potential parameter {\\alpha}. It is found that our results are in good agreement with the those obtained by other methods for short potential range, small l and {\\alpha}. Two special cases are investigated like the s-wave case and Hulth\\'en potential case.
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 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.
An atmospheric backscatter model on wind measurements using far-field approximation method
Institute of Scientific and Technical Information of China (English)
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.
The information-based complexity of approximation problem by adaptive Monte Carlo methods
Institute of Scientific and Technical Information of China (English)
FANG GenSun; DUAN LiQin
2008-01-01
In this paper,we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MWTp,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.
Analytical Approximation Method for the Center Manifold in the Nonlinear Output Regulation Problem
Suzuki, Hidetoshi; Sakamoto, Noboru; Celikovský, Sergej
In nonlinear output regulation problems, it is necessary to solve the so-called regulator equations consisting of a partial differential equation and an algebraic equation. It is known that, for the hyperbolic zero dynamics case, solving the regulator equations is equivalent to calculating a center manifold for zero dynamics of the system. The present paper proposes a successive approximation method for obtaining center manifolds and shows its effectiveness by applying it for an inverted pendulum example.
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
12 CFR 571.25 - Reasonable and simple methods of opting out.
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... CREDIT REPORTING Affiliate Marketing § 571.25 Reasonable and simple methods of opting out. (a) In general... out, such as a form that can be electronically mailed or processed at an Internet Web site, if the... (15 U.S.C. 6801 et seq.), the affiliate sharing opt-out under the Act, and the affiliate marketing...
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Krochik, G. M.
1980-02-01
Stimulated Raman scattering of a randomly modulated pump is investigated by the method of successive approximations. This involves expanding solutions in terms of small parameters, which are ratios of the correlation scales of random effects to other characteristic dynamic scales of the problem. Systems of closed equations are obtained for the moments of the amplitudes of the Stokes and pump waves and of the molecular vibrations. These describe the dynamics of the process allowing for changes in the pump intensity and statistics due to a three-wave interaction. By analyzing equations in higher-order approximations, it is possible to establish the conditions of validity of the first (Markov) and second approximations. In particular, it is found that these are valid for pump intensities JL both above and below the critical value Jcr near which the gain begins to increase rapidly and reproduction of the pump spectrum by the Stokes wave is initiated. Solutions are obtained for average intensities of the Stokes wave and molecular vibrations in the first approximation in a constant pump field. It is established that, for JLgtrsimJcr, the Stokes wave undergoes rapid nonsteady-state amplification which is associated with an increase in the amplitude of the molecular vibrations. The results of the calculations show good agreement with known experimental data.
Application of asymptotic waveform approximation technique to hybrid FE/BI method for 3D scattering
Institute of Scientific and Technical Information of China (English)
PENG Zhen; SHENG XinQing
2007-01-01
The asymptotic waveform evaluation (AWE) technique is a rational function approximation method in computational mathematics, which is used in many applications in computational electromagnetics. In this paper, the performance of the AWE technique in conjunction with hybrid finite element/boundary integral (FE/BI) method is firstly investigated. The formulation of the AWE applied in hybrid FE/BI method is given in detail. The characteristic implementation of the application of the AWE to the hybrid FE/BI method is discussed. Numerical results demonstrate that the AWE technique can greatly speed up the hybrid FE/BI method to acquire wide-band and wide-angle backscatter radar-cross-section (RCS) by complex targets.
One Fairing Method of Cubic B-spline Curves Based on Weighted Progressive Iterative Approximation
Institute of Scientific and Technical Information of China (English)
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.
Approximation methods for a class of discrete Wiener-Hopf equations
Directory of Open Access Journals (Sweden)
Michał A. Nowak
2009-01-01
Full Text Available In this paper, we consider approximation methods for operator equations of the form \\[Au + Bu = f,\\] where \\(A\\ is a discrete Wiener-Hopf operator on \\(l_p\\ (\\(1 \\leq p \\lt \\infty\\ which symbol has roots on the unit circle with arbitrary multiplicities (not necessary integers. Conditions on perturbation \\(B\\ and \\(f\\ are given in order to guarantee the applicability of projection-iterative methods. Effective error estimates, and simultaneously, decaying properties for solutions are obtained in terms of some smooth spaces.
Exact and approximate interior corner problem in neutron diffusion by integral transform methods
Energy Technology Data Exchange (ETDEWEB)
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-Exact Penalty Function Method for Solving a Class of Stochastic Programming
Institute of Scientific and Technical Information of China (English)
Wang Guang-min; Wan Zhong-ping
2003-01-01
We present an approximation-exact penalty function method for solving the single stage stochastic programming problem with continuous random variable. The original problem is transformed into a determinate nonlinear programming problem with a discrete random variable sequence, which is obtained by some discrete method. We construct an exact penalty function and obtain an unconstrained optimization. It avoids the difficulty in solution by the rapid growing of the number of constraints for discrete precision. Under lenient conditions, we prove the equivalence of the minimum solution of penalty function and the solution of the determinate programming, and prove that the solution sequences of the discrete problem converge to a solution to the original problem.
Blasch, Erik; Kadar, Ivan; Salerno, John; Kokar, Mieczyslaw M.; Das, Subrata; Powell, Gerald M.; Corkill, Daniel D.; Ruspini, Enrique H.
2006-05-01
Situation assessment (SA) involves deriving relations among entities, e.g., the aggregation of object states (i.e. classification and location). While SA has been recognized in the information fusion and human factors literature, there still exist open questions regarding knowledge representation and reasoning methods to afford SA. For instance, while lots of data is collected over a region of interest, how does this information get presented to an attention constrained user? The information overload can deteriorate cognitive reasoning so a pragmatic solution to knowledge representation is needed for effective and efficient situation understanding. In this paper, we present issues associated with Level 2 (Situation Assessment) including: (1) user perception and perceptual reasoning representation, (2) knowledge discovery process models, (3) procedural versus logical reasoning about relationships, (4) user-fusion interaction through performance metrics, and (5) syntactic and semantic representations. While a definitive conclusion is not the aim of the paper, many critical issues are proposed in order to characterize future successful strategies to knowledge representation and reasoning strategies for situation assessment.
A simple method to approximate liver size on cross-sectional images using living liver models
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Muggli, D.; Mueller, M.A.; Karlo, C.; Fornaro, J.; Marincek, B. [Institute of Diagnostic Radiology, University Hospital of Zurich, Zurich (Switzerland); Frauenfelder, T. [Institute of Diagnostic Radiology, University Hospital of Zurich, Zurich (Switzerland)], E-mail: thomas.frauenfelder@usz.ch
2009-07-15
Aim: To assess whether a simple. diameter-based formula applicable to cross-sectional images can be used to calculate the total liver volume. Materials and methods: On 119 cross-sectional examinations (62 computed tomography and 57 magnetic resonance imaging) a simple, formula-based method to approximate the liver volume was evaluated. The total liver volume was approximated measuring the largest craniocaudal (cc), ventrodorsal (vd), and coronal (cor) diameters by two readers and implementing the equation: Vol{sub estimated}=ccxvdxcorx0.31. Inter-rater reliability, agreement, and correlation between liver volume calculation and virtual liver volumetry were analysed. Results: No significant disagreement between the two readers was found. The formula correlated significantly with the volumetric data (r > 0.85, p < 0.0001). In 81% of cases the error of the approximated volume was <10% and in 92% of cases <15% compared to the volumetric data. Conclusion: Total liver volume can be accurately estimated on cross-sectional images using a simple, diameter-based equation.
Babuska, Ivo
2010-01-01
The paper addresses a numerical method for solving second order elliptic partial differential equations that describe fields inside heterogeneous media. The scope is general and treats the case of rough coefficients, i.e. coefficients with values in $L^\\infty(\\Omega)$. This class of coefficients includes as examples media with micro-structure as well as media with multiple non-separated length scales. The approach taken here is based on the the generalized finite element method (GFEM) introduced in \\cite{107}, and elaborated in \\cite{102}, \\cite{103} and \\cite{104}. The GFEM is constructed by partitioning the computational domain $\\Omega$ into to a collection of preselected subsets $\\omega_{i},i=1,2,..m$ and constructing finite dimensional approximation spaces $\\Psi_{i}$ over each subset using local information. The notion of the Kolmogorov $n$-width is used to identify the optimal local approximation spaces. These spaces deliver local approximations with errors that decay almost exponentially with the degree...
Approximation by random weighting method for M-test in linear models
Institute of Scientific and Technical Information of China (English)
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.
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
Institute of Scientific and Technical Information of China (English)
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 new method for extraction of approximately vertical lines from natural images
Institute of Scientific and Technical Information of China (English)
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.
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.
Optimal motion planning of an underactuated spacecraft using wavelet approximate method
Institute of Scientific and Technical Information of China (English)
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.
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.
Directory of Open Access Journals (Sweden)
Stefan M. Stefanov
2014-01-01
Full Text Available We consider the data fitting problem, that is, the problem of approximating a function of several variables, given by tabulated data, and the corresponding problem for inconsistent (overdetermined systems of linear algebraic equations. Such problems, connected with measurement of physical quantities, arise, for example, in physics, engineering, and so forth. A traditional approach for solving these two problems is the discrete least squares data fitting method, which is based on discrete l2-norm. In this paper, an alternative approach is proposed: with each of these problems, we associate a nondifferentiable (nonsmooth unconstrained minimization problem with an objective function, based on discrete l1- and/or l∞-norm, respectively; that is, these two norms are used as proximity criteria. In other words, the problems under consideration are solved by minimizing the residual using these two norms. Respective subgradients are calculated, and a subgradient method is used for solving these two problems. The emphasis is on implementation of the proposed approach. Some computational results, obtained by an appropriate iterative method, are given at the end of the paper. These results are compared with the results, obtained by the iterative gradient method for the corresponding “differentiable” discrete least squares problems, that is, approximation problems based on discrete l2-norm.
Semantic Ontology Method of Learning Resource based on the Approximate Subgraph Isomorphism
Directory of Open Access Journals (Sweden)
Lili Zhang
2014-02-01
Full Text Available Digital learning resource ontology is often based on different specification building. It is hard to find resources by linguistic ontology matching method. The existing structural matching method fails to solve the problem of calculation of structural similarity well. For the heterogeneity problem among learning resource ontology, an algorithm is presented based on subgraph approximate isomorphism. First of all, we can preprocess the resource of clustering algorithm through the semantic analysis, then describe the ontology by the directed graph and calculate the similarity, and finally judge the semantic relations through calculating and analyzing different resource between the ontology of different learning resource to achieve semantic compatibility or mapping of ontology. This method is an extension of existing methods in ontology matching. Under the comprehensive application of features such as edit distance and hierarchical relations, the similarity of graph structures between two ontologies is calculated. And, the ontology matching is determined on the condition of subgraph approximate isomorphism based on the alternately mapping of nodes and arcs in the describing graphs of ontologies. An example is used to demonstrate this ontology matching process and the time complexity is analyzed to explain its effectiveness
Anda, E.; Chiappe, G.; Busser, C.; Davidovich, M.; Martins, G.; H-Meisner, F.; Dagotto, E.
2008-03-01
A numerical algorithm to study transport properties of highly correlated local structures is proposed. The method, dubbed the Logarithmic Discretization Embedded Cluster Approximation (LDECA), consists of diagonalizing a finite cluster containing the many-body terms of the Hamiltonian and embedding it into the rest of the system, combined with Wilson's ideas of a logarithmic discretization of the representation of the Hamiltonian. LDECA's rapid convergence eliminates finite-size effects commonly present in the embedding cluster approximation (ECA) method. The physics associated with both one embedded dot and a string of two dots side-coupled to leads is discussed. In the former case, our results accurately agree with Bethe ansatz (BA) data, while in the latter, the results are framed in the conceptual background of a two-stage Kondo problem. A diagrammatic expansion provides the theoretical foundation for the method. It is argued that LDECA allows for the study of complex problems that are beyond the reach of currently available numerical methods.
Directory of Open Access Journals (Sweden)
M. Scherstjanoi
2013-09-01
Full Text Available Models of vegetation dynamics that are designed for application at spatial scales larger than individual forest gaps suffer from several limitations. Typically, either a population average approximation is used that results in unrealistic tree allometry and forest stand structure, or models have a high computational demand because they need to simulate both a series of age-based cohorts and a number of replicate patches to account for stochastic gap-scale disturbances. The detail required by the latter method increases the number of calculations by two to three orders of magnitude compared to the less realistic population average approach. In an effort to increase the efficiency of dynamic vegetation models without sacrificing realism, we developed a new method for simulating stand-replacing disturbances that is both accurate and faster than approaches that use replicate patches. The GAPPARD (approximating GAP model results with a Probabilistic Approach to account for stand Replacing Disturbances method works by postprocessing the output of deterministic, undisturbed simulations of a cohort-based vegetation model by deriving the distribution of patch ages at any point in time on the basis of a disturbance probability. With this distribution, the expected value of any output variable can be calculated from the output values of the deterministic undisturbed run at the time corresponding to the patch age. To account for temporal changes in model forcing (e.g., as a result of climate change, GAPPARD performs a series of deterministic simulations and interpolates between the results in the postprocessing step. We integrated the GAPPARD method in the vegetation model LPJ-GUESS, and evaluated it in a series of simulations along an altitudinal transect of an inner-Alpine valley. We obtained results very similar to the output of the original LPJ-GUESS model that uses 100 replicate patches, but simulation time was reduced by approximately the factor 10
Simplified method for including spatial correlations in mean-field approximations
Markham, Deborah C.; Simpson, Matthew J.; Baker, Ruth E.
2013-06-01
Biological systems involving proliferation, migration, and death are observed across all scales. For example, they govern cellular processes such as wound healing, as well as the population dynamics of groups of organisms. In this paper, we provide a simplified method for correcting mean-field approximations of volume-excluding birth-death-movement processes on a regular lattice. An initially uniform distribution of agents on the lattice may give rise to spatial heterogeneity, depending on the relative rates of proliferation, migration, and death. Many frameworks chosen to model these systems neglect spatial correlations, which can lead to inaccurate predictions of their behavior. For example, the logistic model is frequently chosen, which is the mean-field approximation in this case. This mean-field description can be corrected by including a system of ordinary differential equations for pairwise correlations between lattice site occupancies at various lattice distances. In this work we discuss difficulties with this method and provide a simplification in the form of a partial differential equation description for the evolution of pairwise spatial correlations over time. We test our simplified model against the more complex corrected mean-field model, finding excellent agreement. We show how our model successfully predicts system behavior in regions where the mean-field approximation shows large discrepancies. Additionally, we investigate regions of parameter space where migration is reduced relative to proliferation, which has not been examined in detail before and find our method is successful at correcting the deviations observed in the mean-field model in these parameter regimes.
Car-Parrinello treatment for an approximate density-functional theory method.
Rapacioli, Mathias; Barthel, Robert; Heine, Thomas; Seifert, Gotthard
2007-03-28
The authors formulate a Car-Parrinello treatment for the density-functional-based tight-binding method with and without self-consistent charge corrections. This method avoids the numerical solution of the secular equations, the principal drawback for large systems if the linear combination of atomic orbital ansatz is used. The formalism is applicable to finite systems and for supercells using periodic boundary conditions within the Gamma-point approximation. They show that the methodology allows the application of modern computational techniques such as sparse matrix storage and massive parallelization in a straightforward way. All present bottlenecks concerning computer time and consumption of memory and memory bandwidth can be removed. They illustrate the performance of the method by direct comparison with Born-Oppenheimer molecular dynamics calculations. Water molecules, benzene, the C(60) fullerene, and liquid water have been selected as benchmark systems.
Sweilam, N. H.; Abou Hasan, M. M.
2016-08-01
This paper reports a new spectral algorithm for obtaining an approximate solution for the Lévy-Feller diffusion equation depending on Legendre polynomials and Chebyshev collocation points. The Lévy-Feller diffusion equation is obtained from the standard diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative. A new formula expressing explicitly any fractional-order derivatives, in the sense of Riesz-Feller operator, of Legendre polynomials of any degree in terms of Jacobi polynomials is proved. Moreover, the Chebyshev-Legendre collocation method together with the implicit Euler method are used to reduce these types of differential equations to a system of algebraic equations which can be solved numerically. Numerical results with comparisons are given to confirm the reliability of the proposed method for the Lévy-Feller diffusion equation.
Approximate restoration of translational and rotational symmetries within the Lipkin method
Gao, Y; Toivanen, P
2015-01-01
Background: Nuclear self-consistent mean-field approaches are rooted in the density functional theory and, through the spontaneous symmetry breaking mechanism, allow for including important correlations, while keeping the simplicity of the approach. Because real ground states should have all symmetries of the nuclear Hamiltonian, these methods require subsequent symmetry restoration. Purpose: We implement and study Lipkin method of approximate variation after projection applied to the restoration of the translational or rotational symmetries. Methods: We use Lipkin operators up to quadratic terms in momenta or angular momenta with self-consistently determined values of the Peierls-Yoccoz translational masses or moments of inertia, respectively. Calculations based on Skyrme energy-density functional are performed for heavy, deformed, and paired nuclei. Results: In deformed nuclei, the Peierls-Yoccoz translational masses along three different principal-axes directions of the intrinsic system can be different, w...
Anderson, David F
2011-01-01
A chemical reaction network is a chemical system involving multiple reactions and chemical species. The simplest stochastic models of such networks treat the system as a continuous time Markov chain with the state being the number of molecules of each species and with reactions modeled as possible transitions of the chain. In this paper we provide a general framework for understanding the weak error of numerical approximation techniques in this setting. For such models, there is typically a wide variation in scales in that the different species and reaction rates vary over several orders of magnitude. Quantifying how different numerical approximation techniques behave in this setting therefore requires that these scalings be taken into account in an appropriate manner. We quantify how the error of different methods depends upon both the natural scalings within a given system, and with the step-size of the numerical method. We show that Euler's method, also called explicit tau-leaping, acts as an order one met...
Institute of Scientific and Technical Information of China (English)
ZHANG Juliang; ZHANG Xiangsun
2002-01-01
A robust SQP method, which is analogous to Facchinei's algorithm, is intro duced. The algorithm is globally convergent. It uses automatic rules for choosing penalty parameter, and can efficiently cope with the possible inconsistency of the quadratic search subproblem. In addition, the algorithm employs a differentiable approximate exact penalty function as a merit function. Unlike the merit function in Facchinei's algorithm, which is quite complicated and is not easy to be implemented in practice, this new merit function is very simple. As a result, we can use the Facchinei's idea to construct an algorithm which is easy to be implemented in practice.
A Method for Generating Approximate Similarity Solutions of Nonlinear Partial Differential Equations
Directory of Open Access Journals (Sweden)
Mazhar Iqbal
2014-01-01
Full Text Available Standard application of similarity method to find solutions of PDEs mostly results in reduction to ODEs which are not easily integrable in terms of elementary or tabulated functions. Such situations usually demand solving reduced ODEs numerically. However, there are no systematic procedures available to utilize these numerical solutions of reduced ODE to obtain the solution of original PDE. A practical and tractable approach is proposed to deal with such situations and is applied to obtain approximate similarity solutions to different cases of an initial-boundary value problem of unsteady gas flow through a semi-infinite porous medium.
An Approximate Method for Analysis of Solitary Waves in Nonlinear Elastic Materials
Rushchitsky, J. J.; Yurchuk, V. N.
2016-05-01
Two types of solitary elastic waves are considered: a longitudinal plane displacement wave (longitudinal displacements along the abscissa axis of a Cartesian coordinate system) and a radial cylindrical displacement wave (displacements in the radial direction of a cylindrical coordinate system). The basic innovation is the use of nonlinear wave equations similar in form to describe these waves and the use of the same approximate method to analyze these equations. The distortion of the wave profile described by Whittaker (plane wave) or Macdonald (cylindrical wave) functions is described theoretically
An approximate factorization method for inverse medium scattering with unknown buried objects
Qu, Fenglong; Yang, Jiaqing; Zhang, Bo
2017-03-01
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous medium with different kinds of unknown buried objects inside. By constructing a sequence of operators which are small perturbations of the far-field operator in a suitable way, we prove that each operator in this sequence has a factorization satisfying the Range Identity. We then develop an approximate factorization method for recovering the support of the inhomogeneous medium from the far-field data. Finally, numerical examples are provided to illustrate the practicability of the inversion algorithm.
Niksic, Tamara; Tutis, Tea; Vretenar, Dario; Ring, Peter
2013-01-01
A new implementation of the finite amplitude method (FAM) for the solution of the relativistic quasiparticle random-phase approximation (RQRPA) is presented, based on the relativistic Hartree-Bogoliubov (RHB) model for deformed nuclei. The numerical accuracy and stability of the FAM -- RQRPA is tested in a calculation of the monopole response of $^{22}$O. As an illustrative example, the model is applied to a study of the evolution of monopole strength in the chain of Sm isotopes, including the splitting of the giant monopole resonance in axially deformed systems.
Non-approximate method for designing annular field of two-mirror concentric system
Institute of Scientific and Technical Information of China (English)
Yuanshen Huang; Dongyue Zhu; Baicheng Li; Dawei Zhang; Zhengji Ni; Songlin Zhuang
2012-01-01
Annular field aberrations of a three-reflection concentric system, which are composed of two spherical mirrors, are analyzed. An annular field with a high level of aberration correction exists near the position where the principal ray is perpendicular to the object-image plane. Aberrations are determined by the object height and aperture angle. In this letter, the general expression of the system aberration is derived using the geometric method, and the non-approximate design method is proposed to calculate the radii of the annular fields that have minimum aberrations under different aperture angles. The closer to 0.5 (the ratio of the radius of convex mirror to the radius of concave mirror) is, the smaller the system aberration is. The examples analyzed by LABVIEW indicate that the annular field designed by the proposed method has the smallest aberration in a given system.%Annular field aberrations of a three-reflection concentric system,which are composed of two spherical mirrors,are analyzed.An annular field with a high level of aberration correction exists near the position where the principal ray is perpendicular to the object-image plane.Aberrations are determined by the object height and aperture angle.In this letter,the general expression of the system aberration is derived using the geometric method,and the non-approximate design method is proposed to calculate the radii of the annular fields that have minimum aberrations under different aperture angles.The closer to 0.5 (the ratio of the radius of convex mirror to the radius of concave mirror) is,the smaller the system aberration is.The examples analyzed by LABVIEW indicate that the annular field designed by the proposed method has the smallest aberration in a given system.
Directory of Open Access Journals (Sweden)
Ji-ting Qu
2013-01-01
Full Text Available A new optimal method is presented by combining the weight coefficient with the theory of force analogy method. Firstly, a new mathematical model of location index is proposed, which deals with the determination of a reasonable number of dampers according to values of the location index. Secondly, the optimal locations of dampers are given. It can be specific from stories to spans. Numerical examples are illustrated to verify the effectiveness and feasibility of the proposed mathematical model and optimal method. At last, several significant conclusions are given based on numerical results.
Sakamoto, Noboru; Schaft, Arjan J. van der
2007-01-01
In this paper, an analytical approximation approach for the stabilizing solution of the Hamilton-Jacobi equation using stable manifold theory is proposed. The proposed method gives approximated flows on the stable manifold of the associated Hamiltonian system and provides approximations of the stabl
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Between the transformations, witch can transform the compressible wave equation to the incompressible flow, a kind of relativity character can be found, which have the almost equal character as Lorenz time and space relation. This result leads to a new inference: incompressible wave equation with time and space structure of sonic special relativity is only different description of approximate compressible flow. This conclusion can be extended to Euler equation, and arise the interest of "compressible expression" of Maxwell equation. To study the rule of compressibility and thermodynamic character of metastructure field, a try is made by the using KamanTsian virtual gas method, this would give the relation,similar as mass and energy of special relativity theory.At first searching a transformation, witch can transform the compressible wave equation to the incompressible flow, but it is almost equal Lorenz time and space relation, So arrive to the conclusion: incompressible wave equation with approximate Lorentz transformation is only different description of compressible flow. This conclusion is expected be used to Maxwell equation, because its wave equation is also perfectly equal form. To search the rule of electromagnet and gravity field, by the using of Kaman-Tsian virtual gas method, the relation of mass and energy of relativity theory is given.``
On the optimal polynomial approximation of stochastic PDEs by galerkin and collocation methods
Beck, Joakim
2012-09-01
In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by multivariate polynomials. We first consider the stochastic Galerkin method, and rely on sharp estimates for the decay of the Fourier coefficients of the spectral expansion of u on an orthogonal polynomial basis to build a sequence of polynomial subspaces that features better convergence properties, in terms of error versus number of degrees of freedom, than standard choices such as Total Degree or Tensor Product subspaces. We consider then the Stochastic Collocation method, and use the previous estimates to introduce a new class of Sparse Grids, based on the idea of selecting a priori the most profitable hierarchical surpluses, that, again, features better convergence properties compared to standard Smolyak or tensor product grids. Numerical results show the effectiveness of the newly introduced polynomial spaces and sparse grids. © 2012 World Scientific Publishing Company.
AGCD:a robust periodicity analysis method based on approximate greatest common divisor
Institute of Scientific and Technical Information of China (English)
Juan YU‡; Pei-zhong LU
2015-01-01
Periodicity is one of the most common phenomena in the physical world. The problem of periodicity analysis (or period detection) is a research topic in several areas, such as signal processing and data mining. However, period detection is a very challenging problem, due to the sparsity and noisiness of observational datasets of periodic events. This paper focuses on the problem of period detection from sparse and noisy observational datasets. To solve the problem, a novel method based on the approximate greatest common divisor (AGCD) is proposed. The proposed method is robust to sparseness and noise, and is eﬃcient. Moreover, unlike most existing methods, it does not need prior knowledge of the rough range of the period. To evaluate the accuracy and eﬃciency of the proposed method, comprehensive experiments on synthetic data are conducted. Experimental results show that our method can yield highly accurate results with small datasets, is more robust to sparseness and noise, and is less sensitive to the magnitude of period than compared methods.
Efficient Approximate Method of Global Reliability Analysis for Offshore Platforms in the Ice Zone
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Ice load is the dominative load in the design of offshore platforms in the ice zone, and the extreme ice load is the key factor that affects the safety of platforms. The present paper studies the statistical properties of the global resistance and the extreme responses of the jacket platforms in Bohai Bay, considering the randomness of ice load, dead load, steel elastic modulus, yield strength and structural member dimensions. Then, based on the above results, an efficient approximate method of the global reliability analysis for the offshore platforms is proposed, which converts the implicit nonlinear performance function in the conventional reliability analysis to linear explicit one. Finally, numerical examples of JZ20-2 MSW, JZ20-2NW and JZ20-2 MUQ offshore jacket platforms in the Bohai Bay demonstrate the satisfying efficiency, accuracy and applicability of the proposed method.
Approximate method for solving relaxation problems in terms of material`s damagability under creep
Energy Technology Data Exchange (ETDEWEB)
Nikitenko, A.F.; Sukhorukov, I.V.
1995-03-01
The technology of thermoforming under creep and superplasticity conditions is finding increasing application in machine building for producing articles of a preset shape. After a part is made there are residual stresses in it, which lead to its warping. To remove residual stresses, moulded articles are usually exposed to thermal fixation, i.e., the part is held in compressed state at a certain temperature. Thermal fixation is simply the process of residual stress relaxation, following by accumulation of total creep in the material. Therefore the necessity to develop engineering methods for calculating the time of thermal fixation and relaxation of residual stresses to a safe level, not resulting in warping, becomes evident. The authors present an approximate method of calculation of stress-strain rate of a body during relaxation. They use a system of equations which describes a material`s creep, simultaneously taking into account accumulation of damages in it.
Approximation of weak adjoints by reverse automatic differentiation of BDF methods
Beigel, Dörte; Wirsching, Leonard; Bock, Hans Georg
2011-01-01
With this contribution, we shed light on the relation between the discrete adjoints of multistep backward differentiation formula (BDF) methods and the solution of the adjoint differential equation. To this end, we develop a functional-analytic framework based on a constrained variational problem and introduce the notion of weak adjoint solutions. We devise a finite element Petrov-Galerkin interpretation of the BDF method together with its discrete adjoint scheme obtained by reverse internal numerical differentiation. We show how the finite element approximation of the weak adjoint is computed by the discrete adjoint scheme and prove its asymptotic convergence in the space of normalized functions of bounded variation. We also obtain asymptotic convergence of the discrete adjoints to the classical adjoints on the inner time interval. Finally, we give numerical results for non-adaptive and fully adaptive BDF schemes. The presented framework opens the way to carry over the existing theory on global error estimat...
A convergent mixed method for the Stokes approximation of viscous compressible flow
Karlsen, Kenneth
2009-01-01
We propose a mixed finite element method for the motion of a strongly viscous, ideal, and isentropic gas. At the boundary we impose a Navier-slip condition such that the velocity equation can be posed in mixed form with the vorticity as an auxiliary variable. In this formulation we design a finite element method, where the velocity and vorticity is approximated with the div- and curl- conforming Nedelec elements, respectively, of the first order and first kind. The mixed scheme is coupled to a standard piecewise constant upwind discontinuous Galerkin discretization of the continuity equation. For the time discretization, implicit Euler time stepping is used. Our main result is that the numerical solution converges to a weak solution as the discretization parameters go to zero. The convergence analysis is inspired by the continuous analysis of Feireisl and Lions for the compressible Navier-Stokes equations. Tools used in the analysis include an equation for the effective viscous flux and various renormalizatio...
Approximation-Exact Penalty Function Method for Solving a Class of Stochastic Programming
Institute of Scientific and Technical Information of China (English)
WangGuang-min; WanZhong-ping
2003-01-01
We present an approximation-exact penalty function method for solving the single stage stochastic programming problem with continuous random variable. The original problem is transformed into a determinate nonlinear programming problem with a discrete random variable sequence, which is obtained by some discrete method. We construct an exact penalty function and obtain an unconstrained optimization. It avoids the difficulty in solution by the rapid growing of the number of constraints for discrete precision.Under lenient conditions, we prove the equivalence of the minimum solution of penalty function and the solution of the determinate programming, and prove that the solution sequences of the discrete problem converge to a solution to the original problem.
Communication: An efficient analytic gradient theory for approximate spin projection methods
Hratchian, Hrant P.
2013-03-01
Spin polarized and broken symmetry density functional theory are popular approaches for treating the electronic structure of open shell systems. However, spin contamination can significantly affect the quality of predicted geometries and properties. One scheme for addressing this concern in studies involving broken-symmetry states is the approximate projection method developed by Yamaguchi and co-workers. Critical to the exploration of potential energy surfaces and the study of properties using this method will be an efficient analytic gradient theory. This communication introduces such a theory formulated, for the first time, within the framework of general post-self consistent field (SCF) derivative theory. Importantly, the approach taken here avoids the need to explicitly solve for molecular orbital derivatives of each nuclear displacement perturbation, as has been used in a recent implementation. Instead, the well-known z-vector scheme is employed and only one SCF response equation is required.
Kaporin, I. E.
2012-02-01
In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.
About the Generalized Reasoning Methods and their Use in Semiotic Systems
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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.
Jiang, Lijian
2009-10-02
The use of limited global information in multiscale simulations is needed when there is no scale separation. Previous approaches entail fine-scale simulations in the computation of the global information. The computation of the global information is expensive. In this paper, we propose the use of approximate global information based on partial upscaling. A requirement for partial homogenization is to capture long-range (non-local) effects present in the fine-scale solution, while homogenizing some of the smallest scales. The local information at these smallest scales is captured in the computation of basis functions. Thus, the proposed approach allows us to avoid the computations at the scales that can be homogenized. This results in coarser problems for the computation of global fields. We analyze the convergence of the proposed method. Mathematical formalism is introduced, which allows estimating the errors due to small scales that are homogenized. The proposed method is applied to simulate two-phase flows in heterogeneous porous media. Numerical results are presented for various permeability fields, including those generated using two-point correlation functions and channelized permeability fields from the SPE Comparative Project (Christie and Blunt, SPE Reserv Evalu Eng 4:308-317, 2001). We consider simple cases where one can identify the scales that can be homogenized. For more general cases, we suggest the use of upscaling on the coarse grid with the size smaller than the target coarse grid where multiscale basis functions are constructed. This intermediate coarse grid renders a partially upscaled solution that contains essential non-local information. Numerical examples demonstrate that the use of approximate global information provides better accuracy than purely local multiscale methods. © 2009 Springer Science+Business Media B.V.
Scherstjanoi, M.; Kaplan, J. O.; Lischke, H.
2014-07-01
To be able to simulate climate change effects on forest dynamics over the whole of Switzerland, we adapted the second-generation DGVM (dynamic global vegetation model) LPJ-GUESS (Lund-Potsdam-Jena General Ecosystem Simulator) to the Alpine environment. We modified model functions, tuned model parameters, and implemented new tree species to represent the potential natural vegetation of Alpine landscapes. Furthermore, we increased the computational efficiency of the model to enable area-covering simulations in a fine resolution (1 km) sufficient for the complex topography of the Alps, which resulted in more than 32 000 simulation grid cells. To this aim, we applied the recently developed method GAPPARD (approximating GAP model results with a Probabilistic Approach to account for stand Replacing Disturbances) (Scherstjanoi et al., 2013) to LPJ-GUESS. GAPPARD derives mean output values from a combination of simulation runs without disturbances and a patch age distribution defined by the disturbance frequency. With this computationally efficient method, which increased the model's speed by approximately the factor 8, we were able to faster detect the shortcomings of LPJ-GUESS functions and parameters. We used the adapted LPJ-GUESS together with GAPPARD to assess the influence of one climate change scenario on dynamics of tree species composition and biomass throughout the 21st century in Switzerland. To allow for comparison with the original model, we additionally simulated forest dynamics along a north-south transect through Switzerland. The results from this transect confirmed the high value of the GAPPARD method despite some limitations towards extreme climatic events. It allowed for the first time to obtain area-wide, detailed high-resolution LPJ-GUESS simulation results for a large part of the Alpine region.
Pavlyuchenkov, Ya; Henning, T; Guilloteau, St; Pietu, V; Launhardt, R; Dutrey, A
2007-01-01
We analyze the line radiative transfer in protoplanetary disks using several approximate methods and a well-tested Accelerated Monte Carlo code. A low-mass flaring disk model with uniform as well as stratified molecular abundances is adopted. Radiative transfer in low and high rotational lines of CO, C18O, HCO+, DCO+, HCN, CS, and H2CO is simulated. The corresponding excitation temperatures, synthetic spectra, and channel maps are derived and compared to the results of the Monte Carlo calculations. A simple scheme that describes the conditions of the line excitation for a chosen molecular transition is elaborated. We find that the simple LTE approach can safely be applied for the low molecular transitions only, while it significantly overestimates the intensities of the upper lines. In contrast, the Full Escape Probability (FEP) approximation can safely be used for the upper transitions ($J_{\\rm up} \\ga 3$) but it is not appropriate for the lowest transitions because of the maser effect. In general, the molec...
Werner, Hans-Joachim
2016-11-01
The accuracy of multipole approximations for distant pair energies in local second-order Møller-Plesset perturbation theory (LMP2) as introduced by Hetzer et al. [Chem. Phys. Lett. 290, 143 (1998)] is investigated for three chemical reactions involving molecules with up to 92 atoms. Various iterative and non-iterative approaches are compared, using different energy thresholds for distant pair selection. It is demonstrated that the simple non-iterative dipole-dipole approximation, which has been used in several recent pair natural orbitals (PNO)-LMP2 and PNO-LCCSD (local coupled-cluster with singles and doubles) methods, may underestimate the distant pair energies by up to 50% and can lead to significant errors in relative energies, unless very tight thresholds are used. The accuracy can be much improved by including higher multipole orders and by optimizing the distant pair amplitudes iteratively along with all other amplitudes. A new approach is presented in which very small special PNO domains for distant pairs are used in the iterative approach. This reduces the number of distant pair amplitudes by 3 orders of magnitude and keeps the additional computational effort for the iterative optimization of distant pair amplitudes minimal.
Approximate analytic method for high-apogee twelve-hour orbits of artificial Earth's satellites
Vashkovyaka, M. A.; Zaslavskii, G. S.
2016-09-01
We propose an approach to the study of the evolution of high-apogee twelve-hour orbits of artificial Earth's satellites. We describe parameters of the motion model used for the artificial Earth's satellite such that the principal gravitational perturbations of the Moon and Sun, nonsphericity of the Earth, and perturbations from the light pressure force are approximately taken into account. To solve the system of averaged equations describing the evolution of the orbit parameters of an artificial satellite, we use both numeric and analytic methods. To select initial parameters of the twelve-hour orbit, we assume that the path of the satellite along the surface of the Earth is stable. Results obtained by the analytic method and by the numerical integration of the evolving system are compared. For intervals of several years, we obtain estimates of oscillation periods and amplitudes for orbital elements. To verify the results and estimate the precision of the method, we use the numerical integration of rigorous (not averaged) equations of motion of the artificial satellite: they take into account forces acting on the satellite substantially more completely and precisely. The described method can be applied not only to the investigation of orbit evolutions of artificial satellites of the Earth; it can be applied to the investigation of the orbit evolution for other planets of the Solar system provided that the corresponding research problem will arise in the future and the considered special class of resonance orbits of satellites will be used for that purpose.
An extragradient-like approximation method for variational inequalities and fixed point problems
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Wong Ngai-Ching
2011-01-01
Full Text Available Abstract The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mapping in the intermediate sense and the set of solutions of a variational inequality problem for a monotone and Lipschitz continuous mapping. We introduce an extragradient-like iterative algorithm that is based on the extragradient-like approximation method and the modified Mann iteration process. We establish a strong convergence theorem for two sequences generated by this extragradient-like iterative algorithm. Utilizing this theorem, we also design an iterative process for finding a common fixed point of two mappings, one of which is an asymptotically strict pseudocontractive mapping in the intermediate sense and the other taken from the more general class of Lipschitz pseudocontractive mappings. 1991 MSC: 47H09; 47J20.
Approximation methods of European option pricing in multiscale stochastic volatility model
Ni, Ying; Canhanga, Betuel; Malyarenko, Anatoliy; Silvestrov, Sergei
2017-01-01
In the classical Black-Scholes model for financial option pricing, the asset price follows a geometric Brownian motion with constant volatility. Empirical findings such as volatility smile/skew, fat-tailed asset return distributions have suggested that the constant volatility assumption might not be realistic. A general stochastic volatility model, e.g. Heston model, GARCH model and SABR volatility model, in which the variance/volatility itself follows typically a mean-reverting stochastic process, has shown to be superior in terms of capturing the empirical facts. However in order to capture more features of the volatility smile a two-factor, of double Heston type, stochastic volatility model is more useful as shown in Christoffersen, Heston and Jacobs [12]. We consider one modified form of such two-factor volatility models in which the volatility has multiscale mean-reversion rates. Our model contains two mean-reverting volatility processes with a fast and a slow reverting rate respectively. We consider the European option pricing problem under one type of the multiscale stochastic volatility model where the two volatility processes act as independent factors in the asset price process. The novelty in this paper is an approximating analytical solution using asymptotic expansion method which extends the authors earlier research in Canhanga et al. [5, 6]. In addition we propose a numerical approximating solution using Monte-Carlo simulation. For completeness and for comparison we also implement the semi-analytical solution by Chiarella and Ziveyi [11] using method of characteristics, Fourier and bivariate Laplace transforms.
Esophageal cancer prediction based on qualitative features using adaptive fuzzy reasoning method
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Raed I. Hamed
2015-04-01
Full Text Available Esophageal cancer is one of the most common cancers world-wide and also the most common cause of cancer death. In this paper, we present an adaptive fuzzy reasoning algorithm for rule-based systems using fuzzy Petri nets (FPNs, where the fuzzy production rules are represented by FPN. We developed an adaptive fuzzy Petri net (AFPN reasoning algorithm as a prognostic system to predict the outcome for esophageal cancer based on the serum concentrations of C-reactive protein and albumin as a set of input variables. The system can perform fuzzy reasoning automatically to evaluate the degree of truth of the proposition representing the risk degree value with a weight value to be optimally tuned based on the observed data. In addition, the implementation process for esophageal cancer prediction is fuzzily deducted by the AFPN algorithm. Performance of the composite model is evaluated through a set of experiments. Simulations and experimental results demonstrate the effectiveness and performance of the proposed algorithms. A comparison of the predictive performance of AFPN models with other methods and the analysis of the curve showed the same results with an intuitive behavior of AFPN models.
Diffusion approximation-based simulation of stochastic ion channels: which method to use?
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Danilo ePezo
2014-11-01
Full Text Available To study the effects of stochastic ion channel fluctuations on neural dynamics, several numerical implementation methods have been proposed. Gillespie’s method for Markov Chains (MC simulation is highly accurate, yet it becomes computationally intensive in the regime of high channel numbers. Many recent works aim to speed simulation time using the Langevin-based Diffusion Approximation (DA. Under this common theoretical approach, each implementation differs in how it handles various numerical difficulties – such as bounding of state variables to [0,1]. Here we review and test a set of the most recently published DA implementations (Dangerfield et al., 2012; Linaro et al., 2011; Huang et al., 2013a; Orio and Soudry, 2012; Schmandt and Galán, 2012; Goldwyn et al., 2011; Güler, 2013, comparing all of them in a set of numerical simulations that asses numerical accuracy and computational efficiency on three different models: the original Hodgkin and Huxley model, a model with faster sodium channels, and a multi-compartmental model inspired in granular cells. We conclude that for low channel numbers (usually below 1000 per simulated compartment one should use MC – which is both the most accurate and fastest method. For higher channel numbers, we recommend using the method by Orio and Soudry (2012, possibly combined with the method by Schmandt and Galán (2012 for increased speed and slightly reduced accuracy. Consequently, MC modelling may be the best method for detailed multicompartment neuron models – in which a model neuron with many thousands of channels is segmented into many compartments with a few hundred channels.
逻辑系统L*中基于Г-演绎真度的近似推理%Approximate Reasoning Based onΓ-deduction Truth Degree in L* Logic System
Institute of Scientific and Technical Information of China (English)
郝国平; 惠小静; 赵玛瑙
2015-01-01
This paper introduces theΓ-deduction truth degree of formulas in L* logic system at first. Based onΓ-deduction truth degree, this paper definesΓ-deduction similarity degree and pseudo distance, and discusses some basic properties. Then this paper defines three different types of approximate reasoning models in L* logical system, and conducts a detailed analysis on the relationship between three different types of approximate reasoning models ofΓ-deduction truth degree. Finally, three types of approximate reasoning models are equivalent. The research in this paper lays a good foundation for further research on the divergence and compatibility ofΓ-deduction truth degree and approximate reasoning.%在逻辑系统L*中引入了公式Γ-演绎真度的概念，在Γ-演绎真度的基础上，定义了Γ-演绎相似度与伪距离，并讨论了它的一些基本性质。接着在逻辑系统L*中定义了3种不同类型的近似推理模式，对Γ-演绎真度的3种不同类型的近似推理模式之间的关系进行了详细的研究，结果表明这3种不同类型近似推理模式是等价的。通过对这些理论的研究，为进一步研究基于Γ-演绎真度的发散度、相容度和近似推理奠定了良好的基础。
Wu, Kun; Zhang, Feng; Min, Jinzhong; Yu, Qiu-Run; Wang, Xin-Yue; Ma, Leiming
2016-09-01
The adding method, which could calculate the infrared radiative transfer (IRT) in inhomogeneous atmosphere with multiple layers, has been applied to δ -four-stream discrete ordinate method (DOM). This scheme is referred as δ -4DDA. However, there is a lack of application for adding method of δ -four-stream spherical harmonic expansion approximation (SHM) to solve infrared radiative transfer through multiple layers. In this paper, the adding method for δ -four-stream SHM (δ -4SDA) will be obtained and the accuracy of it will be evaluated as well. The result of δ -4SDA in an idealized medium with homogeneous optical property is significantly more accurate than that of the adding method for δ -two-stream DOM (δ -2DDA). The relative errors of δ -2DDA can be over 15% in thin optical depths for downward emissivity, while errors of δ -4SDA are bounded by 2%. However, the result of δ -4SDA is slightly less accurate than that of δ -4DDA. In a radiation model with realistic atmospheric profile considering gaseous transmission, the accuracy for heating rate of δ -4SDA is significantly superior than that of δ -2DDA, especially for the cloudy sky. The accuracy for heating rate of δ -4SDA is slightly less accurate than that of δ -4DDA under water cloud conditions, while it is superior than that of δ -4DDA in ice cloud cases. Beside, the computational efficiency of δ -4SDA is higher than that of δ -4DDA.
Edwards, Kyle T
2014-07-01
In recent years, liberal democratic societies have struggled with the question of how best to balance expertise and democratic participation in the regulation of emerging technologies. This study aims to explain how national deliberative ethics committees handle the practical tension between scientific expertise, ethical expertise, expert patient input, and lay public input by explaining two institutions' processes for determining the legitimacy or illegitimacy of reasons in public policy decision-making: that of the United Kingdom's Human Fertilisation and Embryology Authority (HFEA) and the United States' American Society for Reproductive Medicine (ASRM). The articulation of these 'methods of legitimation' draws on 13 in-depth interviews with HFEA and ASRM members and staff conducted in January and February 2012 in London and over Skype, as well as observation of an HFEA deliberation. This study finds that these two institutions employ different methods in rendering certain arguments legitimate and others illegitimate: while the HFEA attempts to 'balance' competing reasons but ultimately legitimizes arguments based on health and welfare concerns, the ASRM seeks to 'filter' out arguments that challenge reproductive autonomy. The notably different structures and missions of each institution may explain these divergent approaches, as may what Sheila Jasanoff (2005) terms the distinctive 'civic epistemologies' of the US and the UK. Significantly for policy makers designing such deliberative committees, each method differs substantially from that explicitly or implicitly endorsed by the institution.
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.
Linguistic hesitant fuzzy multi-criteria decision-making method based on evidential reasoning
Zhou, Huan; Wang, Jian-qiang; Zhang, Hong-yu; Chen, Xiao-hong
2016-01-01
Linguistic hesitant fuzzy sets (LHFSs), which can be used to represent decision-makers' qualitative preferences as well as reflect their hesitancy and inconsistency, have attracted a great deal of attention due to their flexibility and efficiency. This paper focuses on a multi-criteria decision-making approach that combines LHFSs with the evidential reasoning (ER) method. After reviewing existing studies of LHFSs, a new order relationship and Hamming distance between LHFSs are introduced and some linguistic scale functions are applied. Then, the ER algorithm is used to aggregate the distributed assessment of each alternative. Subsequently, the set of aggregated alternatives on criteria are further aggregated to get the overall value of each alternative. Furthermore, a nonlinear programming model is developed and genetic algorithms are used to obtain the optimal weights of the criteria. Finally, two illustrative examples are provided to show the feasibility and usability of the method, and comparison analysis with the existing method is made.
Albrecht, Andreas A; Day, Luke; Abdelhadi Ep Souki, Ouala; Steinhöfel, Kathleen
2016-02-01
The analysis of energy landscapes plays an important role in mathematical modelling, simulation and optimisation. Among the main features of interest are the number and distribution of local minima within the energy landscape. Granier and Kallel proposed in 2002 a new sampling procedure for estimating the number of local minima. In the present paper, we focus on improved heuristic implementations of the general framework devised by Granier and Kallel with regard to run-time behaviour and accuracy of predictions. The new heuristic method is demonstrated for the case of partial energy landscapes induced by RNA secondary structures. While the computation of minimum free energy RNA secondary structures has been studied for a long time, the analysis of folding landscapes has gained momentum over the past years in the context of co-transcriptional folding and deeper insights into cell processes. The new approach has been applied to ten RNA instances of length between 99 nt and 504 nt and their respective partial energy landscapes defined by secondary structures within an energy offset ΔE above the minimum free energy conformation. The number of local minima within the partial energy landscapes ranges from 1440 to 3441. Our heuristic method produces for the best approximations on average a deviation below 3.0% from the true number of local minima.
Improved locality-sensitive hashing method for the approximate nearest neighbor problem
Lu, Ying-Hua; Ma, Ting-Huai; Zhong, Shui-Ming; Cao, Jie; Wang, Xin; Abdullah, Al-Dhelaan
2014-08-01
In recent years, the nearest neighbor search (NNS) problem has been widely used in various interesting applications. Locality-sensitive hashing (LSH), a popular algorithm for the approximate nearest neighbor problem, is proved to be an efficient method to solve the NNS problem in the high-dimensional and large-scale databases. Based on the scheme of p-stable LSH, this paper introduces a novel improvement algorithm called randomness-based locality-sensitive hashing (RLSH) based on p-stable LSH. Our proposed algorithm modifies the query strategy that it randomly selects a certain hash table to project the query point instead of mapping the query point into all hash tables in the period of the nearest neighbor query and reconstructs the candidate points for finding the nearest neighbors. This improvement strategy ensures that RLSH spends less time searching for the nearest neighbors than the p-stable LSH algorithm to keep a high recall. Besides, this strategy is proved to promote the diversity of the candidate points even with fewer hash tables. Experiments are executed on the synthetic dataset and open dataset. The results show that our method can cost less time consumption and less space requirements than the p-stable LSH while balancing the same recall.
Miura, Shinichi; Okazaki, Susumu
2001-09-01
In this paper, the path integral molecular dynamics (PIMD) method has been extended to employ an efficient approximation of the path action referred to as the pair density matrix approximation. Configurations of the isomorphic classical systems were dynamically sampled by introducing fictitious momenta as in the PIMD based on the standard primitive approximation. The indistinguishability of the particles was handled by a pseudopotential of particle permutation that is an extension of our previous one [J. Chem. Phys. 112, 10 116 (2000)]. As a test of our methodology for Boltzmann statistics, calculations have been performed for liquid helium-4 at 4 K. We found that the PIMD with the pair density matrix approximation dramatically reduced the computational cost to obtain the structural as well as dynamical (using the centroid molecular dynamics approximation) properties at the same level of accuracy as that with the primitive approximation. With respect to the identical particles, we performed the calculation of a bosonic triatomic cluster. Unlike the primitive approximation, the pseudopotential scheme based on the pair density matrix approximation described well the bosonic correlation among the interacting atoms. Convergence with a small number of discretization of the path achieved by this approximation enables us to construct a method of avoiding the problem of the vanishing pseudopotential encountered in the calculations by the primitive approximation.
Bayesian network modeling method based on case reasoning for emergency decision-making
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XU Lei
2013-06-01
Full Text Available Bayesian network has the abilities of probability expression, uncertainty management and multi-information fusion.It can support emergency decision-making, which can improve the efficiency of decision-making.Emergency decision-making is highly time sensitive, which requires shortening the Bayesian Network modeling time as far as possible.Traditional Bayesian network modeling methods are clearly unable to meet that requirement.Thus, a Bayesian network modeling method based on case reasoning for emergency decision-making is proposed.The method can obtain optional cases through case matching by the functions of similarity degree and deviation degree.Then,new Bayesian network can be built through case adjustment by case merging and pruning.An example is presented to illustrate and test the proposed method.The result shows that the method does not have a huge search space or need sample data.The only requirement is the collection of expert knowledge and historical case models.Compared with traditional methods, the proposed method can reuse historical case models, which can reduce the modeling time and improve the efficiency.
Heats of Segregation of BCC Metals Using Ab Initio and Quantum Approximate Methods
Good, Brian; Chaka, Anne; Bozzolo, Guillermo
2003-01-01
Many multicomponent alloys exhibit surface segregation, in which the composition at or near a surface may be substantially different from that of the bulk. A number of phenomenological explanations for this tendency have been suggested, involving, among other things, differences among the components' surface energies, molar volumes, and heats of solution. From a theoretical standpoint, the complexity of the problem has precluded a simple, unified explanation, thus preventing the development of computational tools that would enable the identification of the driving mechanisms for segregation. In that context, we investigate the problem of surface segregation in a variety of bcc metal alloys by computing dilute-limit heats of segregation using both the quantum-approximate energy method of Bozzolo, Ferrante and Smith (BFS), and all-electron density functional theory. In addition, the composition dependence of the heats of segregation is investigated using a BFS-based Monte Carlo procedure, and, for selected cases of interest, density functional calculations. Results are discussed in the context of a simple picture that describes segregation behavior as the result of a competition between size mismatch and alloying effects
Wang, S.; Zhang, X. N.; Gao, D. D.; Liu, H. X.; Ye, J.; Li, L. R.
2016-08-01
As the solar photovoltaic (PV) power is applied extensively, more attentions are paid to the maintenance and fault diagnosis of PV power plants. Based on analysis of the structure of PV power station, the global partitioned gradually approximation method is proposed as a fault diagnosis algorithm to determine and locate the fault of PV panels. The PV array is divided into 16x16 blocks and numbered. On the basis of modularly processing of the PV array, the current values of each block are analyzed. The mean current value of each block is used for calculating the fault weigh factor. The fault threshold is defined to determine the fault, and the shade is considered to reduce the probability of misjudgments. A fault diagnosis system is designed and implemented with LabVIEW. And it has some functions including the data realtime display, online check, statistics, real-time prediction and fault diagnosis. Through the data from PV plants, the algorithm is verified. The results show that the fault diagnosis results are accurate, and the system works well. The validity and the possibility of the system are verified by the results as well. The developed system will be benefit for the maintenance and management of large scale PV array.
On the enhancement of the approximation order of triangular Shepard method
Dell'Accio, Francesco; Di Tommaso, Filomena; Hormann, Kai
2016-10-01
Shepard's method is a well-known technique for interpolating large sets of scattered data. The classical Shepard operator reconstructs an unknown function as a normalized blend of the function values at the scattered points, using the inverse distances to the scattered points as weight functions. Based on the general idea of defining interpolants by convex combinations, Little suggested to extend the bivariate Shepard operator in two ways. On the one hand, he considers a triangulation of the scattered points and substitutes function values with linear polynomials which locally interpolate the given data at the vertices of each triangle. On the other hand, he modifies the classical point-based weight functions and defines instead a normalized blend of the locally interpolating polynomials with triangle-based weight functions which depend on the product of inverse distances to the three vertices of the corresponding triangle. The resulting triangular Shepard operator interpolates all data required for its definition and reproduces polynomials up to degree 1, whereas the classical Shepard operator reproduces only constants, and has quadratic approximation order. In this paper we discuss an improvement of the triangular Shepard operator.
Garvie, Marcus R; Burkardt, John; Morgan, Jeff
2015-03-01
We describe simple finite element schemes for approximating spatially extended predator-prey dynamics with the Holling type II functional response and logistic growth of the prey. The finite element schemes generalize 'Scheme 1' in the paper by Garvie (Bull Math Biol 69(3):931-956, 2007). We present user-friendly, open-source MATLAB code for implementing the finite element methods on arbitrary-shaped two-dimensional domains with Dirichlet, Neumann, Robin, mixed Robin-Neumann, mixed Dirichlet-Neumann, and Periodic boundary conditions. Users can download, edit, and run the codes from http://www.uoguelph.ca/~mgarvie/ . In addition to discussing the well posedness of the model equations, the results of numerical experiments are presented and demonstrate the crucial role that habitat shape, initial data, and the boundary conditions play in determining the spatiotemporal dynamics of predator-prey interactions. As most previous works on this problem have focussed on square domains with standard boundary conditions, our paper makes a significant contribution to the area.
Institute of Scientific and Technical Information of China (English)
BAI Yu-Lin; CHENG Xiao-Hong; CHEN Xiang-Rong; YANG Xiang-Dong; ZHU Jun
2004-01-01
@@ The intermolecular interactions potentials for two configurations of CH4-Ne complex are calculated with local density approximation methods in the frame of density functional theory. It is found that the calculated potentials have two minima when the distance between the carbon atom of CH4 and the Ne atom takes R = 5.80 a.u.and 6.20a. u. for both the two configurations. For the edge configuration, the corresponding depth of the potential is 0.0669536 eV and 0.0671416 eV. For the face configuration, the corresponding depth of the potential is 0.0737956 eV and 0.0645506 eV. The global minimum occurs at R = 5.80 a.u. for the face configuration with a depth of the potential 0.0737956 eV. The depths of our calculation are in better agreement with the experimental data than the quantum chemical calculation approach, while the position of minimum potential for our calculation is underestimated.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Hernandez, A.; Belendez, T.; Neipp, C.; Marquez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-03-17
He's homotopy perturbation method is used to calculate higher-order approximate periodic solutions of a nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(x). We find He's homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate period of less than 1.56% for all values of oscillation amplitude, while this relative error is 0.30% for the second iteration and as low as 0.057% when the third-order approximation is considered. Comparison of the result obtained using this method with those obtained by different harmonic balance methods reveals that He's homotopy perturbation method is very effective and convenient.
Gadella, M; Negro, J
2016-01-01
We compare three different methods to obtain solutions of Sturm-Liouville problems: a successive approximation method and two other iterative methods. We look for solutions with periodic or anti periodic boundary conditions. With some numerical test over the Mathieu equation, we compare the efficiency of these three methods. As an application, we make a numerical analysis on a model for carbon nanotubes.
A simple, approximate method for analysis of Kerr-Newman black hole dynamics and thermodynamics
Directory of Open Access Journals (Sweden)
Panković V.
2009-01-01
Full Text Available In this work we present a simple approximate method for analysis of the basic dynamical and thermodynamical characteristics of Kerr-Newman black hole. Instead of the complete dynamics of the black hole self-interaction, we consider only the stable (stationary dynamical situations determined by condition that the black hole (outer horizon 'circumference' holds the integer number of the reduced Compton wave lengths corresponding to mass spectrum of a small quantum system (representing the quantum of the black hole self-interaction. Then, we show that Kerr-Newman black hole entropy represents simply the ratio of the sum of static part and rotation part of the mass of black hole on one hand, and the ground mass of small quantum system on the other hand. Also we show that Kerr-Newman black hole temperature represents the negative value of the classical potential energy of gravitational interaction between a part of black hole with reduced mass and a small quantum system in the ground mass quantum state. Finally, we suggest a bosonic great canonical distribution of the statistical ensemble of given small quantum systems in the thermodynamical equilibrium with (macroscopic black hole as thermal reservoir. We suggest that, practically, only the ground mass quantum state is significantly degenerate while all the other, excited mass quantum states, are non-degenerate. Kerr-Newman black hole entropy is practically equivalent to the ground mass quantum state degeneration. Given statistical distribution admits a rough (qualitative but simple modeling of Hawking radiation of the black hole too.
Institute of Scientific and Technical Information of China (English)
崔美华
2012-01-01
利用赋值集的随机化方法,在n值Lukasiewicz命题逻辑系统中引入公式的随机真度,证明了随机真度的MP规则、HS规则及交推理规则；同时引入公式间的随机相似度和随机伪距离,建立了随机逻辑度量空间,推导出随机相似度的若干性质,证明了随机逻辑度量空间中逻辑运算的连续性；并在随机逻辑度量空间中提出了三种不同类型的近似推理模式,证明了三种近似推理模式的等价性.%Using the randomization method of valuation set, the concept of randomized truth degree of formulas is introduced into n-valued Lukasiewicz propositional logic system. The MP rule, HS rule and meet inference rules of randomized truth degree are proved. At the meantime, the concept of randomized similarity and randomized pseudo-distances between formulas are introduced and the randomized logic metric space is bmilt. Several properties of randomized similarity are deduced to prove the continuity of logical operations in this space. Three different types of approximate reasoning patterns are introduced in randomized logic metric space. And they are proved to be equivalent.
Directory of Open Access Journals (Sweden)
Ai-Min Yang
2014-01-01
Full Text Available The Fourier law of one-dimensional heat conduction equation in fractal media is investigated in this paper. An approximate solution to one-dimensional local fractional Volterra integral equation of the second kind, which is derived from the transformation of Fourier flux equation in discontinuous media, is considered. The Picard successive approximation method is applied to solve the temperature field based on the given Mittag-Leffler-type Fourier flux distribution in fractal media. The nondifferential approximate solutions are given to show the efficiency of the present method.
Stochastic approximation methods for fusion-rule estimation in multiple sensor systems
Energy Technology Data Exchange (ETDEWEB)
Rao, N.S.V.
1994-06-01
A system of N sensors S{sub 1}, S{sub 2},{hor_ellipsis},S{sub N} is considered; corresponding to an object with parameter x {element_of} {Re}{sup d}, sensor S{sub i} yields output y{sup (i)}{element_of}{Re}{sup d} according to an unknown probability distribution p{sub i}(y{sup (i)}{vert_bar}x). A training l-sample (x{sub 1}, y{sub 1}), (x{sub 2}, y{sub 2}),{hor_ellipsis},(x{sub l}, y{sub l}) is given where y{sub i} = (y{sub i}({sup 1}), y{sub i}({sup 2}),{hor_ellipsis},y{sub i}({sup N}) and y{sub i}({sup j}) is the output of S{sub j} in response to input X{sub i}. The problem is to estimate a fusion rule f : {Re}{sup Nd} {yields} {Re}{sup d}, based on the sample, such that the expected square error I(f) = {integral}[x {minus} f(y{sup 1}, y{sup 2},{hor_ellipsis},y{sup N})]{sup 2} p(y{sup 1}, y{sup 2},{hor_ellipsis},y{sup N}){vert_bar}x)p(x)dy{sup 1}dy{sup 2} {hor_ellipsis} dy{sup N}dx is to be minimized over a family of fusion rules {lambda} based on the given l-sample. Let f{sub *} {element_of} {lambda} minimize I(f); f{sub *} cannot be computed since the underlying probability distributions are unknown. Three stochastic approximation methods are presented to compute {cflx f}, such that under suitable conditions, for sufficiently large sample, P[I{cflx f} {minus} I(f{sub *}) > {epsilon}] < {delta} for arbitrarily specified {epsilon} > 0 and {delta}, 0 < {delta} < 1. The three methods are based on Robbins-Monro style algorithms, empirical risk minimization, and regression estimation algorithms.
Research on conflict resolution of collaborative design with fuzzy case-based reasoning method
Institute of Scientific and Technical Information of China (English)
HOU Jun-ming; SU Chong; LIANG Shuang; WANG Wan-shan
2009-01-01
Collaborative design is a new style for modern mechanical design to meet the requirement of increasing competition. Designers of different places complete the same work, but the conflict appears in the process of design which may interface the design. Case-based reasoning (CBR) method is applied to the problem of conflict resolution, which is in the artificial intelligence field. However, due to the uncertainties in knowledge representation, attribute description, and similarity measures of CBR, it is very difficult to find the similar cases from case database. A fuzzy CBR method was proposed to solve the problem of conflict resolution in collaborative design. The process of fuzzy CBR was introduced. Based on the feature attributes and their relative weights determined by a fuzzy technique, a fuzzy CBR retrieving mechanism was developed to retrieve conflict resolution cases that tend to enhance the functions of the database. By indexing, calculating the weight and defuzzicating of the cases, the case similarity can be obtained. Then the case consistency was measured to keep the right result. Finally, the fuzzy CBR method for conflict resolution was demonstrated by means of a case study. The prototype system based on web is developed to illustrate the methodology.
Michel, Volker
2013-01-01
Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author’s lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets. Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth’s or the brain’s interior. Specific topics covered include: * the advantages and disadvantages of Fourier, spline, and wavelet methods * theory and numerics of orthogonal polynomials on intervals, spheres, and balls * cubic splines and splines based on reproducing kernels * multiresolution analysis using wavelet...
Optimal approximation method to characterize the resource trade-off functions for media servers
Chang, Ray-I.
1999-08-01
We have proposed an algorithm to smooth the transmission of the pre-recorded VBR media stream. It takes O(n) time complexity, where n is large, this algorithm is not suitable for online resource management and admission control in media servers. To resolve this drawback, we have explored the optimal tradeoff among resources by an O(nlogn) algorithm. Based on the pre-computed resource tradeoff function, the resource management and admission control procedure is as simple as table hashing. However, this approach requires O(n) space to store and maintain the resource tradeoff function. In this paper, while giving some extra resources, a linear-time algorithm is proposed to approximate the resource tradeoff function by piecewise line segments. We can prove that the number of line segments in the obtained approximation function is minimized for the given extra resources. The proposed algorithm has been applied to approximate the bandwidth-buffer-tradeoff function of the real-world Star War movie. While an extra 0.1 Mbps bandwidth is given, the storage space required for the approximation function is over 2000 times smaller than that required for the original function. While an extra 10 KB buffer is given, the storage space for the approximation function is over 2200 over times smaller than that required for the original function. The proposed algorithm is really useful for resource management and admission control in real-world media servers.
Strömberg, Eric A; Nyberg, Joakim; Hooker, Andrew C
2016-12-01
With the increasing popularity of optimal design in drug development it is important to understand how the approximations and implementations of the Fisher information matrix (FIM) affect the resulting optimal designs. The aim of this work was to investigate the impact on design performance when using two common approximations to the population model and the full or block-diagonal FIM implementations for optimization of sampling points. Sampling schedules for two example experiments based on population models were optimized using the FO and FOCE approximations and the full and block-diagonal FIM implementations. The number of support points was compared between the designs for each example experiment. The performance of these designs based on simulation/estimations was investigated by computing bias of the parameters as well as through the use of an empirical D-criterion confidence interval. Simulations were performed when the design was computed with the true parameter values as well as with misspecified parameter values. The FOCE approximation and the Full FIM implementation yielded designs with more support points and less clustering of sample points than designs optimized with the FO approximation and the block-diagonal implementation. The D-criterion confidence intervals showed no performance differences between the full and block diagonal FIM optimal designs when assuming true parameter values. However, the FO approximated block-reduced FIM designs had higher bias than the other designs. When assuming parameter misspecification in the design evaluation, the FO Full FIM optimal design was superior to the FO block-diagonal FIM design in both of the examples.
von Davier, Matthias; Sinharay, Sandip
2009-01-01
This paper presents an application of a stochastic approximation EM-algorithm using a Metropolis-Hastings sampler to estimate the parameters of an item response latent regression model. Latent regression models are extensions of item response theory (IRT) to a 2-level latent variable model in which covariates serve as predictors of the…
Deniz, Furkan Nur; Alagoz, Baris Baykant; Tan, Nusret; Atherton, Derek P
2016-05-01
This paper introduces an integer order approximation method for numerical implementation of fractional order derivative/integrator operators in control systems. The proposed method is based on fitting the stability boundary locus (SBL) of fractional order derivative/integrator operators and SBL of integer order transfer functions. SBL defines a boundary in the parametric design plane of controller, which separates stable and unstable regions of a feedback control system and SBL analysis is mainly employed to graphically indicate the choice of controller parameters which result in stable operation of the feedback systems. This study reveals that the SBL curves of fractional order operators can be matched with integer order models in a limited frequency range. SBL fitting method provides straightforward solutions to obtain an integer order model approximation of fractional order operators and systems according to matching points from SBL of fractional order systems in desired frequency ranges. Thus, the proposed method can effectively deal with stability preservation problems of approximate models. Illustrative examples are given to show performance of the proposed method and results are compared with the well-known approximation methods developed for fractional order systems. The integer-order approximate modeling of fractional order PID controllers is also illustrated for control applications.
Institute of Scientific and Technical Information of China (English)
白振东; 刘虎; 柴雪; 武哲
2008-01-01
为提高飞机多学科优化效率,对气动近似计算模型进行了改进.在比值修正模型所构造的气动近似模型的基础上,引入了基于实例的推理技术对其加以改进.通过采用与飞机气动特性相关的参数作为实例属性,建立了飞机方案实例,并改进了实例检索公式,最后通过复用与当前方案最相似实例的修正因子改进了优化中的气动近似模型.以常规布局民用飞机概念设计为例,采用改进的气动近似模型进行了多学科优化研究.结果表明,对于具有大量设计变量的飞机方案优化问题,采用改进的气动近似模型能够有效提高计算精度与优化效率.%To increase the efficiency of the muhidisciplinary optimization of aircraft,an aerodynamic approximation model is improved.Based on the study of aerodynamic approximation model constructed by the scaling correction model,case-based reasoning technique is introduced to improve the approximation model for optimization.The aircraft case model is constructed by utilizing the plane parameters related to aerodynamic characteristics as attributes of cases,and the formula of case retrieving is improved.Finally,the aerodynamic approximation model for optimization is improved by reusing the correction factors of the most similar aircraft to the current one.The muhidisciplinary optimization of a civil aircraft concept is carried out with the improved aerodynamic approximation model.The results demonstrate that the precision and the efficiency of the optimization can be improved by utilizing the improved aerodynamic approximation model with case-based reasoning technique.
Erhard, Jannis; Bleiziffer, Patrick; Görling, Andreas
2016-09-01
A power series approximation for the correlation kernel of time-dependent density-functional theory is presented. Using this approximation in the adiabatic-connection fluctuation-dissipation (ACFD) theorem leads to a new family of Kohn-Sham methods. The new methods yield reaction energies and barriers of unprecedented accuracy and enable a treatment of static (strong) correlation with an accuracy of high-level multireference configuration interaction methods but are single-reference methods allowing for a black-box-like handling of static correlation. The new methods exhibit a better scaling of the computational effort with the system size than rivaling wave-function-based electronic structure methods. Moreover, the new methods do not suffer from the problem of singularities in response functions plaguing previous ACFD methods and therefore are applicable to any type of electronic system.
A Diffusion Approximation and Numerical Methods for Adaptive Neuron Models with Stochastic Inputs.
Rosenbaum, Robert
2016-01-01
Characterizing the spiking statistics of neurons receiving noisy synaptic input is a central problem in computational neuroscience. Monte Carlo approaches to this problem are computationally expensive and often fail to provide mechanistic insight. Thus, the field has seen the development of mathematical and numerical approaches, often relying on a Fokker-Planck formalism. These approaches force a compromise between biological realism, accuracy and computational efficiency. In this article we develop an extension of existing diffusion approximations to more accurately approximate the response of neurons with adaptation currents and noisy synaptic currents. The implementation refines existing numerical schemes for solving the associated Fokker-Planck equations to improve computationally efficiency and accuracy. Computer code implementing the developed algorithms is made available to the public.
Institute of Scientific and Technical Information of China (English)
HU Xian-lei; ZHANG Qi-sheng; ZHAO Zhong; TIAN Yong; LIU Xiang-hua; WANG Guo-dong
2006-01-01
The influence of positive bending system on plate crown control was researched. The approximation full-load distribution method for pass scheduling was put forward. This method can not only make full use of the mill capacity with decreased pass number, but also give quality product of excellent flatness.
Silver nanodisks: optical properties study using the discrete dipole approximation method.
Brioude, A; Pileni, M P
2005-12-15
The simulated optical properties of silver nanodisks are presented. The extinction, absorption, and scattering efficiencies are calculated using the discrete dipole approximation. The influence of the nanodisk size, truncature (snip), aspect ratio, and environment on the plasmon resonance bands is investigated. In particular, the dipolar and multipolar resonance peak positions have been related to the specific features of the nanodisk geometry. An interpretation of the origins of each multipolar mode is proposed for the first time taking into account this geometry.
Banks, H. T.; Smith, Ralph C.; Wang, Yun
1994-01-01
Based on a distributed parameter model for vibrations, an approximate finite dimensional dynamic compensator is designed to suppress vibrations (multiple modes with a broad band of frequencies) of a circular plate with Kelvin-Voigt damping and clamped boundary conditions. The control is realized via piezoceramic patches bonded to the plate and is calculated from information available from several pointwise observed state variables. Examples from computational studies as well as use in laboratory experiments are presented to demonstrate the effectiveness of this design.
Approximation of conformal mapping via the Szeg\\H{o} kernel method
Pritsker, Igor E.
2013-01-01
We study the uniform approximation of the canonical conformal mapping, for a Jordan domain onto the unit disk, by polynomials generated from the partial sums of the Szeg\\H{o} kernel expansion. These polynomials converge to the conformal mapping uniformly on the closure of any Smirnov domain. We prove estimates for the rate of such convergence on domains with piecewise analytic boundaries, expressed through the smallest exterior angle at the boundary. Furthermore, we show that the rate of appr...
Identifying reasons for delays in acute hospitals using the Day-of-Care Survey method.
Reid, Erica; King, Andrew; Mathieson, Alex; Woodcock, Thomas; Watkin, Simon W
2015-04-01
This paper describes a new tool called 'Day-of-Care Survey', developed to assess inpatient delays in acute hospitals. Using literature review, iterative testing and feedback from professional groups, a national multidisciplinary team developed the survey criteria and methodology. Review teams working in pairs visited wards and used case records and bedside charts to assess the patient's status against severity of illness and service intensity criteria. Patients who did not meet the survey criteria for acute care were identified and delays were categorised. From March 2012 to December 2013, nine acute hospitals across Scotland, Australia and England were surveyed. A total of 3,846 adult general inpatient beds (excluding intensive care and maternity) were reviewed. There were 145 empty beds at the time of surveys across the nine sites, with 270 definite discharges planned on the day of the survey. The total number of patients not meeting criteria for acute care was 798/3,431 (23%, range 18-28%). Six factors accounted for 61% (490/798) of the reasons why patients not meeting acute care criteria remained in hospital. This survey gives important insights into the challenges of managing inpatient flow using system level information as a method to target interventions designed to address delay.
Mugunthan, Pradeep; Shoemaker, Christine A.; Regis, Rommel G.
2005-11-01
The performance of function approximation (FA) methods is compared to heuristic and derivative-based nonlinear optimization methods for automatic calibration of biokinetic parameters of a groundwater bioremediation model of chlorinated ethenes on a hypothetical and a real field case. For the hypothetical case, on the basis of 10 trials on two different objective functions, the FA methods had the lowest mean and smaller deviation of the objective function among all algorithms for a combined Nash-Sutcliffe objective and among all but the derivative-based algorithm for a total squared error objective. The best algorithms in the hypothetical case were applied to calibrate eight parameters to data obtained from a site in California. In three trials the FA methods outperformed heuristic and derivative-based methods for both objective functions. This study indicates that function approximation methods could be a more efficient alternative to heuristic and derivative-based methods for automatic calibration of computationally expensive bioremediation models.
Intelligent design of investment casting mold based on a hybrid reasoning method
Institute of Scientific and Technical Information of China (English)
Jiang Ruisong; Zhang Dinghua; Wang Wenhu; Bu Kun
2009-01-01
A hybrid reasoning model was proposed in which CBR (case-based reasoning) was applied to the conceptual design and RBR (rule-based reasoning) was applied to the detailed design after research of the design process and domain knowledge of the acre-engine turbine blade investment casting mold design field. In the conceptual design stage, the representation and retrieval technologies were researched which improve the retrieval efficiency. Meanwhile, RBR was used to modify the retrieval result. The experimentation shows that the approach in this study can be used to obtain a more satisfactory design result.
Non-Equilibrium Liouville and Wigner Equations: Moment Methods and Long-Time Approximations
Directory of Open Access Journals (Sweden)
Ramon F. Álvarez-Estrada
2014-03-01
Full Text Available We treat the non-equilibrium evolution of an open one-particle statistical system, subject to a potential and to an external “heat bath” (hb with negligible dissipation. For the classical equilibrium Boltzmann distribution, Wc,eq, a non-equilibrium three-term hierarchy for moments fulfills Hermiticity, which allows one to justify an approximate long-time thermalization. That gives partial dynamical support to Boltzmann’s Wc,eq, out of the set of classical stationary distributions, Wc;st, also investigated here, for which neither Hermiticity nor that thermalization hold, in general. For closed classical many-particle systems without hb (by using Wc,eq, the long-time approximate thermalization for three-term hierarchies is justified and yields an approximate Lyapunov function and an arrow of time. The largest part of the work treats an open quantum one-particle system through the non-equilibrium Wigner function, W. Weq for a repulsive finite square well is reported. W’s (< 0 in various cases are assumed to be quasi-definite functionals regarding their dependences on momentum (q. That yields orthogonal polynomials, HQ,n(q, for Weq (and for stationary Wst, non-equilibrium moments, Wn, of W and hierarchies. For the first excited state of the harmonic oscillator, its stationary Wst is a quasi-definite functional, and the orthogonal polynomials and three-term hierarchy are studied. In general, the non-equilibrium quantum hierarchies (associated with Weq for the Wn’s are not three-term ones. As an illustration, we outline a non-equilibrium four-term hierarchy and its solution in terms of generalized operator continued fractions. Such structures also allow one to formulate long-time approximations, but make it more difficult to justify thermalization. For large thermal and de Broglie wavelengths, the dominant Weq and a non-equilibrium equation for W are reported: the non-equilibrium hierarchy could plausibly be a three-term one and possibly not
A Second Order Nonconforming Rectangular Finite Element Method for Approximating Maxwell's Equations
Institute of Scientific and Technical Information of China (English)
Dong-yang SHI; Xiao-bin HAO
2011-01-01
The main objective of this paper is to present a new rectangular nonconforming finite element scheme with the second order convergence behavior for approximation of Maxwell's equations.Then the corresponding optimal error estimates are derived.The difficulty in construction of this finite element scheme is how to choose a compatible pair of degrees of freedom and shape function space so as to make the consistency error due to the nonconformity of the element being of order O(h3),properly one order higher than that of its interpolation error O(h2) in the broken energy norm,where h is the subdivision parameter tending to zero.
AN APPROXIMATION METHOD TO ESTIMATE THE HAUSDORFF MEASURE OF THE SIERPINSKI GASKET
Institute of Scientific and Technical Information of China (English)
Ruan Huojun; Su Weiyi
2004-01-01
In this paper, we firstly define a decreasing sequence {Pn(S)} by the generation of the Sierpinski gasket where each pn(S) can be obtained in finite steps. Then we prove that the Hausdorff measure Hs(S)of the Sierpinski gasket S can be approximated by {Pn(S)} with Pn(S)/(1 + 1/2n-3)s ≤ Hs(S) ≤ pn(S).An algorithm is presented to get Pn(S) for n ≤ 5. As an application, we obtain the best lower bound of Hs(S) till now: Hs(S) ≥ 0.5631.
Methods and tools for simplified dynamic simulations in real time based on expression approximation
Directory of Open Access Journals (Sweden)
Štefan M.
2007-10-01
Full Text Available The core of this paper is the methodology of the dynamicalmodels’ simplification for the real time simulation. The simplified simulation models are based on neuro-fuzzymodelling approach, which was originally designed for predictive control-orientedmodelling of nonlinear dynamical systems. The two ways of the neuro-fuzzymodelling utilization are presented. First, the training of the predictive dynamical neuro-fuzzymodel and, second, the training of the statical approximation of the right-hand side of the system’s state space description. We demonstrate the results on the examples of nonlinear spring damper system and double pendulum.
DEFF Research Database (Denmark)
Eriksen, Janus Juul; Solanko, Lukasz Michal; Nåbo, Lina J.;
2014-01-01
2) wave function coupled to PCM, we introduce dynamical PCM solvent effects only in the Random Phase Approximation (RPA) part of the SOPPA response equations while the static solvent contribution is kept in both the RPA terms as well as in the higher order correlation matrix components of the SOPPA...... functional theory employing a range-separated exchange-correlation functional, we find the PCM-SOPPA/RPA approach to be slightly superior with respect to systematicity. On the other hand, the absolute values of the predicted excitation energies are largely underestimated. This – however – is a well...
Mohammadpour, Mozhdeh; Jamshidi, Zahra
2016-05-01
The prospect of challenges in reproducing and interpretation of resonance Raman properties of molecules interacting with metal clusters has prompted the present research initiative. Resonance Raman spectra based on the time-dependent gradient approximation are examined in the framework of density functional theory using different methods for representing the exchange-correlation functional. In this work the performance of different XC functionals in the prediction of ground state properties, excitation state energies, and gradients are compared and discussed. Resonance Raman properties based on time-dependent gradient approximation for the strongly low-lying charge transfer states are calculated and compared for different methods. We draw the following conclusions: (1) for calculating the binding energy and ground state geometry, dispersion-corrected functionals give the best performance in comparison to ab initio calculations, (2) GGA and meta GGA functionals give good accuracy in calculating vibrational frequencies, (3) excited state energies determined by hybrid and range-separated hybrid functionals are in good agreement with EOM-CCSD calculations, and (4) in calculating resonance Raman properties GGA functionals give good and reasonable performance in comparison to the experiment; however, calculating the excited state gradient by using the hybrid functional on the hessian of GGA improves the results of the hybrid functional significantly. Finally, we conclude that the agreement of charge-transfer surface enhanced resonance Raman spectra with experiment is improved significantly by using the excited state gradient approximation.
Multi-Scaling Sampling: An Adaptive Sampling Method for Discovering Approximate Association Rules
Institute of Scientific and Technical Information of China (English)
Cai-Yan Jia; Xie-Ping Gao
2005-01-01
One of the obstacles of the efficient association rule mining is the explosive expansion of data sets since it is costly or impossible to scan large databases, esp., for multiple times. A popular solution to improve the speed and scalability of the association rule mining is to do the algorithm on a random sample instead of the entire database. But how to effectively define and efficiently estimate the degree of error with respect to the outcome of the algorithm, and how to determine the sample size needed are entangling researches until now. In this paper, an effective and efficient algorithm is given based on the PAC (Probably Approximate Correct) learning theory to measure and estimate sample error. Then, a new adaptive, on-line, fast sampling strategy - multi-scaling sampling - is presented inspired by MRA (Multi-Resolution Analysis) and Shannon sampling theorem, for quickly obtaining acceptably approximate association rules at appropriate sample size. Both theoretical analysis and empirical study have showed that the sampling strategy can achieve a very good speed-accuracy trade-off.
Bisetti, Fabrizio
2012-06-01
Recent trends in hydrocarbon fuel research indicate that the number of species and reactions in chemical kinetic mechanisms is rapidly increasing in an effort to provide predictive capabilities for fuels of practical interest. In order to cope with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix. The components of the approach are described in detail and applied to the ignition of stoichiometric methane-air and iso-octane-air mixtures, here described by two widely adopted chemical kinetic mechanisms. The approach is found to be robust even at relatively large time steps and the global error displays a nominal third-order convergence. The performance of the approach is improved by utilising an adaptive algorithm for the selection of the Krylov subspace size, which guarantees an approximation to the matrix exponential within user-defined error tolerance. The Krylov projection of the Jacobian matrix onto a low-dimensional space is interpreted as a local model reduction with a well-defined error control strategy. Finally, the performance of the approach is discussed with regard to the optimal selection of the parameters governing the accuracy of its individual components. © 2012 Copyright Taylor and Francis Group, LLC.
Gökdoğan, Ahmet; Merdan, Mehmet; Yildirim, Ahmet
2012-01-01
The goal of this study is presented a reliable algorithm based on the standard differential transformation method (DTM), which is called the multi-stage differential transformation method (MsDTM) for solving Hantavirus infection model. The results obtanied by using MsDTM are compared to those obtained by using the Runge-Kutta method (R-K-method). The proposed technique is a hopeful tool to solving for a long time intervals in this kind of systems.
Directory of Open Access Journals (Sweden)
Norhasimah Mahiddin
2014-01-01
Full Text Available The modified decomposition method (MDM and homotopy perturbation method (HPM are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis. The study highlights the significant features of the employed methods and their ability to handle nonlinear partial differential equations. The methods do not need linearization and weak nonlinearity assumptions. Although the main difference between MDM and Adomian decomposition method (ADM is a slight variation in the definition of the initial condition, modification eliminates massive computation work. The approximate analytical solution obtained by MDM logically contains the solution obtained by HPM. It shows that HPM does not involve the Adomian polynomials when dealing with nonlinear problems.
Bailey, Harry E.; Beam, Richard M.
1991-01-01
Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.
Energy Technology Data Exchange (ETDEWEB)
Mitchell, J.S.B. [State Univ. of New York, Stony Brook, NY (United States)
1996-12-31
We show that any rectilinear polygonal subdivision in the plane can be converted into a {open_quotes}guillotine{close_quote} subdivision whose length is at most twice that of the original subdivision. {open_quote}Guillotine{close_quotes} subdivisions have a simple recursive structure that allows one to search for {open_quotes}optimal{close_quotes} such subdivisions in polynomial time, using dynamic programming. In particular, a consequence of our main theorem is a very simple proof that the k-MST problem in the plane has a constant factor polynomial-time approximation algorithm, and the constant factor that we obtain is a substantial improvement over all previous bounds: We obtain a factor of 2 for the L{sub 1} metric, and a factor of 2{radical}2 for the L{sub 2} (Euclidean) metric.
Energy Technology Data Exchange (ETDEWEB)
Kim, S. [Purdue Univ., West Lafayette, IN (United States)
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
Institute of Scientific and Technical Information of China (English)
Fan-wen Meng; Hui-fu Xu
2006-01-01
In this paper, we propose a Sample Average Approximation (SAA) method for a class of Stochastic Mathematical Programs with Complementarity Constraints (SMPCC) recently SAA estimators. In particular we show that under moderate conditions a sequence of weak stationary points of SAA programs converge to a weak stationary point of the true problem with probability approaching one at exponential rate as the sample size tends to infinity.To implement the SAA method more efficiently, we incorporate the method with some techniques such as Scholtes' regularization method and the well known smoothing NCP method. Some preliminary numerical results are reported.
Approximate Solutions of Fractional Riccati Equations Using the Adomian Decomposition Method
Directory of Open Access Journals (Sweden)
Fei Wu
2014-01-01
Full Text Available The fractional derivative equation has extensively appeared in various applied nonlinear problems and methods for finding the model become a popular topic. Very recently, a novel way was proposed by Duan (2010 to calculate the Adomian series which is a crucial step of the Adomian decomposition method. In this paper, it was used to solve some fractional nonlinear differential equations.
Directory of Open Access Journals (Sweden)
J. Prakash
2016-03-01
Full Text Available In this paper, a numerical algorithm based on a modified He-Laplace method (MHLM is proposed to solve space and time nonlinear fractional differential-difference equations (NFDDEs arising in physical phenomena such as wave phenomena in fluids, coupled nonlinear optical waveguides and nanotechnology fields. The modified He-Laplace method is a combined form of the fractional homotopy perturbation method and Laplace transforms method. The nonlinear terms can be easily decomposed by the use of He’s polynomials. This algorithm has been tested against time-fractional differential-difference equations such as the modified Lotka Volterra and discrete (modified KdV equations. The proposed scheme grants the solution in the form of a rapidly convergent series. Three examples have been employed to illustrate the preciseness and effectiveness of the proposed method. The achieved results expose that the MHLM is very accurate, efficient, simple and can be applied to other nonlinear FDDEs.
Champagnat, Nicolas; Faou, Erwan
2010-01-01
We propose extensions and improvements of the statistical analysis of distributed multipoles (SADM) algorithm put forth by Chipot et al. in [6] for the derivation of distributed atomic multipoles from the quantum-mechanical electrostatic potential. The method is mathematically extended to general least-squares problems and provides an alternative approximation method in cases where the original least-squares problem is computationally not tractable, either because of its ill-posedness or its high-dimensionality. The solution is approximated employing a Monte Carlo method that takes the average of a random variable defined as the solutions of random small least-squares problems drawn as subsystems of the original problem. The conditions that ensure convergence and consistency of the method are discussed, along with an analysis of the computational cost in specific instances.
Directory of Open Access Journals (Sweden)
Neeraj Tiwari
2014-06-01
Full Text Available Under inclusion probability proportional to size (IPPS sampling, the exact secondorder inclusion probabilities are often very difficult to obtain, and hence variance of the Horvitz- Thompson estimator and Sen-Yates-Grundy estimate of the variance of Horvitz-Thompson estimator are difficult to compute. Hence the researchers developed some alternative variance estimators based on approximations of the second-order inclusion probabilities in terms of the first order inclusion probabilities. We have numerically compared the performance of the various alternative approximate variance estimators using the split method of sample selection
Directory of Open Access Journals (Sweden)
Ali Sevimlican
2010-01-01
Full Text Available He's variational iteration method (VIM is used for solving space and time fractional telegraph equations. Numerical examples are presented in this paper. The obtained results show that VIM is effective and convenient.
2013-01-01
Mathematical modeling of amperometric biosensor with cyclic reaction is discussed. Analytical expressions pertaining to the concentration of substrate, cosubstrate, reducing agent and medial product and current for hybrid enzyme biosensor are obtained in terms of Thiele module and saturation parameters. In this paper, a powerful analytical method, called homotopy analysis method (HAM) is used to solve the system of nonlinear differential equations. Furthermore, in this work the numerical simu...
DEFF Research Database (Denmark)
Kimiaeifar, Amin; Lund, Erik; Thomsen, Ole Thybo;
2010-01-01
In this work, an analytical method, which is referred to as Parameter-expansion Method is used to obtain the exact solution for the problem of nonlinear vibrations of an inextensible beam. It is shown that one term in the series expansion is sufficient to obtain a highly accurate solution, which ...... is valid for the whole domain of the problem. A comparison of the obtained the numerical solution demonstrates that PEM is effective and convenient for solving such problems. After validation of the obtained results, the system response and stability are also discussed....
An Approximate Method for Calculation of Fluid Force and Response of A Circular Cylinder at Lock-in
Institute of Scientific and Technical Information of China (English)
WANG Yi
2008-01-01
In this paper, equations calculating lift force of a rigid circular cylinder at lock-in in uniform flow are deduced in detail. Besides, equations calculating the lift force on a long flexible circular cylinder at lock-in are deduced based on mode analysis of a multi-degree freedom system. The simplified forms of these equations are also given. Furthermore, an approximate method to predict the forces and response of rigid circular cylinders and long flexible circular cylinders at lock-in is introduced in the case of low mass-damping ratio. A method to eliminate one deficiency of these equations is introduced. Comparison with experimental results shows the effectiveness of this approximate method.
An approximate 3D computational method for real-time computation of induction logging responses
Bensdorp, S.; Petersen, S.A.; Van den Berg, P.M.; Fokkema, J.T.
2014-01-01
Over many years, induction logging systems have been used to create well formation logs. The major drawback for the utilization of these tools is the long simulation time for a single forward computation. We proposed an efficient computational method based on a contrast-type of integral-equation for
Approximation for Transient of Nonlinear Circuits Using RHPM and BPES Methods
Directory of Open Access Journals (Sweden)
H. Vazquez-Leal
2013-01-01
Full Text Available The microelectronics area constantly demands better and improved circuit simulation tools. Therefore, in this paper, rational homotopy perturbation method and Boubaker Polynomials Expansion Scheme are applied to a differential equation from a nonlinear circuit. Comparing the results obtained by both techniques revealed that they are effective and convenient.
Directory of Open Access Journals (Sweden)
Grigis A
2006-01-01
Full Text Available A method for determination and two methods for approximation of the domain of attraction Da(0 of the asymptotically stable zero steady state of an autonomous, ℝ-analytical, discrete dynamical system are presented. The method of determination is based on the construction of a Lyapunov function V, whose domain of analyticity is Da(0. The first method of approximation uses a sequence of Lyapunov functions Vp, which converge to the Lyapunov function V on Da(0. Each Vp defines an estimate Np of Da(0. For any x ∈ Da(0, there exists an estimate which contains x. The second method of approximation uses a ball B(R ⊂ Da(0 which generates the sequence of estimates Mp = f-p(B(R. For any x ∈ Da(0, there exists an estimate which contains x. The cases ||∂0f||<1 and ρ(∂0f < 1 ≤||∂0f|| are treated separately because significant differences occur.
Diversity effect in category-based inductive reasoning of young children: evidence from two methods.
Zhong, Luojin; Lee, Myung Sook; Huang, Yulan; Mo, Lei
2014-02-01
Previous studies have shown that diverse pieces of evidence, rather than similar pieces of evidence, are considered to have greater strength in adults' inductive reasoning. However, this diversity effect is inconsistently recognized by children. Three experiments using the same materials but different tasks examined whether young children consider the diversity principle in their reasoning. Although Experiment 1 applied a data selection task showed five-year-old children in both China and Korea were not sensitive to the diversity of evidence, Experiments 2 and 3 employed an identification task and demonstrated that children as young as five years were sensitive to diverse evidence. These findings indicated that young children, less than nine years of age, may have diversity effect. Methodological and cultural differences were discussed.
Entropy Viscosity Method for High-Order Approximations of Conservation Laws
Guermond, J. L.
2010-09-17
A stabilization technique for conservation laws is presented. It introduces in the governing equations a nonlinear dissipation function of the residual of the associated entropy equation and bounded from above by a first order viscous term. Different two-dimensional test cases are simulated - a 2D Burgers problem, the "KPP rotating wave" and the Euler system - using high order methods: spectral elements or Fourier expansions. Details on the tuning of the parameters controlling the entropy viscosity are given. © 2011 Springer.
Energy Technology Data Exchange (ETDEWEB)
Marino, Ines P. [Nonlinear Dynamics and Chaos Group, Departamento de Matematicas y Fisica Aplicadas y Ciencias de la Naturaleza, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid (Spain)]. E-mail: ines.perez@urjc.es; Miguez, Joaquin [Departamento de Teoria de la Senal y Comunicaciones, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganes, Madrid (Spain)]. E-mail: jmiguez@ieee.org
2006-03-06
We address the problem of estimating the unknown parameters of a primary chaotic system that produces an observed time series. These observations are used to drive a secondary system in a way that ensures synchronization when the two systems have identical parameters. We propose a new method to adaptively adjust the parameters in the secondary system until synchronization is achieved. It is based on the gradient-descent optimization of a suitably defined cost function and can be systematically applied to arbitrary systems. We illustrate its application by estimating the complete parameter vector of a Lorenz system.
NAGAYAMA,Shinobu; Sasao, Tsutomu; BUTLER,Jon T.
2006-01-01
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E89-A, No.12, Dec. 2006, pp.3510-3518,Special Section on VLSI Design and CAD Algorithms. This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. As such, it is in the public domain, and under the provisions of Title 17, United States Code, Section 105, may not be copyrighted. This paper presents an architecture and a synthesis method for compac...
Backman, Ylva; Gardelli, Viktor
2015-01-01
In this study, the age-old distinction between decision method and criterion of rightness, commonly employed in normative ethics, was used to attain a detailed understanding of inter- and intrapersonal variety in students' moral reasoning. A total of 24 Swedish students, 12-15 years of age, were interviewed. Inter- and intrapersonal varieties in…
Yang, Xiaofeng; Zhao, Jia; Wang, Qi
2017-03-01
The Molecular Beam Epitaxial model is derived from the variation of a free energy, that consists of either a fourth order Ginzburg-Landau double well potential or a nonlinear logarithmic potential in terms of the gradient of a height function. One challenge in solving the MBE model numerically is how to develop proper temporal discretization for the nonlinear terms in order to preserve energy stability at the time-discrete level. In this paper, we resolve this issue by developing a first and second order time-stepping scheme based on the "Invariant Energy Quadratization" (IEQ) method. The novelty is that all nonlinear terms are treated semi-explicitly, and the resulted semi-discrete equations form a linear system at each time step. Moreover, the linear operator is symmetric positive definite and thus can be solved efficiently. We then prove that all proposed schemes are unconditionally energy stable. The semi-discrete schemes are further discretized in space using finite difference methods and implemented on GPUs for high-performance computing. Various 2D and 3D numerical examples are presented to demonstrate stability and accuracy of the proposed schemes.
Cakmakci, Ozan
today are functions mapping two dimensional vectors to real numbers. The majority of optical designs to-date have relied on conic sections and polynomials as the functions of choice. The choice of conic sections is justified since conic sections are stigmatic surfaces under certain imaging geometries. The choice of polynomials from the point of view of surface description can be challenged. A polynomial surface description may link a designer's understanding of the wavefront aberrations and the surface description. The limitations of using multivariate polynomials are described by a theorem due to Mairhuber and Curtis from approximation theory. This thesis proposes and applies radial basis functions to represent free-form optical surfaces as an alternative to multivariate polynomials. We compare the polynomial descriptions to radial basis functions using the MTF criteria. The benefits of using radial basis functions for surface description are summarized in the context of specific head-worn displays. The benefits include, for example, the performance increase measured by the MTF, or the ability to increase the field of view or pupil size. Even though Zernike polynomials are a complete and orthogonal set of basis over the unit circle and they can be orthogonalized for rectangular or hexagonal pupils using Gram-Schmidt, taking practical considerations into account, such as optimization time and the maximum number of variables available in current raytrace codes, for the specific case of the single off-axis magnifier with a 3 mm pupil, 15 mm eye relief, 24 degree diagonal full field of view, we found the Gaussian radial basis functions to yield a 20% gain in the average MTF at 17 field points compared to a Zernike (using 66 terms) and an x-y polynomial up to and including 10th order. The linear combination of radial basis function representation is not limited to circular apertures. Visualization tools such as field map plots provided by nodal aberration theory have been
Indian Academy of Sciences (India)
S Unlu; T Babacan; N Cakmak; C Selam
2008-09-01
The violated commutation condition between the total shell model Hamiltonian and Gamow–Teller operator (GT) has been restored by Pyatov method (PM). The considered nuclear model Hamiltonian in PM includes the separable GT residual interaction in ph and pp channels and is differentiated from the traditional schematic model by ℎ0 (restoration term). The influence of the h0 effective interaction on the 2 decay of 48Ca, 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 128,130Te and 136Xe is investigated. All the calculations have been done within the framework of standard QRPA. The results obtained by PM are compared with those of other approaches and experimental data. The influence of the restoration term on the stability of the 2 decay nuclear matrix elements is analysed.
A Perceptually Reweighted Mixed-Norm Method for Sparse Approximation of Audio Signals
DEFF Research Database (Denmark)
Christensen, Mads Græsbøll; Sturm, Bob L.
2011-01-01
In this paper, we consider the problem of finding sparse representations of audio signals for coding purposes. In doing so, it is of utmost importance that when only a subset of the present components of an audio signal are extracted, it is the perceptually most important ones. To this end, we...... propose a new iterative algorithm based on two principles: 1) a reweighted l1-norm based measure of sparsity; and 2) a reweighted l2-norm based measure of perceptual distortion. Using these measures, the considered problem is posed as a constrained convex optimization problem that can be solved optimally...... using standard software. A prominent feature of the new method is that it solves a problem that is closely related to the objective of coding, namely rate-distortion optimization. In computer simulations, we demonstrate the properties of the algorithm and its application to real audio signals....
Approximation methods of mixed l 1/H2 optimization problems for MIMO discrete-time systems
Institute of Scientific and Technical Information of China (English)
李昇平
2004-01-01
The mixed l1/H2 optimization problem for MIMO (multiple input-multiple output) discrete-time systems is eonsidered. This problem is formulated as minimizing the l1-norm of a dosed-loop transfer matrix while maintaining the H2-norm of another closed-loop transfer matrix at prescribed level. The continuity property of the optimal value in respect to changes in the H2-norm constraint is studied. The existence of the optimal solutions of mixed l1/H2 problem is proved. Becatse the solution of the mixed l1/H2 problem is based on the scaled-Q method, it avoids the zero interpolation difficulties. The convergent upper and lower bounds can be obtained by solving a sequence of finite dimensional nonlinear programming for which many efficient numerical optimization algorithms exist.
Energy Technology Data Exchange (ETDEWEB)
Maliassov, S.Y. [Texas A& M Univ., College Station, TX (United States)
1996-12-31
An approach to the construction of an iterative method for solving systems of linear algebraic equations arising from nonconforming finite element discretizations with nonmatching grids for second order elliptic boundary value problems with anisotropic coefficients is considered. The technique suggested is based on decomposition of the original domain into nonoverlapping subdomains. The elliptic problem is presented in the macro-hybrid form with Lagrange multipliers at the interfaces between subdomains. A block diagonal preconditioner is proposed which is spectrally equivalent to the original saddle point matrix and has the optimal order of arithmetical complexity. The preconditioner includes blocks for preconditioning subdomain and interface problems. It is shown that constants of spectral equivalence axe independent of values of coefficients and mesh step size.
Energy Technology Data Exchange (ETDEWEB)
Nakano, Masayoshi, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Minami, Takuya, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Fukui, Hitoshi, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Yoneda, Kyohei, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Shigeta, Yasuteru, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Kishi, Ryohei, E-mail: mnaka@cheng.es.osaka-u.ac.jp [Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531 (Japan); Champagne, Benoît; Botek, Edith [Laboratoire de Chimie Théorique, Facultés Universitaires Notre-Dame de la Paix (FUNDP), rue de Bruxelles, 61, 5000 Namur (Belgium)
2015-01-22
We develop a novel method for the calculation and the analysis of the one-electron reduced densities in open-shell molecular systems using the natural orbitals and approximate spin projected occupation numbers obtained from broken symmetry (BS), i.e., spin-unrestricted (U), density functional theory (DFT) calculations. The performance of this approximate spin projection (ASP) scheme is examined for the diradical character dependence of the second hyperpolarizability (γ) using several exchange-correlation functionals, i.e., hybrid and long-range corrected UDFT schemes. It is found that the ASP-LC-UBLYP method with a range separating parameter μ = 0.47 reproduces semi-quantitatively the strongly-correlated [UCCSD(T)] result for p-quinodimethane, i.e., the γ variation as a function of the diradical character.
Senjean, Bruno; Jensen, Hans Jørgen Aa; Fromager, Emmanuel
2015-01-01
The computation of excitation energies in range-separated ensemble density-functional theory (DFT) is discussed. The latter approach is appealing as it enables the rigorous formulation of a multi-determinant state-averaged DFT method. In the exact theory, the short-range density functional, that complements the long-range wavefunction-based ensemble energy contribution, should vary with the ensemble weights even when the density is held fixed. This weight dependence ensures that the range-separated ensemble energy varies linearly with the ensemble weights. When the (weight-independent) ground-state short-range exchange-correlation functional is used in this context, curvature appears thus leading to an approximate weight-dependent excitation energy. In order to obtain unambiguous approximate excitation energies, we simply propose to interpolate linearly the ensemble energy between equiensembles. It is shown that such a linear interpolation method (LIM) effectively introduces weight dependence effects. LIM has...
Indian Academy of Sciences (India)
Kanat Burak Bozdogan; Duygu Ozturk
2010-06-01
This study presents an approximate method based on the continuum approach and transfer matrix method for lateral stability analysis of buildings. In this method, the whole structure is idealized as an equivalent sandwich beam which includes all deformations. The effect of shear deformations of walls has been taken into consideration and incorporated in the formulation of the governing equations. Initially the stability differential equation of this equivalent sandwich beam is presented, and then shape functions for each storey is obtained by the solution of the differential equations. By using boundary conditions and stability storey transfer matrices obtained by shape functions, system buckling load can be calculated. To verify the presented method, four numerical examples have been solved. The results of the samples demonstrate the agreement between the presented method and the other methods given in the literature.
Institute of Scientific and Technical Information of China (English)
Javad Marzbanrad; Behrooz Mashadi; Amir Afkar; Mostafa Pahlavani
2016-01-01
A numerical study of the crushing of thin-walled circular aluminum tubes has been carried out to investigate the crashworthiness behaviors under axial impact loading. These kinds of tubes are usually used in automobile and train structures to absorb the impact energy. Previous researches show that thin-walled circular tube has the highest energy absorption under axial impact amongst different structures. In this work, the crushing between two rigid flat plates and the tube rupture by 4 and 6 blades cutting tools is modeled with the help of ductile failure criterion using the numerical method. The tube material is aluminum EN AW-7108 T6 and its length and diameter are 300 mm and 50 mm, respectively. Using the artificial neural network (ANN), the most important surfaces of energy absorption parameters, including the maximum displacement of the striker, the maximum axial force, the specific energy absorption and the crushing force efficiency in terms of impact velocity and tube thickness are obtained and compared to each other. The analyses show that the tube rupture by the 6 blades cutting tool has more energy absorption in comparison with others. Furthermore, the results demonstrate that tube cutting with the help of multi-blades cutting tools is more stable, controllable and predictable than tube folding.
Directory of Open Access Journals (Sweden)
Taís Quevedo Marcolino
2014-12-01
Full Text Available The Clinical Reasoning Study supported by the American Occupational Therapy Association/AOTA and the American Occupational Therapy Foundation/AOTF in the United States in the late 1980s, had inaugurated the scientific production in the field and offered an initial framework on clinical reasoning for understanding and conducting clinical cases in Occupational Therapy. Most of the researches in this field have focused on reasoning processes, and point out the need to understand the contents of clinical thoughts, or how occupational therapists act and elaborate hypotheses, based on their background knowledge, in order to produce an explanatory theory. In this direction, this article presents the results of two studies from the author focused on understanding aspects of clinical reasoning of occupational therapists who work sustained by Occupational Therapy Dynamic Method/ MTOD, highlighting similarities and differences on diagnostic and procedural reasoning. The discussion points out need to expand the production of this type of research, in particular with Brazilian professionals, as well as the dissemination and study of this subject in the initial and continuing training of occupational therapists.
Asenchik, O. D.
2017-02-01
A method of approximate calculation of the interaction inverse matrix in the method of discrete dipoles is proposed. The knowledge of this matrix makes it possible to determine the optical response of a system to the action of an electromagnetic wave with an arbitrary shape, which can be represented as a combination of vector spherical wave functions. The number of calculation operations of the matrix in the proposed method is considerably smaller than in the case of its direct calculation. In the case of a change in the refractive index of scattering particles, two methods of approximate calculation of the interaction inverse matrix are also proposed. This makes it possible to calculate the optical response of systems with new characteristics without direct solving equations of a system with a large dimension. The accuracy of the methods is numerically determined for particles with spherical and cubic shapes. It is shown that the methods are computationally efficient and can be used to calculate the values of polarization vectors inside particles and extinction and absorption cross sections of systems.
Zhou, Kang; Hou, Jian; Fu, Hongfei; Wei, Bei; Liu, Yongge
2017-01-01
Relative permeability controls the flow of multiphase fluids in porous media. The estimation of relative permeability is generally solved by Levenberg-Marquardt method with finite difference Jacobian approximation (LM-FD). However, the method can hardly be used in large-scale reservoirs because of unbearably huge computational cost. To eliminate this problem, the paper introduces the idea of simultaneous perturbation to simplify the generation of the Jacobian matrix needed in the Levenberg-Marquardt procedure and denotes the improved method as LM-SP. It is verified by numerical experiments and then applied to laboratory experiments and a real commercial oilfield. Numerical experiment indicates that LM-SP uses only 16.1% computational cost to obtain similar estimation of relative permeability and prediction of production performance compared with LM-FD. Laboratory experiment also shows the LM-SP has a 60.4% decrease in simulation cost while a 68.5% increase in estimation accuracy compared with the earlier published results. This is mainly because LM-FD needs 2n (n is the number of controlling knots) simulations to approximate Jacobian in each iteration, while only 2 simulations are enough in basic LM-SP. The convergence rate and estimation accuracy of LM-SP can be improved by averaging several simultaneous perturbation Jacobian approximations but the computational cost of each iteration may be increased. Considering the estimation accuracy and computational cost, averaging two Jacobian approximations is recommended in this paper. As the number of unknown controlling knots increases from 7 to 15, the saved simulation runs by LM-SP than LM-FD increases from 114 to 1164. This indicates LM-SP is more suitable than LM-FD for multivariate problems. Field application further proves the applicability of LM-SP on large real field as well as small laboratory problems.
Institute of Scientific and Technical Information of China (English)
Ken K. Chin
2011-01-01
We present a generic approximate graphical method for determining the equilibrium Fermi level and majority carrier density of a semiconductor with multiple donors and multiple acceptors compensating each other Simple and easy-to-follow procedures of the graphical method are described. By graphically plotting two wrapping step functions facing each other, one for the positive hole-ionized donor and one for the negative electron-ionized acceptor, we have the crossing point that renders the Fermi level and majority carrier density. Using the graphica method, new equations are derived, such as the carrier compensation proportional to NA/ND, not the widely quoted NA - ND. Visual insight is offered to view not only the result of graphic determination of Fermi level and majoriy carrier density but also the dominant and critical pair of donors and acceptors in compensation. The graphica method presented in this work will help to guide the design, adjustment, and improvement of the multiply doped semiconductors. Comparison of this approximate graphical method with previous work on compensation, and with some experimental results, is made. Future work in the field is proposed.
Anisimova, Maria; Gil, Manuel; Dufayard, Jean-François; Dessimoz, Christophe; Gascuel, Olivier
2011-01-01
Phylogenetic inference and evaluating support for inferred relationships is at the core of many studies testing evolutionary hypotheses. Despite the popularity of nonparametric bootstrap frequencies and Bayesian posterior probabilities, the interpretation of these measures of tree branch support remains a source of discussion. Furthermore, both methods are computationally expensive and become prohibitive for large data sets. Recent fast approximate likelihood-based measures of branch supports (approximate likelihood ratio test [aLRT] and Shimodaira–Hasegawa [SH]-aLRT) provide a compelling alternative to these slower conventional methods, offering not only speed advantages but also excellent levels of accuracy and power. Here we propose an additional method: a Bayesian-like transformation of aLRT (aBayes). Considering both probabilistic and frequentist frameworks, we compare the performance of the three fast likelihood-based methods with the standard bootstrap (SBS), the Bayesian approach, and the recently introduced rapid bootstrap. Our simulations and real data analyses show that with moderate model violations, all tests are sufficiently accurate, but aLRT and aBayes offer the highest statistical power and are very fast. With severe model violations aLRT, aBayes and Bayesian posteriors can produce elevated false-positive rates. With data sets for which such violation can be detected, we recommend using SH-aLRT, the nonparametric version of aLRT based on a procedure similar to the Shimodaira–Hasegawa tree selection. In general, the SBS seems to be excessively conservative and is much slower than our approximate likelihood-based methods. PMID:21540409
Directory of Open Access Journals (Sweden)
Nishimura Tadashi
2004-01-01
Full Text Available Abstract Background Most medical schools in Japan have incorporated mandatory courses on medical ethics. To this date, however, there is no established means of evaluating medical ethics education in Japan. This study looks 1 To develop a brief, objective method of evaluation for moral sensitivity and reasoning; 2 To conduct a test battery for the PIT and the DIT on medical students who are either currently in school or who have recently graduated (residents; 3 To investigate changes in moral sensitivity and reasoning between school years among medical students and residents. Methods Questionnaire survey: Two questionnaires were employed, the Problem Identification Test (PIT for evaluation of moral sensitivity and a portion of the Defining Issues Test (DIT for moral reasoning. Subjects consisted of 559 medical school students and 272 residents who recently graduated from the same medical school located in an urban area of Japan. Results PIT results showed an increase in moral sensitivity in 4th and 5th year students followed by a decrease in 6th year students and in residents. No change in moral development stage was observed. However, DIT results described a gradual rising shift in moral decision-making concerning euthanasia between school years. No valid correlation was observed between PIT and DIT questionnaires. Conclusion This study's questionnaire survey, which incorporates both PIT and DIT, could be used as a brief and objective means of evaluating medical students' moral sensitivity and reasoning in Japan.
A New Method in the Location Problem using Fuzzy Evidential Reasoning
Directory of Open Access Journals (Sweden)
Sh. Rahgan
2012-11-01
Full Text Available One of the most important factors leading to the success of a company is its location. Branches have a strategic importance on an organization’s performance and its competitiveness. The purpose of this study is to present a decision-making model for selecting the most appropriate location for a bank branch. This research is the first study in the bank branch location researches considering various types of uncertainties. This model involves both quantitative and qualitative attributes as well as various types of uncertainty. So, we propose a methodology by integrating the fuzzy AHP and Evidential Reasoning approach. The fuzzy extent analysis is used to determine the weights of attributes and sub-attributes and the interval ER algorithm is used to rank the alternatives. This methodology can be used to help the decision makers, because it is capable of handling incomplete and imprecise judgments. We have demonstrated the applicability of the methodology through a case study.
A Method to Identify and Analyze Biological Programs through Automated Reasoning
Kugler, Hillel; Smith, Austin; Martello, Graziano; Emmott, Stephen
2016-01-01
Predictive biology is elusive because rigorous, data-constrained, mechanistic models of complex biological systems are difficult to derive and validate. Current approaches tend to construct and examine static interaction network models, which are descriptively rich but often lack explanatory and predictive power, or dynamic models that can be simulated to reproduce known behavior. However, in such approaches implicit assumptions are introduced as typically only one mechanism is considered, and exhaustively investigating all scenarios is impractical using simulation. To address these limitations, we present a methodology based on automated formal reasoning, which permits the synthesis and analysis of the complete set of logical models consistent with experimental observations. We test hypotheses against all candidate models, and remove the need for simulation by characterizing and simultaneously analyzing all mechanistic explanations of observed behavior. Our methodology transforms knowledge of complex biological processes from sets of possible interactions and experimental observations to precise, predictive biological programs governing cell function. PMID:27668090
DEFF Research Database (Denmark)
Senjean, Bruno; Knecht, Stefan; Jensen, Hans Jørgen Aa
2015-01-01
of range separation and use of the slope of the linearly interpolated ensemble energy, rather than orbital energies. The range-separated approach is appealing, as it enables the rigorous formulation of a multideterminant state-averaged DFT method. In the exact theory, the short-range density functional......-independent) ground-state short-range exchange-correlation functional is used in this context, curvature appears, thus leading to an approximate weight-dependent excitation energy. In order to obtain unambiguous approximate excitation energies, we propose to interpolate linearly the ensemble energy between...... promising results have been obtained for both single (including charge transfer) and double excitations with spin-independent short-range local and semilocal functionals. Even at the Kohn-Sham ensemble DFT level, which is recovered when the range-separation parameter is set to 0, LIM performs better than...
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The problem of the process of coupled diffusion and reaction in catalyst pellets is considered for the case of second and half order reactions. The Adomian decomposition method is used to solve the non-linear model. For the second, half and first order reactions, analytical approximate solutions are obtained. The variation of reactant concentration in the catalyst pellet and the effectiveness factors at φ＜10 are determined and compared with those by the BAND's finite difference numerical method developed by Newman. At lower values of φ, the decomposition solution with 3 terms gives satisfactory agreement with the numerical solution; at higher values of φ, as the term number in the decomposition method is increased, an acceptable agreement between the two methods is achieved. In general, the solution with 6 terms gives a satisfactory agreement.
Qin, Cheng-Zhi; Wu, Xue-Wei; Jiang, Jing-Chao; Zhu, A.-Xing
2016-08-01
Application of digital terrain analysis (DTA), which is typically a modeling process involving workflow building, relies heavily on DTA domain knowledge of the match between the algorithm (and its parameter settings) and the application context (including the target task, the terrain in the study area, the DEM resolution, etc.), which is referred to as application-context knowledge. However, existing DTA-assisted tools often cannot use application-context knowledge because this type of DTA knowledge has not been formalized to be available for inference in these tools. This situation makes the DTA workflow-building process difficult for users, especially non-expert users. This paper proposes a case-based formalization for DTA application-context knowledge and a corresponding case-based reasoning method. A case in this context consists of a series of indices that formalize the DTA application-context knowledge and the corresponding similarity calculation methods for case-based reasoning. A preliminary experiment to determine the catchment area threshold for extracting drainage networks has been conducted to evaluate the performance of the proposed method. In the experiment, 124 cases of drainage network extraction (50 for evaluation and 74 for reasoning) were prepared from peer-reviewed journal articles. Preliminary evaluation shows that the proposed case-based method is a suitable way to use DTA application-context knowledge to achieve a marked reduction in the modeling burden for users.
Relations between Inductive Reasoning and Deductive Reasoning
Heit, Evan; Rotello, Caren M.
2010-01-01
One of the most important open questions in reasoning research is how inductive reasoning and deductive reasoning are related. In an effort to address this question, we applied methods and concepts from memory research. We used 2 experiments to examine the effects of logical validity and premise-conclusion similarity on evaluation of arguments.…
Giese, Timothy J; York, Darrin M
2010-12-28
We extend the Kohn-Sham potential energy expansion (VE) to include variations of the kinetic energy density and use the VE formulation with a 6-31G* basis to perform a "Jacob's ladder" comparison of small molecule properties using density functionals classified as being either LDA, GGA, or meta-GGA. We show that the VE reproduces standard Kohn-Sham DFT results well if all integrals are performed without further approximation, and there is no substantial improvement in using meta-GGA functionals relative to GGA functionals. The advantages of using GGA versus LDA functionals becomes apparent when modeling hydrogen bonds. We furthermore examine the effect of using integral approximations to compute the zeroth-order energy and first-order matrix elements, and the results suggest that the origin of the short-range repulsive potential within self-consistent charge density-functional tight-binding methods mainly arises from the approximations made to the first-order matrix elements.
Graves, Joseph L.; Reiber, Chris; Thanukos, Anna; Hurtado, Magdalena; Wolpaw, Terry
2016-01-01
Evolutionary science is indispensable for understanding biological processes. Effective medical treatment must be anchored in sound biology. However, currently the insights available from evolutionary science are not adequately incorporated in either pre-medical or medical school curricula. To illuminate how evolution may be helpful in these areas, examples in which the insights of evolutionary science are already improving medical treatment and ways in which evolutionary reasoning can be practiced in the context of medicine are provided. To facilitate the learning of evolutionary principles, concepts derived from evolutionary science that medical students and professionals should understand are outlined. These concepts are designed to be authoritative and at the same time easily accessible for anyone with the general biological knowledge of a first-year medical student. Thus, we conclude that medical practice informed by evolutionary principles will be more effective and lead to better patient outcomes. Furthermore, it is argued that evolutionary medicine complements general medical training because it provides an additional means by which medical students can practice the critical thinking skills that will be important in their future practice. We argue that core concepts from evolutionary science have the potential to improve critical thinking and facilitate more effective learning in medical training. PMID:27744353
Yzer, Marco; Weisman, Susan; Mejia, Nicole; Hennrikus, Deborah; Choi, Kelvin; DeSimone, Susan
2015-08-01
Blue-collar workers typically have high rates of tobacco use but low rates of using tobacco cessation resources available through their health benefits. Interventions to motivate blue-collar tobacco users to use effective cessation support are needed. Reasoned action theory is useful in this regard as it can identify the beliefs that shape tobacco cessation benefit use intentions. However, conventional reasoned action research cannot speak to how those beliefs can best be translated into intervention messages. In the present work, we expand the reasoned action approach by adding additional qualitative inquiry to better understand blue-collar smokers' beliefs about cessation benefit use. Across three samples of unionized blue-collar tobacco users, we identified (1) the 35 attitudinal, normative, and control beliefs that represented tobacco users' belief structure about cessation benefit use; (2) instrumental attitude as most important in explaining cessation intention; (3) attitudinal beliefs about treatment options' efficacy, health effects, and monetary implications of using benefits as candidates for message design; (4) multiple interpretations of cessation beliefs (e.g., short and long-term health effects); and (5) clear implications of these interpretations for creative message design. Taken together, the findings demonstrate how a mixed-method reasoned action approach can inform interventions that promote the use of tobacco cessation health benefits.
Discretizing of linear systems with time-delay Using method of Euler’s and Tustin’s approximations
Directory of Open Access Journals (Sweden)
Bemri H’mida
2015-03-01
Full Text Available Delays deteriorate the control performance and could destabilize the overall system in the theory of discretetime signals and dynamic systems. Whenever a computer is used in measurement, signal processing or control applications, the data as seen from the computer and systems involved are naturally discrete-time because a computer executes program code at discrete points of time. Theory of discrete-time dynamic signals and systems is useful in design and analysis of control systems, signal filters, state estimators and model estimation from time-series of process data system identification. In this paper, a new approximated discretization method and digital design for control systems with delays is proposed. System is transformed to a discrete-time model with time delays. To implement the digital modeling, we used the z-transfer functions matrix which is a useful model type of discrete-time systems, being analogous to the Laplace-transform for continuous-time systems. The most important use of the z-transform is for defining z-transfer functions matrix is employed to obtain an extended discrete-time. The proposed method can closely approximate the step response of the original continuous timedelayed control system by choosing various of energy loss level. Illustrative example is simulated to demonstrate the effectiveness of the developed method.
Guo, Chengan; Yang, Qingshan
2015-07-01
Finding the optimal solution to the constrained l0 -norm minimization problems in the recovery of compressive sensed signals is an NP-hard problem and it usually requires intractable combinatorial searching operations for getting the global optimal solution, unless using other objective functions (e.g., the l1 norm or lp norm) for approximate solutions or using greedy search methods for locally optimal solutions (e.g., the orthogonal matching pursuit type algorithms). In this paper, a neurodynamic optimization method is proposed to solve the l0 -norm minimization problems for obtaining the global optimum using a recurrent neural network (RNN) model. For the RNN model, a group of modified Gaussian functions are constructed and their sum is taken as the objective function for approximating the l0 norm and for optimization. The constructed objective function sets up a convexity condition under which the neurodynamic system is guaranteed to obtain the globally convergent optimal solution. An adaptive adjustment scheme is developed for improving the performance of the optimization algorithm further. Extensive experiments are conducted to test the proposed approach in this paper and the output results validate the effectiveness of the new method.
Regnier, D.; Verrière, M.; Dubray, N.; Schunck, N.
2016-03-01
We describe the software package FELIX that solves the equations of the time-dependent generator coordinate method (TDGCM) in N-dimensions (N ≥ 1) under the Gaussian overlap approximation. The numerical resolution is based on the Galerkin finite element discretization of the collective space and the Crank-Nicolson scheme for time integration. The TDGCM solver is implemented entirely in C++. Several additional tools written in C++, Python or bash scripting language are also included for convenience. In this paper, the solver is tested with a series of benchmarks calculations. We also demonstrate the ability of our code to handle a realistic calculation of fission dynamics.
Energy Technology Data Exchange (ETDEWEB)
Regnier, D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); CEA, DAM, DIF, Arpajon (France); Verriere, M. [CEA, DAM, DIF, Arpajon (France); Dubray, N. [CEA, DAM, DIF, Arpajon (France); Schunck, N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-11-30
In this study, we describe the software package FELIX that solves the equations of the time-dependent generator coordinate method (TDGCM) in NN-dimensions (N ≥ 1) under the Gaussian overlap approximation. The numerical resolution is based on the Galerkin finite element discretization of the collective space and the Crank–Nicolson scheme for time integration. The TDGCM solver is implemented entirely in C++. Several additional tools written in C++, Python or bash scripting language are also included for convenience. In this paper, the solver is tested with a series of benchmarks calculations. We also demonstrate the ability of our code to handle a realistic calculation of fission dynamics.
Directory of Open Access Journals (Sweden)
D. Olvera
2015-01-01
Full Text Available We expand the application of the enhanced multistage homotopy perturbation method (EMHPM to solve delay differential equations (DDEs with constant and variable coefficients. This EMHPM is based on a sequence of subintervals that provide approximate solutions that require less CPU time than those computed from the dde23 MATLAB numerical integration algorithm solutions. To address the accuracy of our proposed approach, we examine the solutions of several DDEs having constant and variable coefficients, finding predictions with a good match relative to the corresponding numerical integration solutions.
Regnier, D; Dubray, N; Schunck, N
2015-01-01
We describe the software package FELIX that solves the equations of the time-dependent generator coordinate method (TDGCM) in N-dimensions (N $\\geq$ 1) under the Gaussian overlap approximation. The numerical resolution is based on the Galerkin finite element discretization of the collective space and the Crank-Nicolson scheme for time integration. The TDGCM solver is implemented entirely in C++. Several additional tools written in C++, Python or bash scripting language are also included for convenience. In this paper, the solver is tested with a series of benchmarks calculations. We also demonstrate the ability of our code to handle a realistic calculation of fission dynamics.
Theory of restriction degree of Triple I method with total inference rules of fuzzy reasoning
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Based on the theory of sustentation degree of Triple I method together with the formulas of a-Triple I modus ponens (MP) and a-Triple I modus tollens( MT), the theory of restriction degree of Triple I method is proposed. Its properties are analyzed, and the general formulas of supremum of a-Triple IMP and infimum of a-Triple I MT are obtained.
MacArt, Jonathan F.; Mueller, Michael E.
2016-12-01
Two formally second-order accurate, semi-implicit, iterative methods for the solution of scalar transport-reaction equations are developed for Direct Numerical Simulation (DNS) of low Mach number turbulent reacting flows. The first is a monolithic scheme based on a linearly implicit midpoint method utilizing an approximately factorized exact Jacobian of the transport and reaction operators. The second is an operator splitting scheme based on the Strang splitting approach. The accuracy properties of these schemes, as well as their stability, cost, and the effect of chemical mechanism size on relative performance, are assessed in two one-dimensional test configurations comprising an unsteady premixed flame and an unsteady nonpremixed ignition, which have substantially different Damköhler numbers and relative stiffness of transport to chemistry. All schemes demonstrate their formal order of accuracy in the fully-coupled convergence tests. Compared to a (non-)factorized scheme with a diagonal approximation to the chemical Jacobian, the monolithic, factorized scheme using the exact chemical Jacobian is shown to be both more stable and more economical. This is due to an improved convergence rate of the iterative procedure, and the difference between the two schemes in convergence rate grows as the time step increases. The stability properties of the Strang splitting scheme are demonstrated to outpace those of Lie splitting and monolithic schemes in simulations at high Damköhler number; however, in this regime, the monolithic scheme using the approximately factorized exact Jacobian is found to be the most economical at practical CFL numbers. The performance of the schemes is further evaluated in a simulation of a three-dimensional, spatially evolving, turbulent nonpremixed planar jet flame.
Vanne, Y V; Saenz, Alejandro; Vanne, Yulian V.
2006-01-01
In recent articles [Mishima et al., Phys. Rev. A, 66, 033401(2002); Chao, Phys. Rev. A, 72, 053414 (2005)] it was proposed to use the residue theorem for the exact calculation of the transition amplitude describing strong-field ionization of atomic systems within Keldysh theory. This should avoid the necessity to apply the method of steepest descent (saddle-point approximation). Comparing the results of both approaches for atomic hydrogen a difference by a factor of 2 was found for the 1s, and an even more drastic deviation for the 2s state. Thus it was concluded that the use of the saddle-point approximation is problematic. In this work the deviations are explained and it is shown that the previous conclusion is based on an unjustified neglect of an important contribution occurring in the application of the residue theorem. Furthermore, the applicability of the method of steepest descent for the ionization of Rydberg states is discussed and an improvement of the standard result is suggested that successfully...
Directory of Open Access Journals (Sweden)
G. Domairry
2009-01-01
Full Text Available An analysis has been performed to study magneto-hydrodynamic (MHD squeeze flow between two parallel infinite disks where one disk is impermeable and the other is porous with either suction or injection of the fluid. We investigate the combined effect of inertia, electromagnetic forces, and suction or injection. With the introduction of a similarity transformation, the continuity and momentum equations governing the squeeze flow are reduced to a single, nonlinear, ordinary differential equation. An approximate solution of the equation subject to the appropriate boundary conditions is derived using the homotopy perturbation method (HPM and compared with the direct numerical solution (NS. Results showing the effect of squeeze Reynolds number, Hartmann number and the suction/injection parameter on the axial and radial velocity distributions are presented and discussed. The approximate solution is found to be highly accurate for the ranges of parameters investigated. Because of its simplicity, versatility and high accuracy, the method can be applied to study linear and nonlinear boundary value problems arising in other engineering applications.
Continuous rigid PC frame box girder cantilever pouring construction reasonable maintenance method
Directory of Open Access Journals (Sweden)
Wulin
2015-08-01
Full Text Available In recent years, prestressed concrete continuous rigid frame box girder plate and web plate produced a large number of non-structural cracks disease caused the attention of large bridge workers, to solve the problem of continuous rigid-frame structure of the cantilever of the disease, this article briefly introduced the cantilever construction method and the performance requirements of modern concrete, through to the modern concrete composition change and keeping in good health on the impact of environment on its early performance analysis summary, points out the present problems of box girder early curing, finally combining with the characteristics of modern concrete performance and the characteristics of the cantilever construction method, puts forward "model attach +manual+automatic water spray mist stick " composite curing method in order to reduce the structural cracks, provides a new train of thought.
Dalmasse, K; Gibson, S E; Fan, Y; Flyer, N
2016-01-01
The Coronal Multichannel Polarimeter (CoMP) routinely performs coronal polarimetric measurements using the Fe XIII 10747 $\\AA$ and 10798 $\\AA$ lines, which are sensitive to the coronal magnetic field. However, inverting such polarimetric measurements into magnetic field data is a difficult task because the corona is optically thin at these wavelengths and the observed signal is therefore the integrated emission of all the plasma along the line of sight. To overcome this difficulty, we take on a new approach that combines a parameterized 3D magnetic field model with forward modeling of the polarization signal. For that purpose, we develop a new, fast and efficient, optimization method for model-data fitting: the Radial-basis-functions Optimization Approximation Method (ROAM). Model-data fitting is achieved by optimizing a user-specified log-likelihood function that quantifies the differences between the observed polarization signal and its synthetic/predicted analogue. Speed and efficiency are obtained by comb...
Ibáñez, Javier; Hernández, Vicente
2011-03-01
Differential Matrix Riccati Equations (DMREs) appear in several branches of science such as applied physics and engineering. For example, these equations play a fundamental role in control theory, optimal control, filtering and estimation, decoupling and order reduction, etc. In this paper a new method based on a theorem proved in this paper is described for solving DMREs by a piecewise-linearized approach. This method is applied for developing two block-oriented algorithms based on diagonal Padé approximants. MATLAB versions of the above algorithms are developed, comparing, under equal conditions, accuracy and computational costs with other piecewise-linearized algorithms implemented by the authors. Experimental results show the advantages of solving stiff or non-stiff DMREs by the implemented algorithms.
Christian, Karen Jeanne
2011-01-01
Students often use study groups to prepare for class or exams; yet to date, we know very little about how these groups actually function. This study looked at the ways in which undergraduate organic chemistry students prepared for exams through self-initiated study groups. We sought to characterize the methods of social regulation, levels of…
Fletcher, Logan; Carruthers, Peter
2012-01-01
This article considers the cognitive architecture of human meta-reasoning: that is, metacognition concerning one's own reasoning and decision-making. The view we defend is that meta-reasoning is a cobbled-together skill comprising diverse self-management strategies acquired through individual and cultural learning. These approximate the monitoring-and-control functions of a postulated adaptive system for metacognition by recruiting mechanisms that were designed for quite other purposes.
Fletcher, Logan; Carruthers, Peter
2012-05-19
This article considers the cognitive architecture of human meta-reasoning: that is, metacognition concerning one's own reasoning and decision-making. The view we defend is that meta-reasoning is a cobbled-together skill comprising diverse self-management strategies acquired through individual and cultural learning. These approximate the monitoring-and-control functions of a postulated adaptive system for metacognition by recruiting mechanisms that were designed for quite other purposes.
DEFF Research Database (Denmark)
Kildemoes, Helle Wallach; Hendriksen, Carsten; Morten, Andersen
2011-01-01
ABSTRACT Purpose To develop a pharmacoepidemiologic method for drug utilization analysis according to indication, gender, and age by means of register-based information. Statin utilization in 2005 was applied as an example. Methods Following the recommendations for statin therapy, we constructed...... an indication hierarchy with eight mutually exclusive levels of register markers of cardiovascular disease and diabetes. Danish residents, as of January 1, 1996, were followed at the individual level in nationwide registers with respect to dispensed prescriptions of cardiovascular drugs and antidiabetics (1996...... with no register marker or primary hypertension accounted for almost 50% of all incident female users; among men, the figure was 35%. The proportion of incident users with ischemic heart disease or myocardial infarction increased with age. Conclusion The proposed indication hierarchy provided new insight...
On Element SDD Approximability
Avron, Haim; Toledo, Sivan
2009-01-01
This short communication shows that in some cases scalar elliptic finite element matrices cannot be approximated well by an SDD matrix. We also give a theoretical analysis of a simple heuristic method for approximating an element by an SDD matrix.
2015-01-01
How can we advance knowledge? Which methods do we need in order to make new discoveries? How can we rationally evaluate, reconstruct and offer discoveries as a means of improving the ‘method’ of discovery itself? And how can we use findings about scientific discovery to boost funding policies, thus fostering a deeper impact of scientific discovery itself? The respective chapters in this book provide readers with answers to these questions. They focus on a set of issues that are essential to the development of types of reasoning for advancing knowledge, such as models for both revolutionary findings and paradigm shifts; ways of rationally addressing scientific disagreement, e.g. when a revolutionary discovery sparks considerable disagreement inside the scientific community; frameworks for both discovery and inference methods; and heuristics for economics and the social sciences.
Approximate iterative algorithms
Almudevar, Anthony Louis
2014-01-01
Iterative algorithms often rely on approximate evaluation techniques, which may include statistical estimation, computer simulation or functional approximation. This volume presents methods for the study of approximate iterative algorithms, providing tools for the derivation of error bounds and convergence rates, and for the optimal design of such algorithms. Techniques of functional analysis are used to derive analytical relationships between approximation methods and convergence properties for general classes of algorithms. This work provides the necessary background in functional analysis a
Energy Technology Data Exchange (ETDEWEB)
Wang, S.W.; Georgopoulos, P.G. [Environmental and Occupational Health Sciences Inst., Piscataway, NJ (United States); Li, G.; Rabitz, H. [Princeton Univ., NJ (United States). Dept. of Chemistry
1998-07-01
Atmospheric chemistry mechanisms are the most computationally intensive components of photochemical air quality simulation models (PAQSMs). The development of a photochemical mechanism, that accurately describes atmospheric chemistry while being computationally efficient for use in PAQSMs, is a difficult undertaking that has traditionally been pursued through semiempirical (diagnostic) lumping approaches. The limitations of these diagnostic approaches are often associated with inaccuracies due to the fact that the lumped mechanisms have typically been optimized to fit the concentration profile of a specific species. Formal mathematical methods for model reduction have the potential (demonstrated through past applications in other areas) to provide very effective solutions to the need for computational efficiency combined with accuracy. Such methods, that can be used to condense a chemical mechanism, include kinetic lumping and domain separation. An application of the kinetic lumping method, using the direct constrained approximately lumping (DCAL) approach, to the atmospheric photochemistry of alkanes is presented in this work. It is shown that the lumped mechanism generated through the application of the DCAL method has the potential to overcome the limitations of existing semiempirical approaches, especially in relation to the consistent and accurate calculation of the time-concentration profiles of multiple species.
Case-Based Reasoning Method in Cost Estimation of Drilling Wells
Hossein Shams Mianaei; Seyed Hossein Iranmanesh
2013-01-01
Aim of study is the cost estimation of drilling6T8T 6T8Twells6T8T 6T8Tusing6T Case-Based 6TReasoning6T8T (CBR) method which6T8T is created based6T8T 6T8Ton6T8T 6T8Tthe6T8T 6T8Tviewpoint of using presented6T8T 6T8Tsolutions6T8T 6T8Tfor6T8T 6T8Tprevious6T8T 6T8Tsolved6T8T 6T8Tproblems6T8T in order 6T8Tto solve6T8T new 6T8Tsimilar problems6T8T. 6T8TIn companies6T8T 6T8Tor6T8T 6T8Torganizations6T8T which 6T8Tcost estimation, scheduling,6T8T 6T8Tdesign6T8T, planning 6T8Tand project activities6T8T ...
Yi, Longtao; Sun, Tianxi; Wang, Kai; Qin, Min; Yang, Kui; Wang, Jinbang; Liu, Zhiguo
2016-08-01
Confocal three-dimensional micro X-ray fluorescence (3D MXRF) is an excellent surface analysis technology. For a confocal structure, only the X-rays from the confocal volume can be detected. Confocal 3D MXRF has been widely used for analysing elements, the distribution of elements and 3D image of some special samples. However, it has rarely been applied to analysing surface topography by surface scanning. In this paper, a confocal 3D MXRF technology based on polycapillary X-ray optics was proposed for determining surface topography. A corresponding surface adaptive algorithm based on a progressive approximation method was designed to obtain surface topography. The surface topography of the letter "R" on a coin of the People's Republic of China and a small pit on painted pottery were obtained. The surface topography of the "R" and the pit are clearly shown in the two figures. Compared with the method in our previous study, it exhibits a higher scanning efficiency. This approach could be used for two-dimensional (2D) elemental mapping or 3D elemental voxel mapping measurements as an auxiliary method. It also could be used for analysing elemental mapping while obtaining the surface topography of a sample in 2D elemental mapping measurement.
Froelich, P.; Weyrich, Wolf
1984-06-01
Basic electrodynamical and collision theory presumptions related to Compton scattering are critically reconsidered (with particular emphasis on identifying the proper transition matrix element effectively controlling the process, and on framing it within time dependent perturbation theory and scattering theory) in order to indicate the main features and the validity of the proposed method. The on-energy-shell transition matrix element governing the cross-sectional formula is obtained from Furry's two-potential formalism, which makes possible a treatment of the primary electron-photon interaction to first order while incorporating the effects of the final state Coulombic interaction to all orders. Furry's procedure, in addition to defining clearly which initial and final states should enter the transition matrix element, also brings additional insight into the nature of the so-called ``sudden impulse approximation.'' A treatment is proposed in which the decisive transition matrix element is obtained without explicit calculation of the distorted continuum solutions implied by Furry's procedure, but is instead extracted from the dispersion relations of the ``beat-frequency'' dependent generalized polarizability by means of the L2 treatment based on the complex-coordinate method. The practical advantage of the method will be its ability to incorporate correlation between the ejected electron and the electrons remaining in the ion.
Institute of Scientific and Technical Information of China (English)
An Haichao; Chen Shenyan; Huang Hai
2016-01-01
This paper is to address structural optimization problems where multiple structure cases or multiple payload cases can be considered simultaneously. Both types of optimization problems involve multiple finite element models at each iteration step, which draws high demands in opti-mization methods. Considering the common characteristic for these two types of problems, which is that the design domain keeps the same no matter what the structure cases or payload cases are, both problems can be formulated into the unified expressions. A two-level multipoint approxima-tion (TMA) method is firstly improved with the use of analytical sensitivity analysis for structural mass, and then this improved method is utilized to tackle these two types of problems. Based on the commercial finite element software MSC.Patran/Nastran, an optimization system for multiple structure cases and multiple payload cases is developed. Numerical examples are conducted to ver-ify its feasibility and efficiency, and the necessity for the simultaneous optimizations of multiple structure cases and multiple payload cases are illustrated as well.
Energy Technology Data Exchange (ETDEWEB)
Hermeline, F
2008-12-15
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)
Neese, Frank; Wennmohs, Frank; Hansen, Andreas
2009-03-01
Coupled-electron pair approximations (CEPAs) and coupled-pair functionals (CPFs) have been popular in the 1970s and 1980s and have yielded excellent results for small molecules. Recently, interest in CEPA and CPF methods has been renewed. It has been shown that these methods lead to competitive thermochemical, kinetic, and structural predictions. They greatly surpass second order Møller-Plesset and popular density functional theory based approaches in accuracy and are intermediate in quality between CCSD and CCSD(T) in extended benchmark studies. In this work an efficient production level implementation of the closed shell CEPA and CPF methods is reported that can be applied to medium sized molecules in the range of 50-100 atoms and up to about 2000 basis functions. The internal space is spanned by localized internal orbitals. The external space is greatly compressed through the method of pair natural orbitals (PNOs) that was also introduced by the pioneers of the CEPA approaches. Our implementation also makes extended use of density fitting (or resolution of the identity) techniques in order to speed up the laborious integral transformations. The method is called local pair natural orbital CEPA (LPNO-CEPA) (LPNO-CPF). The implementation is centered around the concepts of electron pairs and matrix operations. Altogether three cutoff parameters are introduced that control the size of the significant pair list, the average number of PNOs per electron pair, and the number of contributing basis functions per PNO. With the conservatively chosen default values of these thresholds, the method recovers about 99.8% of the canonical correlation energy. This translates to absolute deviations from the canonical result of only a few kcal mol-1. Extended numerical test calculations demonstrate that LPNO-CEPA (LPNO-CPF) has essentially the same accuracy as parent CEPA (CPF) methods for thermochemistry, kinetics, weak interactions, and potential energy surfaces but is up to 500
格值语义归结推理方法%Lattice-valued Semantic Resolution Reasoning Method
Institute of Scientific and Technical Information of China (English)
张家锋; 徐扬; 何星星
2011-01-01
归结自动推理是人工智能领域的一个重要研究方向,语义归结方法是对归结原理的一种改进,它利用限制参与归结子句类型和归结文字顺序的方法来提高推理效率.基于格蕴涵代数的格值逻辑系统的α-归结原理提供了一种处理带有模糊性和不可比较性信息的工具,它能对格值逻辑系统中在一定真值水平下的不可满足逻辑公式给出反驳证明.首先研究了格值逻辑系统上一类广义子句集的性质,该类子句集在任意赋值下能分为两个非空子集,接着讨论了这类广义子句集的语义归结方法,并证明了其可靠性和完备性.%Resolution-based automated reasoning is one of most important research directions in AI;semantic method is one of the most important reform methods for resolution principle tin semantic resolution method;it utilizes the techno logy restraining the type of clauses and the order of literals participated in resolution procedure to reduce the redundant clauses;and can improve the efficiency of reasoning;a -resolution principle on lattice-valued logic based on lattice impli cation algebra provides a alternative tool to handle the automated reasoning problem with uncomparability and fuzziness information. It can refutably prove the unsatisfiability of logical formulae in lattice-valued logic system. Firstly;this pa per discussed the property of one class of generalized clause set on lattice-valued prepositional logic LP(X);this genera lized clause set can be divided into two non-empty sets;the semantic resolution method on it was investigated and sound theorem and weak complete theorem of this semantic resolution method were proved.
Gilev, Konstantin V; Eremina, Elena; Yurkin, Maxim A; Maltsev, Valeri P
2010-03-15
The discrete sources method (DSM) and the discrete dipole approximation (DDA) were compared for simulation of light scattering by a red blood cell (RBC) model. We considered RBCs with diameters up to 8 mum (size parameter up to 38), relative refractive indices 1.03 and 1.06, and two different orientations. The agreement in the angle-resolved S(11) element of the Mueller matrix obtained by these methods is generally good, but it deteriorates with increasing scattering angle, diameter and refractive index of a RBC. Based on the DDA simulations with very fine discretization (up to 93 dipoles per wavelength) for a single RBC, we attributed most of the disagreement to the DSM, which results contain high-frequency ripples. For a single orientation of a RBC the DDA is comparable to or faster than the DSM. However, the relation is reversed when a set of particle orientations need to be simulated at once. Moreover, the DSM requires about an order of magnitude less computer memory. At present, application of the DSM for massive calculation of light scattering patterns of RBCs is hampered by its limitations in size parameter of a RBC due to the high number of harmonics used for calculations.
Frozen Gaussian approximation-based two-level methods for multi-frequency Schrödinger equation
Lorin, E.; Yang, X.
2016-10-01
In this paper, we develop two-level numerical methods for the time-dependent Schrödinger equation (TDSE) in multi-frequency regime. This work is motivated by attosecond science (Corkum and Krausz, 2007), which refers to the interaction of short and intense laser pulses with quantum particles generating wide frequency spectrum light, and allowing for the coherent emission of attosecond pulses (1 attosecond=10-18 s). The principle of the proposed methods consists in decomposing a wavefunction into a low/moderate frequency (quantum) contribution, and a high frequency contribution exhibiting a semi-classical behavior. Low/moderate frequencies are computed through the direct solution to the quantum TDSE on a coarse mesh, and the high frequency contribution is computed by frozen Gaussian approximation (Herman and Kluk, 1984). This paper is devoted to the derivation of consistent, accurate and efficient algorithms performing such a decomposition and the time evolution of the wavefunction in the multi-frequency regime. Numerical simulations are provided to illustrate the accuracy and efficiency of the derived algorithms.
Rational offset approximation of rational Bézier curves
Institute of Scientific and Technical Information of China (English)
CHENG Min; WANG Guo-jin
2006-01-01
The problem of parametric speed approximation of a rational curve is raised in this paper. Offset curves are widely used in various applications. As for the reason that in most cases the offset curves do not preserve the same polynomial or rational polynomial representations, it arouses difficulty in applications. Thus approximation methods have been introduced to solve this problem. In this paper, it has been pointed out that the crux of offset curve approximation lies in the approximation of parametric speed. Based on the Jacobi polynomial approximation theory with endpoints interpolation, an algebraic rational approximation algorithm of offset curve, which preserves the direction of normal, is presented.
Institute of Scientific and Technical Information of China (English)
宋爽; 那日萨; 张杨
2014-01-01
依据消费者心理学及品牌行为理论，从消费者感知质量、感知价值、品牌声誉、期望达成度4个维度建立了品牌转换意向模型；通过对网络消费者在线评论中评价词、情感词的提取和语义分析，结合模糊情感语料库和品牌转换意向推理规则，模糊推理出消费者品牌转换意向，进而推理出消费者的品牌转换意向的转换类型。以淘宝网上4种化妆品为例进行消费者品牌转换意向研究，得到较合理的结论并给予营销性建议，验证了所提方法的有效性。%Based on consumer psychology and experiential marketing theory,a model of customer switching intention was established from four dimensions:perceived quality,perceived value,brand reputation and expectation.Then se-mantic analysis on the valuation words and emotional words extracted from the consumer online reviews was made.Fur-thermore,combined with fuzzy sentiment corpus and fuzzy inference,the consumer's brand switching intention was computed,and the customer's switching intention types was identified.Finally,an experimental study with the case of four types of cosmetics on the TaoBao site was carried out,and reasonable conclusions and some marketing advices were obtained,which all verify the validity of the method.
Bozkaya, Uğur; Sherrill, C David
2016-05-07
An efficient implementation is presented for analytic gradients of the coupled-cluster singles and doubles (CCSD) method with the density-fitting approximation, denoted DF-CCSD. Frozen core terms are also included. When applied to a set of alkanes, the DF-CCSD analytic gradients are significantly accelerated compared to conventional CCSD for larger molecules. The efficiency of our DF-CCSD algorithm arises from the acceleration of several different terms, which are designated as the "gradient terms": computation of particle density matrices (PDMs), generalized Fock-matrix (GFM), solution of the Z-vector equation, formation of the relaxed PDMs and GFM, back-transformation of PDMs and GFM to the atomic orbital (AO) basis, and evaluation of gradients in the AO basis. For the largest member of the alkane set (C10H22), the computational times for the gradient terms (with the cc-pVTZ basis set) are 2582.6 (CCSD) and 310.7 (DF-CCSD) min, respectively, a speed up of more than 8-folds. For gradient related terms, the DF approach avoids the usage of four-index electron repulsion integrals. Based on our previous study [U. Bozkaya, J. Chem. Phys. 141, 124108 (2014)], our formalism completely avoids construction or storage of the 4-index two-particle density matrix (TPDM), using instead 2- and 3-index TPDMs. The DF approach introduces negligible errors for equilibrium bond lengths and harmonic vibrational frequencies.
Negara, Ardiansyah
2015-05-01
Anisotropy of hydraulic properties of the subsurface geologic formations is an essential feature that has been established as a consequence of the different geologic processes that undergo during the longer geologic time scale. With respect to subsurface reservoirs, in many cases, anisotropy plays significant role in dictating the direction of flow that becomes no longer dependent only on driving forces like the pressure gradient and gravity but also on the principal directions of anisotropy. Therefore, there has been a great deal of motivation to consider anisotropy into the subsurface flow and transport models. In this dissertation, we present subsurface flow modeling in single and dual continuum anisotropic porous media, which include the single-phase groundwater flow coupled with the solute transport in anisotropic porous media, the two-phase flow with gravity effect in anisotropic porous media, and the natural gas flow in anisotropic shale reservoirs. We have employed the multipoint flux approximation (MPFA) method to handle anisotropy in the flow model. The MPFA method is designed to provide correct discretization of the flow equations for general orientation of the principal directions of the permeability tensor. The implementation of MPFA method is combined with the experimenting pressure field approach, a newly developed technique that enables the solution of the global problem breaks down into the solution of multitude of local problems. The numerical results of the study demonstrate the significant effects of anisotropy of the subsurface formations. For the single-phase groundwater flow coupled with the solute transport modeling in anisotropic porous media, the results shows the strong impact of anisotropy on the pressure field and the migration of the solute concentration. For the two-phase flow modeling with gravity effect in anisotropic porous media, it is observed that the buoyancy-driven flow, which emerges due to the density differences between the
Energy Technology Data Exchange (ETDEWEB)
Belendez, A [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Pascual, C [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); Neipp, C [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Belendez, T [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-02-15
A modified He's homotopy perturbation method is used to calculate higher-order analytical approximate solutions to the relativistic and Duffing-harmonic oscillators. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. The approximate formulae obtained show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation, including the limiting cases of amplitude approaching zero and infinity. For the relativistic oscillator, only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 1.6% for small and large values of oscillation amplitude, while this relative error is 0.65% for two iterations with two harmonics and as low as 0.18% when three harmonics are considered in the second approximation. For the Duffing-harmonic oscillator the relative error is as low as 0.078% when the second approximation is considered. Comparison of the result obtained using this method with those obtained by the harmonic balance methods reveals that the former is very effective and convenient.
DEFF Research Database (Denmark)
Dole, Shelley; Hilton, Annette; Hilton, Geoff
2015-01-01
Proportional reasoning is widely acknowledged as a key to success in school mathematics, yet students’ continual difficulties with proportion-related tasks are well documented. This paper draws on a large research study that aimed to support 4th to 9th grade teachers to design and implement tasks...... to foster students’ proportional reasoning. Classroom data revealed limited initial teacher knowledge and awareness of the pervasive nature of proportional reasoning required in the mathematics curriculum. Teacher capacity to seize teachable moments for building students’ proportional reasoning skills...... increased throughout the project. From this background, this paper presents an analysis of the proportional reasoning demands and opportunities of topics within the school mathematics curriculum in Australia. Implications for the study of whole number arithmetic (WNA) and other topics to promote...
Approximate Representations and Approximate Homomorphisms
Moore, Cristopher
2010-01-01
Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups: functions f:G -> U_d such that Pr[f(xy) = f(x) f(y)] is large, or more generally Exp_{x,y} ||f(xy) - f(x)f(y)||^2$ is small, where x and y are uniformly random elements of the group G and U_d denotes the unitary group of degree d. We bound these quantities in terms of the ratio d / d_min where d_min is the dimension of the smallest nontrivial representation of G. As an application, we bound the extent to which a function f : G -> H can be an approximate homomorphism where H is another finite group. We show that if H's representations are significantly smaller than G's, no such f can be much more homomorphic than a random function. We interpret these results as showing that if G is quasirandom, that is, if d_min is large, then G cannot be embedded in a small number of dimensi...
CERN. Geneva
2015-01-01
Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...
Sparse approximation with bases
2015-01-01
This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...
Berker, Selim
2007-01-01
Moral particularists argue that because reasons for action are irreducibly context-dependent, the traditional quest in ethics for true and exceptionless moral principles is hopelessly misguided. In making this claim, particularists assume a general framework according to which reasons are the ground floor normative units undergirding all other normative properties and relations. They then argue that there is no cashing out in finite terms either (i) when a given non-normative feature gives ri...
Directory of Open Access Journals (Sweden)
Cristinel Mortici
2015-01-01
Full Text Available In this survey we present our recent results on analysis of gamma function and related functions. The results obtained are in the theory of asymptotic analysis, approximation of gamma and polygamma functions, or in the theory of completely monotonic functions. The motivation of this first part is the work of C. Mortici [Product Approximations via Asymptotic Integration Amer. Math. Monthly 117 (2010 434-441] where a simple strategy for constructing asymptotic series is presented. The classical asymptotic series associated to Stirling, Wallis, Glaisher-Kinkelin are rediscovered. In the second section we discuss some new inequalities related to Landau constants and we establish some asymptotic formulas.
Directory of Open Access Journals (Sweden)
Eriksson Charli
2009-12-01
Full Text Available Abstract Background Alcohol consumption among adolescents is a serious public health concern. Research has shown that prevention programs targeting parents can help prevent underage drinking. The problem is that parental participation in these kinds of interventions is generally low. Therefore, the aim of the present study is to examine non-participation in a parental support program aiming to prevent underage alcohol drinking. The Health Belief Model has been used as a tool for the analysis. Methods To understand non-participation in a parental program a quasi-experimental mixed-method design was used. The participants in the study were invited to participate in a parental program targeting parents with children in school years 7-9. A questionnaire was sent home to the parents before the program started. Two follow-up surveys were also carried out. The inclusion criteria for the study were that the parents had answered the questionnaire in school year 7 and either of the questionnaires in the two subsequent school years (n = 455. Multinomial logistic regression analysis was used to examine reasons for non-participation. The final follow-up questionnaire included an opened-ended question about reasons for non-participation. A qualitative content analysis was carried out and the two largest categories were included in the third model of the multinomial logistic regression analysis. Results Educational level was the most important socio-demographic factor for predicting non-participation. Parents with a lower level of education were less likely to participate than those who were more educated. Factors associated with adolescents and alcohol did not seem to be of significant importance. Instead, program-related factors predicted non-participation, e.g. parents who did not perceive any need for the intervention and who did not attend the information meeting were more likely to be non-participants. Practical issues, like time demands, also seemed to
Yin, George; Wang, Le Yi; Zhang, Hongwei
2014-12-01
Stochastic approximation methods have found extensive and diversified applications. Recent emergence of networked systems and cyber-physical systems has generated renewed interest in advancing stochastic approximation into a general framework to support algorithm development for information processing and decisions in such systems. This paper presents a survey on some recent developments in stochastic approximation methods and their applications. Using connected vehicles in platoon formation and coordination as a platform, we highlight some traditional and new methodologies of stochastic approximation algorithms and explain how they can be used to capture essential features in networked systems. Distinct features of networked systems with randomly switching topologies, dynamically evolving parameters, and unknown delays are presented, and control strategies are provided.
Quantitative Algebraic Reasoning
DEFF Research Database (Denmark)
Mardare, Radu Iulian; Panangaden, Prakash; Plotkin, Gordon
2016-01-01
We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We deﬁne an equality relation indexed by rationals: a =ε b which we think of as saying that “a is approximately equal to b up to an error of ε”. We have 4 interesting examples where we have a quantitative...
Schantz, Clémence; Sim, Kruy Leang; Ly, Ek Meng; Barennes, Hubert; Sudaroth, So; Goyet, Sophie
2015-05-01
First documented in 1741, the practice of episiotomy substantially increased worldwide during the 20th century. However, research shows that episiotomy is not effective in reducing severe perineal trauma and may be harmful. Using a mixed-methods approach, we conducted a study in 2013-14 on why obstetricians and midwives in a large maternity hospital in Phnom Penh, Cambodia, still do routine episiotomies. The study included the extent of the practice, based on medical records; a retrospective analysis of the delivery notes of a random sample of 365 patients; and 22 in-depth interviews with obstetricians, midwives and recently delivered women. Of the 365 women, 345 (94.5%, 95% CI: 91.7-96.6) had had an episiotomy. Univariate analysis showed that nulliparous women underwent episiotomy more frequently than multiparous women (OR 7.1, 95% CI 2.0-24.7). The reasons given for this practice by midwives and obstetricians were: fear of perineal tears, the strong belief that Asian women have a shorter and harder perineum than others, lack of time in overcrowded delivery rooms, and the belief that Cambodian women would be able to have a tighter and prettier vagina through this practice. A restrictive episiotomy policy and information for pregnant women about birthing practices through antenatal classes should be implemented as soon as possible.
Sufficient reason and reason enough
Romero, Gustavo E
2014-01-01
I offer an analysis of the Principle of Sufficient Reason and its relevancy for the scientific endeavour. I submit that the world is not, and cannot be, rational - only some brained beings are. The Principle of Sufficient Reason is not a necessary truth nor a physical law. It is just a guiding metanomological hypothesis justified a posteriori by its success in helping us to unveil the mechanisms that operate in Nature.
Energy Technology Data Exchange (ETDEWEB)
Rogers, J.; Porter, K.
2012-03-01
This paper updates previous work that describes time period-based and other approximation methods for estimating the capacity value of wind power and extends it to include solar power. The paper summarizes various methods presented in utility integrated resource plans, regional transmission organization methodologies, regional stakeholder initiatives, regulatory proceedings, and academic and industry studies. Time period-based approximation methods typically measure the contribution of a wind or solar plant at the time of system peak - sometimes over a period of months or the average of multiple years.
DEFF Research Database (Denmark)
Tylén, Kristian; Fusaroli, Riccardo; Stege Bjørndahl, Johanne
2015-01-01
Many types of everyday and specialized reasoning depend on diagrams: we use maps to find our way, we draw graphs and sketches to communicate concepts and prove geometrical theorems, and we manipulate diagrams to explore new creative solutions to problems. The active involvement and manipulation...... of representational artifacts for purposes of thinking and communicating is discussed in relation to C.S. Peirce’s notion of diagrammatical reasoning. We propose to extend Peirce’s original ideas and sketch a conceptual framework that delineates different kinds of diagram manipulation: Sometimes diagrams...
Liu, Q.; Liu, F.; Turner, I.; Anh, V.
2007-03-01
In this paper we present a random walk model for approximating a Lévy-Feller advection-dispersion process, governed by the Lévy-Feller advection-dispersion differential equation (LFADE). We show that the random walk model converges to LFADE by use of a properly scaled transition to vanishing space and time steps. We propose an explicit finite difference approximation (EFDA) for LFADE, resulting from the Grünwald-Letnikov discretization of fractional derivatives. As a result of the interpretation of the random walk model, the stability and convergence of EFDA for LFADE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.
1992-08-31
Psicologia , 4(3), 183-198. 94 Guyote, M.J. and Sternberg, R.J. (1981). A transitive-chain theory of syllogistic reasoning. Cognitive Psychology, 13(4), 461...personal connections. Journal of Social Psychology, 20, 39-59. Newell, A. (1990). Unified Theories of Cognition. Cambridge, Massachusetts: Harvard
Sun, Zhigang
2016-01-01
We proposed a distributed approximating functional method for efficiently describing the electronic dynamics in atoms and molecules in the presence of the Coulomb singularities, using the kernel of a grid representation derived by using the solutions of the Coulomb differential equation based upon the Schwartz's interpolation formula, and a grid representation using the Lobatto/Radau shape functions. The elements of the resulted Hamiltonian matrix are confined in a narrow diagonal band, which is similar to that using the (higher order) finite difference methods. However, the spectral convergence properties of the original grid representations are retained in the proposed distributed approximating functional method for solving the Schr\\"odinger equation involving the Coulomb singularity. Thus the method is effective for solving the electronic Schr\\"odinger equation using iterative methods where the action of the Hamiltonian matrix on the wave function need to evaluate many times. The method is investigated by ...
Approximate and renormgroup symmetries
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling
2009-07-01
''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)
Orecchia, Lorenzo; Vishnoi, Nisheeth K
2011-01-01
We give a novel spectral approximation algorithm for the balanced separator problem that, given a graph G, a constant balance b \\in (0,1/2], and a parameter \\gamma, either finds an \\Omega(b)-balanced cut of conductance O(\\sqrt(\\gamma)) in G, or outputs a certificate that all b-balanced cuts in G have conductance at least \\gamma, and runs in time \\tilde{O}(m). This settles the question of designing asymptotically optimal spectral algorithms for balanced separator. Our algorithm relies on a variant of the heat kernel random walk and requires, as a subroutine, an algorithm to compute \\exp(-L)v where L is the Laplacian of a graph related to G and v is a vector. Algorithms for computing the matrix-exponential-vector product efficiently comprise our next set of results. Our main result here is a new algorithm which computes a good approximation to \\exp(-A)v for a class of PSD matrices A and a given vector u, in time roughly \\tilde{O}(m_A), where m_A is the number of non-zero entries of A. This uses, in a non-trivia...
Meier, Patrick; Rauhut, Guntram
2015-12-01
Three different approaches for calculating Franck-Condon factors beyond the harmonic approximation are compared and discussed in detail. Duschinsky effects are accounted for either by a rotation of the initial or final wavefunctions - which are obtained from state-specific configuration-selective vibrational configuration interaction calculations - or by a rotation of the underlying multi-dimensional potential energy surfaces being determined from explicitly correlated coupled-cluster approaches. An analysis of the Duschinsky effects in dependence on the rotational angles and the anisotropy of the wavefunction is provided. Benchmark calculations for the photoelectron spectra of ClO2, HS-2 and ZnOH- are presented. An application of the favoured approach for calculating Franck-Condon factors to the oxidation of Zn(H2O)+ and Zn2(H2O)+ demonstrates its applicability to systems with more than three atoms.
Approximate Modified Policy Iteration
Scherrer, Bruno; Ghavamzadeh, Mohammad; Geist, Matthieu
2012-01-01
Modified policy iteration (MPI) is a dynamic programming (DP) algorithm that contains the two celebrated policy and value iteration methods. Despite its generality, MPI has not been thoroughly studied, especially its approximation form which is used when the state and/or action spaces are large or infinite. In this paper, we propose three approximate MPI (AMPI) algorithms that are extensions of the well-known approximate DP algorithms: fitted-value iteration, fitted-Q iteration, and classification-based policy iteration. We provide an error propagation analysis for AMPI that unifies those for approximate policy and value iteration. We also provide a finite-sample analysis for the classification-based implementation of AMPI (CBMPI), which is more general (and somehow contains) than the analysis of the other presented AMPI algorithms. An interesting observation is that the MPI's parameter allows us to control the balance of errors (in value function approximation and in estimating the greedy policy) in the fina...
Ordered cones and approximation
Keimel, Klaus
1992-01-01
This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.
A B-Spline-Based Colocation Method to Approximate the Solutions to the Equations of Fluid Dynamics
Energy Technology Data Exchange (ETDEWEB)
Johnson, Richard Wayne; Landon, Mark Dee
1999-07-01
The potential of a B-spline collocation method for numerically solving the equations of fluid dynamics is discussed. It is known that B-splines can resolve curves with drastically fewer data than can their standard shape function counterparts. This feature promises to allow much faster numerical simulations of fluid flow than standard finite volume/finite element methods without sacrificing accuracy. An example channel flow problem is solved using the method.
A B-Spline-Based Colocation Method to Approximate the Solutions to the Equations of Fluid Dynamics
Energy Technology Data Exchange (ETDEWEB)
M. D. Landon; R. W. Johnson
1999-07-01
The potential of a B-spline collocation method for numerically solving the equations of fluid dynamics is discussed. It is known that B-splines can resolve complex curves with drastically fewer data than can their standard shape function counterparts. This feature promises to allow much faster numerical simulations of fluid flow than standard finite volume/finite element methods without sacrificing accuracy. An example channel flow problem is solved using the method.
Institute of Scientific and Technical Information of China (English)
Liu Jin-Cun; Hou Guo-Lin
2010-01-01
In this paper, the generalised two-dimensional differential transform method (DTM) of solving the time-fractional coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the generalised two-dimensional DTM is effective for the coupled equations.
Energy Technology Data Exchange (ETDEWEB)
Caldeira, Alexandre D. [Centro Tecnico Aeroespacial (CTA-IEAv), Sao Jose dos Campos, SP (Brazil). Inst. de Estudos Avancados
2000-07-01
This work deals with the cell neutron spectra calculated with the transport equation for an infinite medium applied to the homogenized cell. Considering a radioisotope production reactor fuel cell, as a sample case, the maximum deviation found between the approximated and the S{sub N} methods was 13%. (author)
Energy Technology Data Exchange (ETDEWEB)
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Pascual, C.; Gallego, S.; Ortuno, M.; Neipp, C. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2007-11-26
A modified He's homotopy perturbation method (HHPM) is used to calculate the periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to x{sup 1/3}. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified HHPM works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 0.6% for small and large values of oscillation amplitude, while this relative error is 0.17% for the second iteration and as low as 0.024% when the third approximation is considered. Comparison of the result obtained using this method with those obtained by different harmonic balance methods reveals that the former is very effective and convenient.
Chartier, Daniel
1996-01-01
Exposes two groups of adults in vocational-education training programs to two different programs (Logo-Educability exercises and Logical Reasoning Workshops) designed to improve their cognitive skills. Argues that low improvement scores for both groups demonstrate the inefficacy of the programs in helping students transfer learned cognitive skills…
CranSLIK v1.0: stochastic prediction of oil spill transport and fate using approximation methods
Directory of Open Access Journals (Sweden)
B. J. Snow
2014-07-01
Full Text Available This paper investigates the development of a model, called CranSLIK, to predict the transport and transformations of a point mass oil spill via a stochastic approach. Initially the various effects on destination are considered and key parameters are chosen which are expected to dominate the displacement. The variables considered are: wind velocity, surface water velocity, spill size, and spill age. For a point mass oil spill, it is found that the centre of mass can be determined by the wind and current data only, and the spill size and age can then be used to reconstruct the surface of the spill. These variables are sampled and simulations are performed using an open-source Lagrangian approach-based code, MEDSLIK II. Regression modelling is applied to create two sets of polynomials: one for the centre of mass, and one for the spill size. Simulations performed for a real oil spill case show that a minimum of approximately 80% of the oil is captured by CranSLIK. Finally, Monte Carlo simulation is implemented to allow for consideration of the most likely destination for the oil spill, when the distributions for the oceanographic conditions are known.
Kopka, Piotr; Wawrzynczak, Anna; Borysiewicz, Mieczyslaw
2016-11-01
In this paper the Bayesian methodology, known as Approximate Bayesian Computation (ABC), is applied to the problem of the atmospheric contamination source identification. The algorithm input data are on-line arriving concentrations of the released substance registered by the distributed sensors network. This paper presents the Sequential ABC algorithm in detail and tests its efficiency in estimation of probabilistic distributions of atmospheric release parameters of a mobile contamination source. The developed algorithms are tested using the data from Over-Land Atmospheric Diffusion (OLAD) field tracer experiment. The paper demonstrates estimation of seven parameters characterizing the contamination source, i.e.: contamination source starting position (x,y), the direction of the motion of the source (d), its velocity (v), release rate (q), start time of release (ts) and its duration (td). The online-arriving new concentrations dynamically update the probability distributions of search parameters. The atmospheric dispersion Second-order Closure Integrated PUFF (SCIPUFF) Model is used as the forward model to predict the concentrations at the sensors locations.
用同伦摄动法解Kdv-Burgers方程%Homotopy Perturbation Method and Approximate Solutions of Kdv-Burgers Equaition
Institute of Scientific and Technical Information of China (English)
李阳; 王佩臣
2011-01-01
利用行波变换将Kdv-Burgers方程化为常微分方程,并结合同伦摄动方法求它的二阶近似解.%Some discussion and gets to some conclusion are made on how to transform Kdv-Burgers equation into the ordinary differential equation with traveling wave transform method and homotopy perturbation method.And get the equations of second order approximate solutions.
Energy Technology Data Exchange (ETDEWEB)
Hayashi, Nobuhiko, E-mail: n-hayashi@21c.osakafu-u.ac.j [Nanoscience and Nanotechnology Research Center (N2RC), Osaka Prefecture University, 1-2 Gakuen-cho, Sakai 599-8570 (Japan) and CREST (JST), 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan); Nagai, Yuki [Department of Physics, University of Tokyo, Tokyo 113-0033 (Japan); JST, TRIP, Chiyoda, Tokyo 102-0075 (Japan); Higashi, Yoichi [Department of Mathematical Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Sakai 599-8531 (Japan)
2010-12-15
We theoretically discuss the magnetic-field-angle dependence of the zero-energy density of states (ZEDOS) in superconductors. Point-node and line-node superconducting gaps on spherical and cylindrical Fermi surfaces are considered. The Doppler-shift (DS) method and the Kramer-Pesch approximation (KPA) are used to calculate the ZEDOS. Numerical results show that consequences of the DS method are corrected by the KPA.
Hayashi, Nobuhiko; Nagai, Yuki; Higashi, Yoichi
2010-12-01
We theoretically discuss the magnetic-field-angle dependence of the zero-energy density of states (ZEDOS) in superconductors. Point-node and line-node superconducting gaps on spherical and cylindrical Fermi surfaces are considered. The Doppler-shift (DS) method and the Kramer-Pesch approximation (KPA) are used to calculate the ZEDOS. Numerical results show that consequences of the DS method are corrected by the KPA.
Approximating Stationary Statistical Properties
Institute of Scientific and Technical Information of China (English)
Xiaoming WANG
2009-01-01
It is well-known that physical laws for large chaotic dynamical systems are revealed statistically. Many times these statistical properties of the system must be approximated numerically. The main contribution of this manuscript is to provide simple and natural criterions on numerical methods (temporal and spatial discretization) that are able to capture the stationary statistical properties of the underlying dissipative chaotic dynamical systems asymptotically. The result on temporal approximation is a recent finding of the author, and the result on spatial approximation is a new one. Applications to the infinite Prandtl number model for convection and the barotropic quasi-geostrophic model are also discussed.
Hayes, Brett K; Heit, Evan; Swendsen, Haruka
2010-03-01
Inductive reasoning entails using existing knowledge or observations to make predictions about novel cases. We review recent findings in research on category-based induction as well as theoretical models of these results, including similarity-based models, connectionist networks, an account based on relevance theory, Bayesian models, and other mathematical models. A number of touchstone empirical phenomena that involve taxonomic similarity are described. We also examine phenomena involving more complex background knowledge about premises and conclusions of inductive arguments and the properties referenced. Earlier models are shown to give a good account of similarity-based phenomena but not knowledge-based phenomena. Recent models that aim to account for both similarity-based and knowledge-based phenomena are reviewed and evaluated. Among the most important new directions in induction research are a focus on induction with uncertain premise categories, the modeling of the relationship between inductive and deductive reasoning, and examination of the neural substrates of induction. A common theme in both the well-established and emerging lines of induction research is the need to develop well-articulated and empirically testable formal models of induction. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website.
Ahlkrona, Josefin; Lötstedt, Per; Kirchner, Nina; Zwinger, Thomas
2016-03-01
We propose and implement a new method, called the Ice Sheet Coupled Approximation Levels (ISCAL) method, for simulation of ice sheet flow in large domains during long time-intervals. The method couples the full Stokes (FS) equations with the Shallow Ice Approximation (SIA). The part of the domain where SIA is applied is determined automatically and dynamically based on estimates of the modeling error. For a three dimensional model problem, ISCAL computes the solution substantially faster with a low reduction in accuracy compared to a monolithic FS. Furthermore, ISCAL is shown to be able to detect rapid dynamic changes in the flow. Three different error estimations are applied and compared. Finally, ISCAL is applied to the Greenland Ice Sheet on a quasi-uniform grid, proving ISCAL to be a potential valuable tool for the ice sheet modeling community.
Ahlkrona, Josefin; Kirchner, Nina; Zwinger, Thomas
2015-01-01
We propose and implement a new method, called the Ice Sheet Coupled Approximation Levels (ISCAL) method, for simulation of ice sheet flow in large domains under long time-intervals. The method couples the exact, full Stokes (FS) equations with the Shallow Ice Approximation (SIA). The part of the domain where SIA is applied is determined automatically and dynamically based on estimates of the modeling error. For a three dimensional model problem where the number of degrees of freedom is comparable to a real world application, ISCAL performs almost an order of magnitude faster with a low reduction in accuracy compared to a monolithic FS. Furthermore, ISCAL is shown to be able to detect rapid dynamic changes in the flow. Three different error estimations are applied and compared. Finally, ISCAL is applied to the Greenland Ice Sheet, proving ISCAL to be a potential valuable tool for the ice sheet modeling community.
Directory of Open Access Journals (Sweden)
Chi-Chang Wang
2013-09-01
Full Text Available This paper seeks to use the proposed residual correction method in coordination with the monotone iterative technique to obtain upper and lower approximate solutions of singularly perturbed non-linear boundary value problems. First, the monotonicity of a non-linear differential equation is reinforced using the monotone iterative technique, then the cubic-spline method is applied to discretize and convert the differential equation into the mathematical programming problems of an inequation, and finally based on the residual correction concept, complex constraint solution problems are transformed into simpler questions of equational iteration. As verified by the four examples given in this paper, the method proposed hereof can be utilized to fast obtain the upper and lower solutions of questions of this kind, and to easily identify the error range between mean approximate solutions and exact solutions.
Tailleux, Remi
2010-01-01
In order to help achieve a future better understanding of the role of internal energy in turbulent stratified fluids, a new method is proposed for constructing Boussinesq models that conserve energy exactly, and that are endowed with a fully internally consistent description of thermodynamics.
Energy Technology Data Exchange (ETDEWEB)
Frankena, M.W.; Owen, B.M.
1993-07-15
The FERC's failure to investigate the Entergy/GSU merger's effects on market power may force other agencies to examine electric utility mergers on their own. The competitive effects of the proposed merger Entergy and Gulf States Utilities (GSU) will not be further investigated by the Federal Energy Regulatory Commission (FERC), according to a January 1993 order. The FERC's primary justification is that the [open quotes]open access[close quotes] transmission conditions offered by the merging parties eliminated concern over market power in transmission and bulk power. The FERC's reasoning is flawed. If the merger were to lead to an increase in market power, the proposed transmission conditions would not prevent the merged firm from exercising that power. The FERC also justifies its decision not to investigate the competitive effects of the merger on the grounds that no intervenor had demonstrated that present competition between the two systems is more than de minimis. This is not an appropriate standard. Intervenors demonstrated that Entergy's and GSU's transmission system offer alternative contract routes for bulk power between generators and customers. Even if Entergy and GSU both do not actually sell significant amounts of the same transmission-service, an antitrust evaluation should consider whether the availability of a second, independent route constrains the pricing of the first. The FERC's reasoning indicates that it has lost its way in carrying out its responsibilities to protect consumers. Open access to transmission systems may play an important role in increasing competition in bulk power markets. However, the FERC's goal should be to promote competition, not merely to open access for its own sake. In its enthusiasm to secure [open quotes]open access[close quotes], the FERC appears willing to ignore possible reductions in competition.
Energy Technology Data Exchange (ETDEWEB)
Karagiannis, Georgios; Lin, Guang
2014-02-15
Generalized polynomial chaos (gPC) expansions allow the representation of the solution of a stochastic system as a series of polynomial terms. The number of gPC terms increases dramatically with the dimension of the random input variables. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs if the evaluations of the system are expensive, the evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solution, both in spacial and random domains, by coupling Bayesian model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spacial points via (1) Bayesian model average or (2) medial probability model, and their construction as functions on the spacial domain via spline interpolation. The former accounts the model uncertainty and provides Bayes-optimal predictions; while the latter, additionally, provides a sparse representation of the solution by evaluating the expansion on a subset of dominating gPC bases when represented as a gPC expansion. Moreover, the method quantifies the importance of the gPC bases through inclusion probabilities. We design an MCMC sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed method is suitable for, but not restricted to, problems whose stochastic solution is sparse at the stochastic level with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the good performance of the proposed method and make comparisons with others on 1D, 14D and 40D in random space elliptic stochastic partial differential equations.
Lorin, E.; Yang, X.; Antoine, X.
2016-06-01
The paper is devoted to develop efficient domain decomposition methods for the linear Schrödinger equation beyond the semiclassical regime, which does not carry a small enough rescaled Planck constant for asymptotic methods (e.g. geometric optics) to produce a good accuracy, but which is too computationally expensive if direct methods (e.g. finite difference) are applied. This belongs to the category of computing middle-frequency wave propagation, where neither asymptotic nor direct methods can be directly used with both efficiency and accuracy. Motivated by recent works of the authors on absorbing boundary conditions (Antoine et al. (2014) [13] and Yang and Zhang (2014) [43]), we introduce Semiclassical Schwarz Waveform Relaxation methods (SSWR), which are seamless integrations of semiclassical approximation to Schwarz Waveform Relaxation methods. Two versions are proposed respectively based on Herman-Kluk propagation and geometric optics, and we prove the convergence and provide numerical evidence of efficiency and accuracy of these methods.
Indian Academy of Sciences (India)
KAUSHIK MAJI
2016-08-01
We propose a variant of the multiconfiguration time-dependent Hartree (MCTDH) method within the framework of Hermite-distributed approximating functional (HDAF) method. The discretized Hamiltonian is a highly banded Toeplitz matrix which significantly reduces computational cost in terms of both storage and number of operations. The method proposed is employed to carry out the study of tunnelling dynamics of two coupled double well oscillators. We have calculated the orthogonality time \\tau , which is a measure of the time interval for an initial state to evolve into its orthogonal state. It is observed that the coupling has a significant effect on \\tau .
Directory of Open Access Journals (Sweden)
Jae-Hong Pyo
2013-01-01
Full Text Available The stabilized Gauge-Uzawa method (SGUM, which is a 2nd-order projection type algorithm used to solve Navier-Stokes equations, has been newly constructed in the work of Pyo, 2013. In this paper, we apply the SGUM to the evolution Boussinesq equations, which model the thermal driven motion of incompressible fluids. We prove that SGUM is unconditionally stable, and we perform error estimations on the fully discrete finite element space via variational approach for the velocity, pressure, and temperature, the three physical unknowns. We conclude with numerical tests to check accuracy and physically relevant numerical simulations, the Bénard convection problem and the thermal driven cavity flow.
Bousserez, Nicolas
2016-01-01
This paper provides a detailed theoretical analysis of methods to approximate the solutions of high-dimensional (>10^6) linear Bayesian problems. An optimal low-rank projection that maximizes the information content of the Bayesian inversion is proposed and efficiently constructed using a scalable randomized SVD algorithm. Useful optimality results are established for the associated posterior error covariance matrix and posterior mean approximations, which are further investigated in a numerical experiment consisting of a large-scale atmospheric tracer transport source-inversion problem. This method proves to be a robust and efficient approach to dimension reduction, as well as a natural framework to analyze the information content of the inversion. Possible extensions of this approach to the non-linear framework in the context of operational numerical weather forecast data assimilation systems based on the incremental 4D-Var technique are also discussed, and a detailed implementation of a new Randomized Incr...
Song, Li-Na; Wang, Wei-Guo
2012-08-01
By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper, we are concerned with the partial regularity for the weak solutions of energy minimizing p-harmonic maps under the controllable growth condition. We get the interior partial regularity by the p-harmonic approximation method together with the technique used to get the decay estimation on some Degenerate elliptic equations and the obstacle problem by Tan and Yan. In particular, we directly get the optimal regularity.
Institute of Scientific and Technical Information of China (English)
宋丽娜; 王维国
2012-01-01
By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.
Moraes Rêgo, Patrícia Helena; Viana da Fonseca Neto, João; Ferreira, Ernesto M.
2015-08-01
The main focus of this article is to present a proposal to solve, via UDUT factorisation, the convergence and numerical stability problems that are related to the covariance matrix ill-conditioning of the recursive least squares (RLS) approach for online approximations of the algebraic Riccati equation (ARE) solution associated with the discrete linear quadratic regulator (DLQR) problem formulated in the actor-critic reinforcement learning and approximate dynamic programming context. The parameterisations of the Bellman equation, utility function and dynamic system as well as the algebra of Kronecker product assemble a framework for the solution of the DLQR problem. The condition number and the positivity parameter of the covariance matrix are associated with statistical metrics for evaluating the approximation performance of the ARE solution via RLS-based estimators. The performance of RLS approximators is also evaluated in terms of consistence and polarisation when associated with reinforcement learning methods. The used methodology contemplates realisations of online designs for DLQR controllers that is evaluated in a multivariable dynamic system model.
Chatterjee, Koushik; Pastorczak, Ewa; Jawulski, Konrad; Pernal, Katarzyna
2016-06-01
A perfect-pairing generalized valence bond (GVB) approximation is known to be one of the simplest approximations, which allows one to capture the essence of static correlation in molecular systems. In spite of its attractive feature of being relatively computationally efficient, this approximation misses a large portion of dynamic correlation and does not offer sufficient accuracy to be generally useful for studying electronic structure of molecules. We propose to correct the GVB model and alleviate some of its deficiencies by amending it with the correlation energy correction derived from the recently formulated extended random phase approximation (ERPA). On the examples of systems of diverse electronic structures, we show that the resulting ERPA-GVB method greatly improves upon the GVB model. ERPA-GVB recovers most of the electron correlation and it yields energy barrier heights of excellent accuracy. Thanks to a balanced treatment of static and dynamic correlation, ERPA-GVB stays reliable when one moves from systems dominated by dynamic electron correlation to those for which the static correlation comes into play.
一种集成式不确定推理方法研究%Research on an Ensemble Method of Uncertainty Reasoning
Institute of Scientific and Technical Information of China (English)
贺怀清; 李建伏
2011-01-01
Ensemble learning is a machine learning paradigm where multiple models are strategically generated and combined to obtain better predictive performance than a single learning method.It was proven that ensemble learning is feasible and tends to yield better results.Uncertainty reasoning is one of the important directions in artificial intelligence.Various uncertainty reasoning methods have been developed and all have their own advantages and disadvantages.Motivated by ensemble learning, an ensemble method of uncertainty reasoning was proposed.The main idea of the new method is in accordance with the basic framework of ensemble learning,where multiple uncertainty reasoning methods is used in time and the result of various reasoning methods is integrated by some rules as the final result.Finally, theoretical analysis and experimental tests show that the ensemble uncertainty reasoning method is effective and feasible.%集成学习是采用某种规则把一系列学习器的结果进行整合以获得比单个学习器更好的学习效果的一种机器学习方法.研究表明集成学习是可行的,能取得比传统学习方法更好的性能.不确定推理是人工智能的重要研究方向之一,目前已经开发出了多种不确定推理方法,这些方法在实际应用中各有优缺点.借鉴集成学习,提出一种集成式不确定推理方法,其基本思想是按照一定的策略集成多种不确定推理方法,以提高推理的准确性.理论分析和实验结果验证了方法的合理性和可行性.
Approximate kernel competitive learning.
Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang
2015-03-01
Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches.
Directory of Open Access Journals (Sweden)
K. V. Dobrego
2015-01-01
Full Text Available Differential approximation is derived from radiation transfer equation by averaging over the solid angle. It is one of the more effective methods for engineering calculations of radia- tive heat transfer in complex three-dimensional thermal power systems with selective and scattering media. The new method for improvement of accuracy of the differential approximation based on using of auto-adaptable boundary conditions is introduced in the paper. The efficiency of the named method is proved for the test 2D-systems. Self-consistent auto-adaptable boundary conditions taking into consideration the nonorthogonal component of the incident to the boundary radiation flux are formulated. It is demonstrated that taking in- to consideration of the non- orthogonal incident flux in multi-dimensional systems, such as furnaces, boilers, combustion chambers improves the accuracy of the radiant flux simulations and to more extend in the zones adjacent to the edges of the chamber.Test simulations utilizing the differential approximation method with traditional boundary conditions, new self-consistent boundary conditions and “precise” discrete ordinates method were performed. The mean square errors of the resulting radiative fluxes calculated along the boundary of rectangular and triangular test areas were decreased 1.5–2 times by using auto- adaptable boundary conditions. Radiation flux gaps in the corner points of non-symmetric sys- tems are revealed by using auto-adaptable boundary conditions which can not be obtained by using the conventional boundary conditions.
Directory of Open Access Journals (Sweden)
Lin Shao
2016-01-01
Full Text Available Due to large numbers of antennas and users, matrix inversion is complicated in linear precoding techniques for massive MIMO systems. Several approximated matrix inversion methods, including the Neumann series, have been proposed to reduce the complexity. However, the Neumann series does not converge fast enough. In this paper, to speed up convergence, a new joint Newton iteration and Neumann series method is proposed, with the first iteration result of Newton iteration method being employed to reconstruct the Neumann series. Then, a high probability convergence condition is established, which can offer useful guidelines for practical massive MIMO systems. Finally, simulation examples are given to demonstrate that the new joint Newton iteration and Neumann series method has a faster convergence rate compared to the previous Neumann series, with almost no increase in complexity when the iteration number is greater than or equal to 2.
26 CFR 1.412(c)(2)-1 - Valuation of plan assets; reasonable actuarial valuation methods.
2010-04-01
... determined under paragraph (b)(7) of this section. Assuming the numerical data of Example 6, the application... the funding standard account based on the retroactive application of its new method as of the first... valuation methods. 1.412(c)(2)-1 Section 1.412(c)(2)-1 Internal Revenue INTERNAL REVENUE SERVICE,...
Directory of Open Access Journals (Sweden)
Didier COURBET
2013-07-01
Full Text Available If multidisciplinarity is necessary, first, for studying the widest possible set of communication phenomena (organizational, in groups, interpersonal, media, computer-mediated communication... and, secondly, for grasping the complexity of the different moments of the same phenomenon of communication (production, content, reception, circulation ..., methodological pluralism is also important. However, French research in communication sciences leaves in the shade a number of phenomena and moments of communication that could be better understood thanks to the experimental method. We will underline that the epistemological issues related to rational use of the experimental method in communication sciences are not negligible: it allows the study of objects that cannot be investigated with other methods and offers the opportunity to build knowledge by the refutation of hypotheses and theoretical propositions. We will clarify some epistemological misunderstandings concerning this method. First, it is actually a method of studying complex systems and communication processes. Secondly, its use is not incompatible with constructivism.
Anderson, O. L.; Briley, W. R.; Mcdonald, H.
1978-01-01
An approximate analysis is presented for calculating three-dimensional, low Mach number, laminar viscous flows in curved passages with large secondary flows and corner boundary layers. The analysis is based on the decomposition of the overall velocity field into inviscid and viscous components with the overall velocity being determined from superposition. An incompressible vorticity transport equation is used to estimate inviscid secondary flow velocities to be used as corrections to the potential flow velocity field. A parabolized streamwise momentum equation coupled to an adiabatic energy equation and global continuity equation is used to obtain an approximate viscous correction to the pressure and longitudinal velocity fields. A collateral flow assumption is invoked to estimate the viscous correction to the transverse velocity fields. The approximate analysis is solved numerically using an implicit ADI solution for the viscous pressure and velocity fields. An iterative ADI procedure is used to solve for the inviscid secondary vorticity and velocity fields. This method was applied to computing the flow within a turbine vane passage with inlet flow conditions of M = 0.1 and M = 0.25, Re = 1000 and adiabatic walls, and for a constant radius curved rectangular duct with R/D = 12 and 14 and with inlet flow conditions of M = 0.1, Re = 1000, and adiabatic walls.
Matveev, Alexei V; Rösch, Notker
2008-06-28
We suggest an approximate relativistic model for economical all-electron calculations on molecular systems that exploits an atomic ansatz for the relativistic projection transformation. With such a choice, the projection transformation matrix is by definition both transferable and independent of the geometry. The formulation is flexible with regard to the level at which the projection transformation is approximated; we employ the free-particle Foldy-Wouthuysen and the second-order Douglas-Kroll-Hess variants. The (atomic) infinite-order decoupling scheme shows little effect on structural parameters in scalar-relativistic calculations; also, the use of a screened nuclear potential in the definition of the projection transformation shows hardly any effect in the context of the present work. Applications to structural and energetic parameters of various systems (diatomics AuH, AuCl, and Au(2), two structural isomers of Ir(4), and uranyl dication UO(2) (2+) solvated by 3-6 water ligands) show that the atomic approximation to the conventional second-order Douglas-Kroll-Hess projection (ADKH) transformation yields highly accurate results at substantial computational savings, in particular, when calculating energy derivatives of larger systems. The size-dependence of the intrinsic error of the ADKH method in extended systems of heavy elements is analyzed for the atomization energies of Pd(n) clusters (n
Mistry, Rashmita S; White, Elizabeth S; Chow, Kirby A; Griffin, Katherine M; Nenadal, Lindsey
2016-01-01
Mixed methods research approaches are gaining traction across various social science disciplines, including among developmental scientists. In this chapter, we discuss the utility of a mixed methods research approach in examining issues related to equity and justice. We incorporate a brief overview of quantitative and qualitative monomethod research approaches in our larger discussion of the advantages, procedures, and considerations of employing a mixed methods design to advance developmental science from an equity and justice perspective. To better illustrate the theoretical and practical significance of a mixed methods research approach, we include examples of research conducted on children and adolescents' conceptions of economic inequality as one example of developmental science research with an equity and justice frame.
2013-01-01
Background The European CHOICE study was a cross-sectional survey that evaluated women’s combined hormonal contraceptive choices before and after contraceptive counseling in Austria, Belgium, Czech Republic and Slovakia, the Netherlands, Poland, Sweden, Switzerland, Israel, Russia, and Ukraine. The changes in method selection before and after counseling were reported previously. In this paper we present the reasons given by the 18,787 participating women for selecting their contraceptive method of choice, as well as their perceptions about the contraceptive pill, patch, and ring after counseling. Methods Women with an interest in a combined hormonal contraceptive method (pill, patch, or ring) were counseled using a standardized counseling leaflet. The women completed questionnaires, which included questions on why they had selected a particular method of contraception, and the extent to which they agreed with statements about the attributes of the pill, patch, and ring. The results for each country were compared with the percentages for all countries combined by using a binomial regression model. Multiple logistic regression models were used to investigate the extent to which the probability of choosing a method was related to prespecified aspects (i.e. perceptions) of each contraceptive method. Results ‘Easy to use’, ‘convenience’, and ‘regular menstrual bleeding’ were important selection criteria. ‘Nondaily administration’ was one of the main reasons women selected the patch or ring. ‘Daily use’ and ‘will forget to take it’ were the primary reasons for not selecting the pill, while the main reasons for not choosing the patch included ‘not discrete, visible’ and ‘can fall off’. In a small number of instances, the ring was rejected because some women don’t like to use a ‘foreign body’. Women’s perceptions influenced their contraceptive decisions: positive perceptions about a method increased the likelihood that a woman
Ribeiro, Apoena A; Purger, Flávia; Rodrigues, Jonas A; Oliveira, Patrícia R A; Lussi, Adrian; Monteiro, Antonio Henrique; Alves, Haimon D L; Assis, Joaquim T; Vasconcellos, Adalberto B
2015-01-01
This in vivo study aimed to evaluate the influence of contact points on the approximal caries detection in primary molars, by comparing the performance of the DIAGNOdent pen and visual-tactile examination after tooth separation to bitewing radiography (BW). A total of 112 children were examined and 33 children were selected. In three periods (a, b, and c), 209 approximal surfaces were examined: (a) examiner 1 performed visual-tactile examination using the Nyvad criteria (EX1); examiner 2 used DIAGNOdent pen (LF1) and took BW; (b) 1 week later, after tooth separation, examiner 1 performed the second visual-tactile examination (EX2) and examiner 2 used DIAGNOdent again (LF2); (c) after tooth exfoliation, surfaces were directly examined using DIAGNOdent (LF3). Teeth were examined by computed microtomography as a reference standard. Analyses were based on diagnostic thresholds: D1: D 0 = health, D 1 –D 4 = disease; D2: D 0 , D 1 = health, D 2 –D 4 = disease; D3: D 0 –D 2 = health, D 3 , D 4 = disease. At D1, the highest sensitivity/specificity were observed for EX1 (1.00)/LF3 (0.68), respectively. At D2, the highest sensitivity/ specificity were observed for LF3 (0.69)/BW (1.00), respectively. At D3, the highest sensitivity/specificity were observed for LF3 (0.78)/EX1, EX2 and BW (1.00). EX1 showed higher accuracy values than LF1, and EX2 showed similar values to LF2. We concluded that the visual-tactile examination showed better results in detecting sound surfaces and approximal caries lesions without tooth separation. However, the effectiveness of approximal caries lesion detection of both methods was increased by the absence of contact points. Therefore, regardless of the method of detection, orthodontic separating elastics should be used as a complementary tool for the diagnosis of approximal noncavitated lesions in primary molars.
Chacón Rebollo, Tomás
2015-03-01
This paper introduces a variational multi-scale method where the sub-grid scales are computed by spectral approximations. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. This allows to element-wise calculate the sub-grid scales by means of the associated spectral expansion. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a finite number of modes. We apply this general framework to the convection-diffusion equation, by analytically computing the family of eigenfunctions. We perform a convergence and error analysis. We also present some numerical tests that show the stability of the method for an odd number of spectral modes, and an improvement of accuracy in the large resolved scales, due to the adding of the sub-grid spectral scales.
Institute of Scientific and Technical Information of China (English)
Jun Ma; Lixin Guo; Xiangzhe Cheng
2009-01-01
The optical wave scattering from one-dimensional (1D) lossy dielectric Gaussian random rough surface is studied. The tapered incident wave is introduced into the classical Kirchhoff approximation (KA), and the shadowing effect is also taken into account to make the KA results have a high accuracy. The definition of the bistatic scattering coefficient of the modified KA and the method of moment (MOM) are unified. The characteristics of the optical wave scattering from the lossy dielectric Gaussian random rough surface of different parameters are analyzed by implementing MOM.
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
二阶核近似有限粒子方法的改进%Modified finite particle method with second kernel approximation
Institute of Scientific and Technical Information of China (English)
李建成; 袁德奎; 陶建华
2013-01-01
该文对基于相容性核近似方法的二阶核近似光滑粒子流体动力学方法(K2_SPH方法)中函数及导数的核近似估计方法进行了改进,提出了一种改进的二阶核近似有限粒子方法(SK2_FPM方法).以一维情况为例对SPH方法、K2_SPH方法和SK2_FPM方法的核近似精度进行了理论推导和比较分析,并用Poiseuille流动、Couette流动以及一阶线性驻波问题三个经典算例对模型进行了检验.结果表明,随着核近似精度的改进,SK2 FPM方法较传统SPH方法和K2_SPH方法在计算精度和稳定性上都有一定程度的提高.%According to the kernel approximation for the function as well as the derivatives in K2_SPH,which is based on the particle consistency method,a modified finite particle method is introduced,namely a simplified second kernel approximation finite particle method (SK2_FPM).Taking one dimensional case as an example,the accuracy characteristics of kemel approximation for SPH,K2_SPH and SK2_FPM are theoretically derived and taken a comparative analysis among them.Then SK2_FPM is verified with three classic examples,which are Poiseuille flow,Couette flow and linear Standing Wave problem.With the improvement of kernel approximation,the results of SK2_FPM show that,higher accuracy and more stability compared with traditional SPH and K2_SPH to some extent.
Raval, Vaishali V.; Martini, Tanya S.; Raval, Pratiksha H.
2010-01-01
Although cross-cultural research concerning children's emotions is growing, few studies have examined emotion dysregulation in culturally diverse populations. This study compared 6- to 8-year-old children's reported methods of expressing and controlling anger, sadness, and physical pain, and their justifications for doing so across four groups in…
An Approximate Model of Microchannel Cooling
Institute of Scientific and Technical Information of China (English)
ShipingYu; MingdaoXin
1994-01-01
Forced convective heat transfer in micro-rectangular channels can be described by a group of two-dimensional differential equations.These equations take the conduction in microchannel wall along the direction of flow of coolants into account,which are more generalized than those which neglect the conduction.For the same reason,they are suitable particularly for gases-cooled microchannels.With only numerical solution to the equations till today,an approximate analytic solution is derived here,From this solution,a rather simple formula can be introduced further,by which the differences between considering the conduction and neglecting it are easily found.In addition,the reasonableness of the classical fin method is also discussed.An experimental example of air-cooled microchannels is illustrated.
DEFF Research Database (Denmark)
Jeong, Cheol-Ho; Ih, Jeong-Guon; Rindel, Jens Holger
2008-01-01
The phased beam tracing method (PBTM) was suggested as a medium-frequency simulation technique for the calculation of impulse response, although main assumptions of geometric acoustics still hold. The phased method needs the reflection coefficient for characterizing the acoustic property...... of a surface and the complex wave number for describing the propagation characteristics. In this study, two types of approximate real reflection coefficients derived from the measured absorption coefficient were tested for a practical applicability. As a test example, pressure impulse responses and energy......-frequency range in octave bands above the Schroeder cutoff frequency. A comparison was made between angle-dependent and angle-independent reflection coefficients in the calculation of acoustic measures. Although the angle-dependent reflection coefficient yielded best matched results with measured data...
Liu, Rentao; Jiang, Jiping; Guo, Liang; Shi, Bin; Liu, Jie; Du, Zhaolin; Wang, Peng
2016-06-01
In-depth filtering of emergency disposal technology (EDT) and materials has been required in the process of environmental pollution emergency disposal. However, an urgent problem that must be solved is how to quickly and accurately select the most appropriate materials for treating a pollution event from the existing spill control and clean-up materials (SCCM). To meet this need, the following objectives were addressed in this study. First, the material base and a case base for environment pollution emergency disposal were established to build a foundation and provide material for SCCM screening. Second, the multiple case-based reasoning model method with a difference-driven revision strategy (DDRS-MCBR) was applied to improve the original dual case-based reasoning model method system, and screening and decision-making was performed for SCCM using this model. Third, an actual environmental pollution accident from 2012 was used as a case study to verify the material base, case base, and screening model. The results demonstrated that the DDRS-MCBR method was fast, efficient, and practical. The DDRS-MCBR method changes the passive situation in which the choice of SCCM screening depends only on the subjective experience of the decision maker and offers a new approach to screening SCCM.
Goldie, John; Schwartz, Lisa; McConnachie, Alex; Jolly, Brian; Morrison, Jillian
2004-12-01
Although ethics is an important part of modern curricula, measures of students' ethical disposition have not been easy to develop. A potential method is to assess students' written justifications for selecting one option from a preset range of answers to vignettes and compare these justifications with predetermined 'expert' consensus. We describe the development of and reliability estimation for such a method -- the Ethics in Health Care Instrument (EHCI). Seven raters classified the responses of ten subjects to nine vignettes, on two occasions. The first stage of analysis involved raters' judging how consistent with consensus were subjects' justifications using generalizability theory, and then rating consensus responses on the action justification and values recognition hierarchies. The inter-rater reliability was 0.39 for the initial rating. Differential performance on questions was identified as the largest source of variance. Hence reliability was investigated also for students' total scores over the nine consensus vignettes. Rater effects were the largest source of variance identified. Examination of rater performance showed lack of rater consistency. D-studies were performed which showed acceptable reliability could nevertheless be obtained using four raters per EHCI. This study suggests that the EHCI has potential as an assessment instrument although further testing is required of all components of the methodology.
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
Approximation by planar elastic curves
DEFF Research Database (Denmark)
Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge
2016-01-01
We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient-driven...
Institute of Scientific and Technical Information of China (English)
赵良才; 张石生
2012-01-01
本文的目的是在Hilbert空间中引入和研究了一种新的迭代序列,用以寻求具逆-强单调映象的广义平衡问题的解集与无限簇非扩张映象的不动点集的公共元.在适当的条件下,用黏性逼近法证明了逼近于这一公共元的强收敛定理.应用该结论,我们证明了逼近于平衡问题和变分不等式问题的强收敛定理.所得结果改进和推广了文献的相应结果.%The purpose of this paper is to introduce a new iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem with inverse-strongly monotone mapping and the set of common fixed point for a family of infinite nonexpansive mappings in Hilbert space. It is shown that under suitable conditions by the viscosity approximation methods, some strong convergence theorems for approximating to this common elements are proved. Using this result, we prove two new strong convergence theorems in equilibrium problems and variational inequalities. The results presented in the paper extend and improve some recent results.
Directory of Open Access Journals (Sweden)
Geršicová Zuzana
2016-06-01
Full Text Available The paper deals with class teachers’ thinking and reasoning processes and the possibilities of influencing teachers’ ability to create a favourable classroom social climate. This paper describes personal and social education as one of the means and methods of such influencing. The results of the research carried out indicate that teachers have a very high opinion regarding their ability to create a favourable classroom social climate. The issues of personal and social education in the work of a class teacher are the topic of the project KEGA 002DTI-4/2013 being solved by a team of professionals at Dubnica Institute of Technology in Dubnica nad Váhom.
Energy Technology Data Exchange (ETDEWEB)
Nakata, Manabu; Okada, Takashi; Komai, Yoshinori; Nohara, Hiroki [Kyoto Univ. (Japan). Hospital
1996-08-01
Modern linear accelerators have four independent jaws and multileaf collimators (MLC) of 1 cm width at the isocenter. Asymmetric fields defined by such independent jaws and irregular multileaf collimated fields can be used to match adjacent fields or to spare the spinal cord in external photon beam radiotherapy. We have developed a new approximate algorithm for depth dose calculations at the collimator rotation axis. The program is based on Clarkson`s principle, and uses a more accurate modification of Day`s method for asymmetric fields. Using this method, tissue-maximum ratios (TMR) and field factors of ten kinds of asymmetric fields and ten different irregular multileaf collimated fields were calculated and compared with the measured data for 6 MV and 15 MV photon beams. The dose accuracy with the general A/Pe method was about 3%, however, with the new modified Day`s method, accuracy was within 1.7% for TMR and 1.2% for field factors. The calculated TMR and field factors were found to be in good agreement with measurements for both the 6 MV and 15 MV photon beams. (author)
Directory of Open Access Journals (Sweden)
Ziyun Deng
2016-09-01
Full Text Available In order to develop a Supercomputing Cloud Platform (SCP prototype system using Service-Oriented Architecture (SOA and Petri nets, we researched some technologies for Web service composition. Specifically, in this paper, we propose a reliability calculation method for Web service compositions, which uses Fuzzy Reasoning Colored Petri Net (FRCPN to verify the Web service compositions. We put forward a definition of semantic threshold similarity for Web services and a formal definition of FRCPN. We analyzed five kinds of production rules in FRCPN, and applied our method to the SCP prototype. We obtained the reliability value of the end Web service as an indicator of the overall reliability of the FRCPN. The method can test the activity of FRCPN. Experimental results show that the reliability of the Web service composition has a correlation with the number of Web services and the range of reliability transition values.
Directory of Open Access Journals (Sweden)
Blackwell Emily J
2012-06-01
Full Text Available Abstract Background The use of electronic training devices for dog training is controversial. The aims of this study were to give an indication of the extent to which dog owners use these devices in England, identify factors associated with their use, and compare owner report of outcomes. A convenience sample of dog owners in England was used to identify numbers using electronic training devices and identify reasons for use. Factors associated with use of remote e-collars only were determined by comparing dogs trained using these devices with two control populations matched for reason of use (recall / chasing problems. Comparison groups were: those using other ‘negative reinforcement / positive punishment’ training techniques, and those using ‘positive reinforcement / negative punishment’ based methods. A multinominal logistic regression model was used to compare factors between categories of training method. Owner reported success for use was compared using chi-squared analysis. Results For England only, 3.3% (n = 133 owners reported using remote activated e-collars, 1.4% (n = 54 reported use of bark activated e-collars, and 0.9% (n = 36 reported using electronic boundary fences. In comparison with the e-collar group, owners using reward based training methods for recall / chasing were 2.8 times more likely to be female and 2.7 times less likely to have attended agility training. Owners using other aversive methods for recall / chasing were 2.8 times more likely to have attended puppy classes than those using e-collars. However, the model only explained 10% variance between groups. A significantly higher proportion of owners in the reward group reported training success than those in the e-collar group. Conclusions In conclusion, a fairly low proportion of owners select to use electronic training devices. For a population matched by reason for training method use, characteristics of dogs, including occurrence of undesired
Logic and human reasoning: an assessment of the deduction paradigm.
Evans, Jonathan St B T
2002-11-01
The study of deductive reasoning has been a major paradigm in psychology for approximately the past 40 years. Research has shown that people make many logical errors on such tasks and are strongly influenced by problem content and context. It is argued that this paradigm was developed in a context of logicist thinking that is now outmoded. Few reasoning researchers still believe that logic is an appropriate normative system for most human reasoning, let alone a model for describing the process of human reasoning, and many use the paradigm principally to study pragmatic and probabilistic processes. It is suggested that the methods used for studying reasoning be reviewed, especially the instructional context, which necessarily defines pragmatic influences as biases.
ANDRE, Frédéric; HOU, Longfeng; SOLOVJOV, Vladimir P.
2016-01-01
The main restriction of k-distribution approaches for applications in radiative heat transfer in gaseous media arises from the use of a scaling or correlation assumption to treat non-uniform situations. It is shown that those cases can be handled exactly by using a multidimensional k-distribution that addresses the problem of spectral correlations without using any simplifying assumptions. Nevertheless, the approach cannot be suggested for engineering applications due to its computational cost. Accordingly, a more efficient method, based on the so-called Multi-Spectral Framework, is proposed to approximate the previous exact formulation. The model is assessed against reference LBL calculations and shown to outperform usual k-distribution approaches for radiative heat transfer in non-uniform media.
Directory of Open Access Journals (Sweden)
M. M. Rashidi
2012-01-01
Full Text Available In this study, a steady, incompressible, and laminar-free convective flow of a two-dimensional electrically conducting viscoelastic fluid over a moving stretching surface through a porous medium is considered. The boundary-layer equations are derived by considering Boussinesq and boundary-layer approximations. The nonlinear ordinary differential equations for the momentum and energy equations are obtained and solved analytically by using homotopy analysis method (HAM with two auxiliary parameters for two classes of visco-elastic fluid (Walters’ liquid B and second-grade fluid. It is clear that by the use of second auxiliary parameter, the straight line region in ℏ-curve increases and the convergence accelerates. This research is performed by considering two different boundary conditions: (a prescribed surface temperature (PST and (b prescribed heat flux (PHF. The effect of involved parameters on velocity and temperature is investigated.
Approximate Bayesian computation.
Directory of Open Access Journals (Sweden)
Mikael Sunnåker
Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.
Diophantine approximation and badly approximable sets
DEFF Research Database (Denmark)
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
. The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension......Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X....... Applications of our general framework include those from number theory (classical, complex, p-adic and formal power series) and dynamical systems (iterated function schemes, rational maps and Kleinian groups)....
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2012-05-01
Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.
Directory of Open Access Journals (Sweden)
KUDRYAVTSEV Pavel Gennadievich
2015-02-01
Full Text Available The paper deals with possibilities to use quasi-homogenous approximation for discription of properties of dispersed systems. The authors applied statistical polymer method based on consideration of average structures of all possible macromolecules of the same weight. The equiations which allow evaluating many additive parameters of macromolecules and the systems with them were deduced. Statistical polymer method makes it possible to model branched, cross-linked macromolecules and the systems with them which are in equilibrium or non-equilibrium state. Fractal analysis of statistical polymer allows modeling different types of random fractal and other objects examined with the mehods of fractal theory. The method of fractal polymer can be also applied not only to polymers but also to composites, gels, associates in polar liquids and other packaged systems. There is also a description of the states of colloid solutions of silica oxide from the point of view of statistical physics. This approach is based on the idea that colloid solution of silica dioxide – sol of silica dioxide – consists of enormous number of interacting particles which are always in move. The paper is devoted to the research of ideal system of colliding but not interacting particles of sol. The analysis of behavior of silica sol was performed according to distribution Maxwell-Boltzmann and free path length was calculated. Using this data the number of the particles which can overcome the potential barrier in collision was calculated. To model kinetics of sol-gel transition different approaches were studied.
Pérez, Alejandro; Tuckerman, Mark E.; Müser, Martin H.
2009-05-01
The problems of ergodicity and internal consistency in the centroid and ring-polymer molecular dynamics methods are addressed in the context of a comparative study of the two methods. Enhanced sampling in ring-polymer molecular dynamics (RPMD) is achieved by first performing an equilibrium path integral calculation and then launching RPMD trajectories from selected, stochastically independent equilibrium configurations. It is shown that this approach converges more rapidly than periodic resampling of velocities from a single long RPMD run. Dynamical quantities obtained from RPMD and centroid molecular dynamics (CMD) are compared to exact results for a variety of model systems. Fully converged results for correlations functions are presented for several one dimensional systems and para-hydrogen near its triple point using an improved sampling technique. Our results indicate that CMD shows very similar performance to RPMD. The quality of each method is further assessed via a new χ2 descriptor constructed by transforming approximate real-time correlation functions from CMD and RPMD trajectories to imaginary time and comparing these to numerically exact imaginary time correlation functions. For para-hydrogen near its triple point, it is found that adiabatic CMD and RPMD both have similar χ2 error.
Approximations in diagnosis: motivations and techniques
Harmelen, van F.A.H.; Teije, A. ten
1995-01-01
We argue that diagnosis should not be seen as solving a problem with a unique definition, but rather that there exists a whole space of reasonable notions of diagnosis. These notions can be seen as mutual approximations. We present a number of reasons for choosing among different notions of diagnos
Energy Technology Data Exchange (ETDEWEB)
Ball, J.R.
1986-04-01
This document is a supplement to a ''Handbook for Cost Estimating'' (NUREG/CR-3971) and provides specific guidance for developing ''quick'' approximate estimates of the cost of implementing generic regulatory requirements for nuclear power plants. A method is presented for relating the known construction costs for new nuclear power plants (as contained in the Energy Economic Data Base) to the cost of performing similar work, on a back-fit basis, at existing plants. Cost factors are presented to account for variations in such important cost areas as construction labor productivity, engineering and quality assurance, replacement energy, reworking of existing features, and regional variations in the cost of materials and labor. Other cost categories addressed in this handbook include those for changes in plant operating personnel and plant documents, licensee costs, NRC costs, and costs for other government agencies. Data sheets, worksheets, and appropriate cost algorithms are included to guide the user through preparation of rough estimates. A sample estimate is prepared using the method and the estimating tools provided.
Institute of Scientific and Technical Information of China (English)
LI; AnYang; WANG; YuBin; DOU; YuSheng; WEN; ZhenYi
2007-01-01
The potential energy curves for the X1∑+g, B1△g and B′1∑+g states of C2 have been studied by using MRCI and approximate CI methods, and are benchmarked against the calculations of full configuration interaction (FCI). The results obtained by MRCI method agree with the FCI very well, and even are accurate enough to compare other approximate methods as benchmark, when the calculations of FCI are not feasible. The approximate CI methods mentioned in this paper are reliable for treating chemical problems.
Beyond the random phase approximation
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian S.
2013-01-01
We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for ab initio calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density...
Energy Technology Data Exchange (ETDEWEB)
Chalasani, P.; Saias, I. [Los Alamos National Lab., NM (United States); Jha, S. [Carnegie Mellon Univ., Pittsburgh, PA (United States)
1996-04-08
As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs. In this paper the authors show that pricing an arbitrary path-dependent option is {number_sign}-P hard. They show that certain types f path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these they design deterministic polynomial-time approximate algorithms. They show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation to the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, the algorithms have guaranteed error bounds that are polynormally small (and in some cases exponentially small) in the maturity n. For the error analysis they derive large-deviation results for random walks that may be of independent interest.
Random Attractors of Stochastic Modified Boussinesq Approximation
Institute of Scientific and Technical Information of China (English)
郭春晓
2011-01-01
The Boussinesq approximation is a reasonable model to describe processes in body interior in planetary physics. We refer to [1] and [2] for a derivation of the Boussinesq approximation, and [3] for some related results of existence and uniqueness of solution.
Asgharzadeh, Hafez; Borazjani, Iman
2017-02-01
diagonal of the Jacobian further improves the performance by 42-74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal and full Jacobian, respectivley, when the stretching factor was increased. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.
Leike, Reimar H
2016-01-01
In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a ranking function that quantifies how "embarrassing" it is to communicate a given approximation. We show that there is only one ranking under the requirements that (1) the best ranked approximation is the non-approximated belief and (2) that the ranking judges approximations only by their predictions for actual outcomes. We find that this ranking is equivalent to the Kullback-Leibler divergence that is frequently used in the literature. However, there seems to be confusion about the correct order in which its functional arguments, the approximated and non-approximated beliefs, should be used. We hope that our elementary derivation settles the apparent confusion. We show for example that when approximating beliefs with Gaussian distributions the optimal approximation is given by moment matching. This is in contrast to many su...
Edison, John R; Monson, Peter A
2014-07-14
Recently we have developed a dynamic mean field theory (DMFT) for lattice gas models of fluids in porous materials [P. A. Monson, J. Chem. Phys. 128(8), 084701 (2008)]. The theory can be used to describe the relaxation processes in the approach to equilibrium or metastable states for fluids in pores and is especially useful for studying system exhibiting adsorption/desorption hysteresis. In this paper we discuss the extension of the theory to higher order by means of the path probability method (PPM) of Kikuchi and co-workers. We show that this leads to a treatment of the dynamics that is consistent with thermodynamics coming from the Bethe-Peierls or Quasi-Chemical approximation for the equilibrium or metastable equilibrium states of the lattice model. We compare the results from the PPM with those from DMFT and from dynamic Monte Carlo simulations. We find that the predictions from PPM are qualitatively similar to those from DMFT but give somewhat improved quantitative accuracy, in part due to the superior treatment of the underlying thermodynamics. This comes at the cost of greater computational expense associated with the larger number of equations that must be solved.
Variational Approximate Inference Methods for Graphical Models%概率图模型中的变分近似推理方法
Institute of Scientific and Technical Information of China (English)
程强; 陈峰; 董建武; 徐文立
2012-01-01
概率图模型将图论和概率论相结合,为多个变量之间复杂依赖关系的表示提供了统一的框架,在计算机视觉、自然语言处理和计算生物学等领域有着广泛的应用.概率推理(包括计算边缘概率和计算最大概率状态等问题)是概率图模型研究及应用的核心问题.本文主要介绍概率图模型近似推理方法中变分推理的最新研究成果.在变分近似推理的框架下,系统地归纳了概率图模型推理问题的基本研究思路,综述了目前主要的近似推理方法,并分析了近似算法的单调性、收敛性和全局性等性质.最后,对概率图模型近似推理方法的研究方向和应用前景作了展望.%Graphical models bring together graph theory and probability theory in a powerful and compact formalism for multivariate statistical modeling. They have been successfully applied to a wide variety of fields, including computer vision, natural language processing, and computational biology. Probabilistic inference, such as finding the most probable assignment and computing the marginals, is the core problem to be solved in the applications of graphical models. In this paper, a detailed survey of the achievements on variational approximate inference methods obtained in recent years is presented. Besides, a discussion of future trend on approximate inference of graphical models is given.
An Efficient Fast Approximate Control Vector Parameterization Method%一种高效的快速近似控制向量参数化方法
Institute of Scientific and Technical Information of China (English)
李国栋; 胡云卿; 刘兴高
2015-01-01
控制向量参数化(Control vector parameterization, CVP)方法是目前求解流程工业中最优操作问题的主流数值方法,然而,该方法的主要缺点之一是计算效率较低,这是因为在求解生成的非线性规划(Nonlinear programming, NLP)问题时,需要随着控制参数的调整,反复不断地求解相关的微分方程组,这也是CVP方法中最耗时的部分。为了提高CVP方法的计算效率,本文提出一种新颖的快速近似方法,能够有效减少微分方程组、函数值以及梯度的计算量。最后,两个经典的最优控制问题上的测试结果及与国外成熟的最优控制软件的比较研究表明：本文提出的快速近似CVP 方法在精度和效率上兼有良好的表现。%The control vector parameterization (CVP) method is currently popular for solving optimal control problems in process industries. However, one of its main disadvantages is the low computational efficiency, because the relevant differential equations in solving the generated nonlinear programming (NLP) problem should be calculated repeatedly with the adjustment of control, which is the most time-consuming part of the CVP method. A new fast approximate approach with less computational expenses on differential equations, function values and gradients is therefore proposed to improve the computational efficiency of the CVP method in this paper. The proposed approach is demonstrated to have marked advantages in terms of accuracy and efficiency, in contrast to mature optimal control softwares, on two classic optimal control problems.
Global approximation of convex functions
Azagra, D
2011-01-01
We show that for every (not necessarily bounded) open convex subset $U$ of $\\R^n$, every (not necessarily Lipschitz or strongly) convex function $f:U\\to\\R$ can be approximated by real analytic convex functions, uniformly on all of $U$. In doing so we provide a technique which transfers results on uniform approximation on bounded sets to results on uniform approximation on unbounded sets, in such a way that not only convexity and $C^k$ smoothness, but also local Lipschitz constants, minimizers, order, and strict or strong convexity, are preserved. This transfer method is quite general and it can also be used to obtain new results on approximation of convex functions defined on Riemannian manifolds or Banach spaces. We also provide a characterization of the class of convex functions which can be uniformly approximated on $\\R^n$ by strongly convex functions.
Approximation of distributed delays
Lu, Hao; Eberard, Damien; Simon, Jean-Pierre
2010-01-01
We address in this paper the approximation problem of distributed delays. Such elements are convolution operators with kernel having bounded support, and appear in the control of time-delay systems. From the rich literature on this topic, we propose a general methodology to achieve such an approximation. For this, we enclose the approximation problem in the graph topology, and work with the norm defined over the convolution Banach algebra. The class of rational approximates is described, and a constructive approximation is proposed. Analysis in time and frequency domains is provided. This methodology is illustrated on the stabilization control problem, for which simulations results show the effectiveness of the proposed methodology.
Nelli, Jennifer; Tremblay, Steven; Caluyong, Myka B.; Freeman, Jeffrey; Stokes, Yehudis; Stiell, Ian G.; Nathan, Howard; Smyth, Catherine E.
2016-01-01
Background. Chronic pain (CP) accounts for 10–16% of emergency department (ED) visits, contributing to ED overcrowding and leading to adverse events. Objectives. To describe patients with CP attending the ED and identify factors contributing to their visit. Methods. We used a mixed-method design combining interviews and questionnaires addressing pain, psychological distress, signs of opioid misuse, and disability. Participants were adults who attended the EDs of a large academic tertiary care center for their CP problem. Results. Fifty-eight patients (66% women; mean age 46.5, SD = 16.9) completed the study. The most frequently cited reason (60%) for ED visits was inability to cope with pain. Mental health problems were common, including depression (61%) and anxiety (45%). Participants had questions about the etiology of their pain, concerns about severe pain-related impairment, and problems with medication renewals or efficacy and sometimes felt invalidated in the ED. Although most participants had a primary care physician, the ED was seen as the only or best option when pain became unmanageable. Conclusions. Patients with CP visiting the ED often present with complex difficulties that cannot be addressed in the ED. Better access to interdisciplinary pain treatment is needed to reduce the burden of CP on the ED. PMID:27829785
Kuvychko, Igor
2000-10-01
Vision is a part of a larger informational system that converts visual information into knowledge structures. These structures drive vision process, resolving ambiguity and uncertainty via feedback, and provide image understanding, that is an interpretation of visual information in terms of such knowledge models. The solution to Image Understanding problems is suggested in form of active multilevel hierarchical networks represented dually as discrete and continuous structures. Computational intelligence methods transform images into model-based knowledge representation. Certainty Dimension converts attractors in neural networks into fuzzy sets, preserving input-output relationships. Symbols naturally emerge in such networks. Symbolic Space is a dual structure that combines closed distributed space split by the set of fuzzy regions, and discrete set of symbols equivalent to the cores of regions represented as points in the Certainty dimension. Model Space carries knowledge in form of links and relations between the symbols, and supports graph, diagrammatic and topological operations. Composition of spaces works similar to M. Minsky frames and agents, Gerard Edelman's maps of maps, etc., combining machine learning, classification and analogy together with induction, deduction and other methods of higher level model-based reasoning. Based on such principles, an Image Understanding system can convert images into knowledge models, effectively resolving uncertainty and ambiguity via feedback projections and does not require supercomputers.
Directory of Open Access Journals (Sweden)
Patricia A. Poulin
2016-01-01
Full Text Available Background. Chronic pain (CP accounts for 10–16% of emergency department (ED visits, contributing to ED overcrowding and leading to adverse events. Objectives. To describe patients with CP attending the ED and identify factors contributing to their visit. Methods. We used a mixed-method design combining interviews and questionnaires addressing pain, psychological distress, signs of opioid misuse, and disability. Participants were adults who attended the EDs of a large academic tertiary care center for their CP problem. Results. Fifty-eight patients (66% women; mean age 46.5, SD = 16.9 completed the study. The most frequently cited reason (60% for ED visits was inability to cope with pain. Mental health problems were common, including depression (61% and anxiety (45%. Participants had questions about the etiology of their pain, concerns about severe pain-related impairment, and problems with medication renewals or efficacy and sometimes felt invalidated in the ED. Although most participants had a primary care physician, the ED was seen as the only or best option when pain became unmanageable. Conclusions. Patients with CP visiting the ED often present with complex difficulties that cannot be addressed in the ED. Better access to interdisciplinary pain treatment is needed to reduce the burden of CP on the ED.
Poulin, Patricia A; Nelli, Jennifer; Tremblay, Steven; Small, Rebecca; Caluyong, Myka B; Freeman, Jeffrey; Romanow, Heather; Stokes, Yehudis; Carpino, Tia; Carson, Amanda; Shergill, Yaadwinder; Stiell, Ian G; Taljaard, Monica; Nathan, Howard; Smyth, Catherine E
2016-01-01
Background. Chronic pain (CP) accounts for 10-16% of emergency department (ED) visits, contributing to ED overcrowding and leading to adverse events. Objectives. To describe patients with CP attending the ED and identify factors contributing to their visit. Methods. We used a mixed-method design combining interviews and questionnaires addressing pain, psychological distress, signs of opioid misuse, and disability. Participants were adults who attended the EDs of a large academic tertiary care center for their CP problem. Results. Fifty-eight patients (66% women; mean age 46.5, SD = 16.9) completed the study. The most frequently cited reason (60%) for ED visits was inability to cope with pain. Mental health problems were common, including depression (61%) and anxiety (45%). Participants had questions about the etiology of their pain, concerns about severe pain-related impairment, and problems with medication renewals or efficacy and sometimes felt invalidated in the ED. Although most participants had a primary care physician, the ED was seen as the only or best option when pain became unmanageable. Conclusions. Patients with CP visiting the ED often present with complex difficulties that cannot be addressed in the ED. Better access to interdisciplinary pain treatment is needed to reduce the burden of CP on the ED.
Web service composition method based on approximate skyline algorithm%基于近似的skyline算法的Web服务组合方法
Institute of Scientific and Technical Information of China (English)
段静珊; 周彦晖
2014-01-01
The vigorous development of cloud computing brings new opportunities and challenges to the development of the combination of Web services. Traditional service composition methods focus on achieving value-added service to meet the gro-wing demand of the users, but there are a lot of the same functionality of the specific non-functional type of services on the In-ternet. How to select the combination of Web services from these services in accordance with user preferences, especially the services that meet the specific needs of the user, becomes a problem to be solved. The article uses the AHP algorithm to quantify user preferences. Then we integrate the relative user preferences weight into the approximate skyline query algorithms to pick out the right combination of Web services in order to meet the user’s need. Validity and extendibility of the method are verified through a series of experiments.%云计算的蓬勃发展，为 Web 组合服务的发展带来了新的机遇和挑战，传统的服务组合方法中只注重实现服务增值以满足用户日益增长的需求，而互联网上存在着大量的功能性相同、非功能性不同的具体服务。在这些服务中挑选出符合用户偏好的 Web 组合服务，尤其是符合用户特定需求的 Web 组合服务成为一个亟待解决的问题。文章采用 AHP 算法量化用户偏好，再将得到的用户相对偏好权重融入到近似的skyline查询算法中，挑选出合适的Web组合服务，来满足用户的需求。最后通过一系列实验验证所提出方法的有效性和可扩展性。
Proportional Reasoning and the Visually Impaired
Hilton, Geoff; Hilton, Annette; Dole, Shelley L.; Goos, Merrilyn; O'Brien, Mia
2012-01-01
Proportional reasoning is an important aspect of formal thinking that is acquired during the developmental years that approximate the middle years of schooling. Students who fail to acquire sound proportional reasoning often experience difficulties in subjects that require quantitative thinking, such as science, technology, engineering, and…
基于向量相似度的新的证据推理方法磁%New Evidence Reasoning Method Based on Vector Similarity
Institute of Scientific and Technical Information of China (English)
陶李; 关欣; 孙贵东
2015-01-01
D‐S证据理论在信息融合领域有着广泛的应用，但有时在应用过程中会遇到一些与人的逻辑思维不相符的情况，尤其是在证据高度冲突的情况下，针对这一问题论文提出了一种基于向量相似度的证据组合方法。该方法通过向量相似度定义了证据可信度并以此生成证据权重，基于所获权重对冲突因子进行分配，最后结合D‐S组合规则完成证据推理。算例分析表明新方法能有效处理几种常见的悖论与证据高度冲突的情况。%Dempster‐Shafer evidence theory is widely used in the field of decision‐level information fusion .But some‐times some situation which is not consistent with people's logic thinking is encountered in the application process ,especially in the case of highly conflict evidence .A kind of evidence combination method is put forward based on vector similarity in or‐der to solve this problem .This method defines the evidence reliability by vector similarity and generates the weight of evi‐dence based on the weight of evidence conflict is distributed .In the end ,the D‐S evidence combination rules are combined to complete the evidence reasoning .The examples show that the new method can efficiently solve the paradox of several com‐mon and highly conflict evidence .
Approximation techniques for engineers
Komzsik, Louis
2006-01-01
Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.
Achieser, N I
2004-01-01
A pioneer of many modern developments in approximation theory, N. I. Achieser designed this graduate-level text from the standpoint of functional analysis. The first two chapters address approximation problems in linear normalized spaces and the ideas of P. L. Tchebysheff. Chapter III examines the elements of harmonic analysis, and Chapter IV, integral transcendental functions of the exponential type. The final two chapters explore the best harmonic approximation of functions and Wiener's theorem on approximation. Professor Achieser concludes this exemplary text with an extensive section of pr
Directory of Open Access Journals (Sweden)
Marta Lucia de Oliveira Carvalho
2005-10-01
Full Text Available OBJETIVO: Identificar as representações sobre os métodos contraceptivos que poderiam ser alternativas à esterilização, para um grupo de mulheres esterilizadas, visando a entender os motivos de rejeição a esses métodos. MÉTODOS: Trata-se de trabalho descritivo, qualitativo, cuja população estudada foi constituída por 31 mulheres esterilizadas, aleatoriamente selecionadas da listagem de pacientes atendidas pelo Programa de Planejamento Familiar de um ambulatório de um hospital universitário. As informações foram obtidas das mulheres estudadas por meio de entrevistas semi-estruturadas. As transcrições foram analisadas segundo o método de Análise de Conteúdo. RESULTADOS: A rejeição aos métodos contraceptivos esteve baseada em representações resultantes de informações técnicas recebidas em serviços de saúde, de vivências anteriores com esses métodos ou de informações recebidas do meio social. A rejeição aos métodos hormonais e DIU baseou-se principalmente em representações de baixa inocuidade; os métodos comportamentais (Tabela, Billings foram rejeitados por representações de baixa eficácia; os métodos de barreira (diafragma e camisinha, por dificuldades no uso desses métodos relacionados a padrões culturais de exercício da sexualidade e representações de baixa eficácia. CONCLUSÕES: A opção pela esterilização feminina pode ser indicativa de rejeição às alternativas contraceptivas oferecidas pelos serviços de saúde. Os profissionais da área de saúde reprodutiva devem aprofundar seu conhecimento sobre os fatores pessoais, socioeconômicos e culturais que podem influenciar as mulheres na procura por um método contraceptivo que assegure maior controle de sua própria fecundidade.OBJECTIVE: To identify the representations of contraceptive methods within a group of sterilized women, aiming at understanding the reasons why they refused those methods. METHODS: A descriptive qualitative study
Expectation Consistent Approximate Inference
DEFF Research Database (Denmark)
Opper, Manfred; Winther, Ole
2005-01-01
We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability dis...
Energy Technology Data Exchange (ETDEWEB)
Price, Richard H [Department of Physics, University of Utah, Salt Lake City, UT 84112 (United States)
2004-02-07
In searching for and interpreting signals from binary mergers, gravitational wave detectors need information about the features of gravitational wave bursts generated by these strong field events. Numerical relativity will ultimately provide the answers, but not on the time scale needed by the first detectors. We propose here a method in which exact numerical solutions to Einstein's equations, for periodic sources and standing waves, are used as an approximation to the strong field quasistationary epoch of inspiral. We discuss how this approximation changes the mathematical nature of the computation, and we report on progress with this problem and on remaining challenges.
Weighted approximation with varying weight
Totik, Vilmos
1994-01-01
A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.
Approximate Implicitization Using Linear Algebra
Directory of Open Access Journals (Sweden)
Oliver J. D. Barrowclough
2012-01-01
Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.
DEFF Research Database (Denmark)
Tønder, Lars
2014-01-01
This article takes up recent discussions of nature and the sensorium in order to rethink public reason in deeply divided societies. The aim is not to reject the role of reason-giving but rather to infuse it with new meaning, bringing the reasonable back to its sensorially inflected circumstances....
Inductive Reasoning and Writing
Rooks, Clay; Boyd, Robert
2003-01-01
Induction, properly understood, is not merely a game, nor is it a gimmick, nor is it an artificial way of explaining an element of reasoning. Proper understanding of inductive reasoning--and the various types of reasoning that the authors term inductive--enables the student to evaluate critically other people's writing and enhances the composition…
Teaching for Ethical Reasoning
Sternberg, Robert J.
2012-01-01
This article argues for the importance of teaching for ethical reasoning. Much of our teaching is in vain if it is not applied to life in an ethical manner. The article reviews lapses in ethical reasoning and the great costs they have had for society. It proposes that ethical reasoning can be taught across the curriculum. It presents an eight-step…
Value Function Approximation or Stopping Time Approximation
DEFF Research Database (Denmark)
Stentoft, Lars
2014-01-01
, by Carriere. In this paper, we provide a thorough comparison of these two methods and relate them to the work of Tsitsiklis and Van Roy. Although the methods are often considered to be similar, this analysis allows us to point out an important but often overlooked difference between them. We further show that...