Partition Of Interval Research Articles

Path integrals, supersymmetric quantum mechanics, and the Atiyah-Singer index theorem for twisted Dirac

Feynman’s time-slicing construction approximates the path integral by a product, determined by a partition of a finite time interval, of approximate propagators. This paper formulates general conditions to impose on a short-time approximation to the propagator in a general class of imaginary-time quantum mechanics on a Riemannian manifold which ensure that these products converge. The limit defines a path integral which agrees pointwise with the heat kernel for a generalized Laplacian. The result is a rigorous construction of the propagator for supersymmetric quantum mechanics, with potential, as a path integral. Further, the class of Laplacians includes the square of the twisted Dirac operator, which corresponds to an extension of N = 1/2 supersymmetric quantum mechanics. General results on the rate of convergence of the approximate path integrals suffice in this case to derive the local version of the Atiyah-Singer index theorem.

A partitioning algorithm for the mixed integer nonlinear programming problem

An interval partitioning method (IPM) is proposed to solve the (non-convex) mixed integer nonlinear programming problem (MINLP). The MINLP is encountered in many application areas and solving this problem bears practical importance. This paper proposes an IPM where two tree search strategies (breadth first and mixed breadth/depth first) and three variable subdivision methods are implemented. Two proposed variable subdivision methods are novel and they prioritise variables hierarchically according to several features. The IPM is implemented on a set of non-convex MINLP instances extracted from the MINLP benchmarks and numerical results show that its performance is quite promising.

Study on Dynamic Reconfiguration of Distribution Network Considering Distribution Generation

A new dynamic reconfiguration method considering distribution generation (DG) was presented. The dynamic reconfiguration problem was solved from three aspects: firstly, the time interval partition of the entire scheduling period was optimized by load distribution variation index; secondly, a plurality of time intervals were optimized and reconfigured by using the multi-objective particle swarm optimization model of multi-period encoding; finally, the optimal time interval numbers was determined by gradually approaching the falling threshold of net loss. If the system contained DG, DG’s output curve was determined by the analysis of its dynamic characteristics. The results of the test showed that the proposed method was effective to solve the dynamic reconfiguration with DG.

A partitioning algorithm for the mixed integer nonlinear programming problem

An interval partitioning method (IPM) is proposed to solve the (non-convex) mixed integer nonlinear programming problem (MINLP). The MINLP is encountered in many application areas and solving this problem bears practical importance. This paper proposes an IPM where two tree search strategies (breadth first and mixed breadth/depth first) and three variable subdivision methods are implemented. Two proposed variable subdivision methods are novel and they prioritise variables hierarchically according to several features. The IPM is implemented on a set of non-convex MINLP instances extracted from the MINLP benchmarks and numerical results show that its performance is quite promising.

Fuzzy time series forecasting based on optimal partitions of intervals and optimal weighting vectors

In this paper, we propose a new fuzzy time series (FTS) forecasting method based on optimal partitions of intervals in the universe of discourse and optimal weighting vectors of two-factors second-order fuzzy-trend logical relationship groups (TSFTLRGs). The proposed method uses particle swarm optimization (PSO) techniques to obtain the optimal partitions of intervals and the optimal weighting vectors simultaneously. The proposed FTS forecasting method outperforms the existing methods for forecasting the TAIEX and the NTD/USD exchange rates in terms of forecasting accuracy rates. It provides us with a useful way to deal with forecasting problems to get higher forecasting accuracy rates.

On the mixing properties of piecewise expanding maps under composition with permutations, II: Maps of non-constant orientation

For an integer [Formula: see text], let [Formula: see text] be the partition of the unit interval [Formula: see text] into [Formula: see text] equal subintervals, and let [Formula: see text] be the class of piecewise linear maps on [Formula: see text] with constant slope [Formula: see text] on each element of [Formula: see text]. We investigate the effect on mixing properties when [Formula: see text] is composed with the interval exchange map given by a permutation [Formula: see text] interchanging the [Formula: see text] subintervals of [Formula: see text]. This extends the work in a previous paper [N. P. Byott, M. Holland and Y. Zhang, DCDS 33 (2013) 3365–3390], where we considered only the “stretch-and-fold” map [Formula: see text].

On fuzzy-qualitative descriptions and entropy

This paper models the assessments of a group of experts when evaluating different magnitudes, features or objects by using linguistic descriptions. A new general representation of linguistic descriptions is provided by unifying ordinal and fuzzy perspectives. Fuzzy-qualitative labels are proposed as a generalization of the concept of qualitative labels over a well-ordered set. A lattice structure is established in the set of fuzzy-qualitative labels to enable the introduction of fuzzy-qualitative descriptions as L-fuzzy sets. A theorem is given that characterizes finite fuzzy partitions using fuzzy-qualitative labels, the cores and supports of which are qualitative labels. This theorem leads to a mathematical justification for commonly-used fuzzy partitions of real intervals via trapezoidal fuzzy sets. The information of a fuzzy-qualitative label is defined using a measure of specificity, in order to introduce the entropy of fuzzy-qualitative descriptions.

Nationwide Multicenter Reference Interval Study for 28 Common Biochemical Analytes in China.

A nationwide multicenter study was conducted in the China to explore sources of variation of reference values and establish reference intervals for 28 common biochemical analytes, as a part of the International Federation of Clinical Chemistry and Laboratory Medicine, Committee on Reference Intervals and Decision Limits (IFCC/C-RIDL) global study on reference values. A total of 3148 apparently healthy volunteers were recruited in 6 cities covering a wide area in China. Blood samples were tested in 2 central laboratories using Beckman Coulter AU5800 chemistry analyzers. Certified reference materials and value-assigned serum panel were used for standardization of test results. Multiple regression analysis was performed to explore sources of variation. Need for partition of reference intervals was evaluated based on 3-level nested ANOVA. After secondary exclusion using the latent abnormal values exclusion method, reference intervals were derived by a parametric method using the modified Box-Cox formula. Test results of 20 analytes were made traceable to reference measurement procedures. By the ANOVA, significant sex-related and age-related differences were observed in 12 and 12 analytes, respectively. A small regional difference was observed in the results for albumin, glucose, and sodium. Multiple regression analysis revealed BMI-related changes in results of 9 analytes for man and 6 for woman. Reference intervals of 28 analytes were computed with 17 analytes partitioned by sex and/or age. In conclusion, reference intervals of 28 common chemistry analytes applicable to Chinese Han population were established by use of the latest methodology. Reference intervals of 20 analytes traceable to reference measurement procedures can be used as common reference intervals, whereas others can be used as the assay system-specific reference intervals in China.

Schedule-Based Passenger Assignment for High-Speed Rail Networks considering the Ticket-Booking Process

This paper proposes a schedule-based passenger assignment method for high-speed rail networks considering the ticket-booking process. Passengers book tickets to reserve seats during the presale period in high-speed rail systems and passengers on trains are determined during the ticket-booking process. The ticket-booking process is modeled as a continuous and deterministic predecision process. A solution algorithm is designed using the discretization of the continuous process by partitioning the ticket-booking time and the optimal paths remain constant in any partition interval. Finally, an application to the Chinese high-speed rail network is presented. A comparison of the numerical results with the reality is conducted to validate the efficiency and precision of the method and algorithm. Based on the results, the operating efficiency of the current train schedule is evaluated and some specific improvement measures are proposed.

Optimal Interval Division

This paper develops a theory of optimal interval division for capacity-constrained problems in which a continuum is divided into finitely many intervals, or classes, and choices are class-targeted. Examples include the location of public facilities by a social planner, the distribution of product characteristics by firms, coarse matching, bounded memory, and mechanism design with limited communication.Optimal interval division refers to the problem of finding the interval partition of a given continuum maximizing an associated value, constrained by the number of classes. The value of each finite interval partition is derived by summation from a basic primitive that I call a cell function defined over all subintervals. I identify an important and common property of cell functions: they are submodular over the interval structure. This yields the following results.First, the maximum value exhibits decreasing marginal returns in the number of classes, and converges rapidly with an additional simple condition. Second, I uncover a novel sandwiching property: when allowing an extra class, the new optimal cut- offs are more spread compared with the original optimal ones in the sense that each new cut point lands in a different original partition element. This property helps elucidate the effects of various capacity constraints on economic behavior. Third, by a characterization theorem, I show that a submodular optimal interval division problem can often be interpreted as scalar quantization in information theory with a general error function, despite arising from seemingly unrelated contexts like coarse matching.

The importance of having an appropriate relational data segmentation in ATLAS

In this paper we describe specific technical solutions put in place in various database applications of the ATLAS experiment at LHC where we make use of several partitioning techniques available in Oracle 11g. With the broadly used range partitioning and its option of automatic interval partitioning we add our own logic in PLSQL procedures and scheduler jobs to sustain data sliding windows in order to enforce various data retention policies. We also make use of the new Oracle 11g reference partitioning in the Nightly Build System to achieve uniform data segmentation. However the most challenging issue was to segment the data of the new ATLAS Distributed Data Management system (Rucio), which resulted in tens of thousands list type partitions and sub-partitions. Partition and sub-partition management, index strategy, statistics gathering and queries execution plan stability are important factors when choosing an appropriate physical model for the application data management. The so-far accumulated knowledge and analysis on the new Oracle 12c version features that could be beneficial will be shared with the audience.

Capacitated Max-Batching with interval graph compatibilities

We consider the problem of partitioning interval graphs into cliques of bounded size. Each interval has a weight, and the weight of a clique is the maximum weight of any interval in the clique. The goal is then to find such a partition of minimum total weight. This graph problem can also be interpreted as a batch scheduling problem. Solving a long-standing open question, we show NP-hardness, even if the bound on the clique sizes is constant. Moreover, we give a PTAS for this case.

Computing oscillatory integrals: Partition of the integration interval based on the singularity and the wave number of the integrand

In this paper, we develop composite moment-free numerical quadratures for computing highly os- cillatory integrals with singularities and stationary points. The composite quadrature rules for computing highly oscillatory integrals with a smooth integrand and without a stationary point are developed based on partitioning the integration domain according to the values of the derivative of the oscillator and the wave number. The moment-free Filon-type quadrature is used for each of the oscillatory integrals de ned on the subintervals. The composite quadrature rules for computing highly oscillatory integrals with singularities and stationary points are developed by partitioning the integration domain according to the singularity of the integrand and the wave number, such that the integral de ned on a subinterval has either a weak singularity without rapid oscillation or oscillation without a singularity or stationary point. The classical quadrature rules for weakly singular integrals using graded points are employed for computing the singular integral without rapid oscillation and the modified moment-free Filon-type method is used for computing the oscillatory integrals. Unlike the existing methods, the proposed methods do not have to compute the inverse of the oscillator or to utilize the integral of special functions.

Multi-objective optimization of heat exchanger networks based on analysis of minimum temperature difference and accumulated CO2 emissions

A multi-objective optimization method of heat exchanger network (HEN) on the basis of partition of minimum approach temperature (ΔTmin) intervals is proposed to minimize the total annual cost and accumulated CO2 emissions in construction and operation phases. In this method, both dominant and recessive CO2 emissions are considered, and the effects of ΔTmin on multi-objective optimization problems of HEN are investigated. We find that a multi-objective optimization problem may reduce to a single objective optimization problem as ΔTmin changes. The critical ΔTmin that distinguishes the intervals for the single objective optimization and the multi-objective optimization problem can be identified by combining the pinch analysis and mathematical programming method. The optimal structure and CO2 emissions of HEN are obtained in the single objective optimization problem, whereas the Pareto front of two objectives and a trade-off strategy are obtained in the multi-objective optimization problem. The HEN in a vacuum gas oil hydro-treating unit in a refinery is taken as a case study. Results indicate that the partition of ΔTmin intervals helps to identify the nature of the multi-objective optimization problems and reduce the computation loads of the multi-objective optimization problem of HENs. In addition, the optimal solutions of HEN obtained by the ε-constraint method distribute uniformly, and the dominant objective changes gently within the intervals of ΔTmin for the multi-objective optimization.

A reinsurance game between two insurance companies with nonlinear risk processes

In this paper, we consider a stochastic differential reinsurance game between two insurance companies with nonlinear (quadratic) risk control processes. We assume that the goal of each insurance company is to maximize the exponential utility of the difference between its terminal surplus and that of its competitor at a fixed terminal time T. First, we give an explicit partition (including nine subsets) of time interval [0,T]. Further, on every subset, an explicit Nash equilibrium strategy is derived by solving a pair of Hamilton–Jacobi–Bellman equations. Finally, for some special cases, we analyze the impact of time t and quadratic control parameter on the Nash equilibrium strategy and obtain some simple partition of [0,T]. Based on these results, we apply some numerical analysis of the time t, quadratic control parameter and competition sensitivity parameter on the Nash equilibrium strategy and the value function.

Trigonometric Fourier-series solutions of the point reactor kinetics equations

In this paper, a new method based on the Fourier series is introduced to obtain approximate solutions to the systems of the point kinetics equations. These systems are stiff involving equations with slowly and rapidly varying components. They are solved numerically using Fourier series expansion over a partition of the total time interval. Approximate solution requires determining the series coefficients over each time step in that partition. These coefficients are determined using the high order derivatives of the dependent variables at the beginning of the time step introducing a system of linear algebraic equations to be solved at each step. The obtained algebraic system is similar to the Vandermonde system. Evaluation of the inverse of the Vandermonde matrix is required to determine the coefficients of the Fourier series. Because the obtained Vandermonde matrix has a special structure, due to the properties of the sine and cosine functions, a new formula is introduced to determine its inverse using standard computations. The new method solves the general linear and non-linear kinetics problems with six groups of delayed neutrons. The validity of the algorithm is tested with five different types of reactivities including step reactivity insertion, ramp input, oscillatory reactivity changes, a reactivity as a function of the neutron density and finally temperature feedback reactivity. Comparisons are made with analytical and conventional numerical methods used to solve the point kinetics equations. The results confirm the theoretical analysis and indicate the validity of the method for all applications considered.

Decision Diagrams for XACML Policy Evaluation and Management

One of the primary challenges to apply the XACML access control policy language in applications is the performance problem of policy evaluation engines, particularly when they experience a great number of policies. Some existing works attempted to solve this problem, but only for some particular use-cases: either supporting simple policies with equality comparisons or predefined attribute values. Due to the lack of carefully checking the XACML model, they did not have original policy evaluation semantics. Therefore, they cannot handle errors containing indeterminate decisions, or ignore the critical attribute setting that leads to potential missing attribute attacks. In this paper, we build up the XACML logical model and propose a decision diagram approach using the data interval partition aggregation. It can parse and transform complex logical expressions in policies into decision tree structures, which efficiently improve the policy evaluation performance. Our approach can also be applied to solve other policy management problems such as policy redundancy detection, policy testings and comparisons, or authorization reverse queries.

A hybrid fuzzy time series model based on granular computing for stock price forecasting

Given the high potential benefits and impacts of accurate stock market predictions, considerable research attention has been devoted to time series forecasting for stock markets. Over long periods, the accuracy of fuzzy time series model forecasting is invariably affected by interval length, and formulating effective interval partitioning methods can be very difficult. Previous studies largely relied on distance partitioning, but this approach neglects the distribution of datasets and can only handle scalar forecasting. But the magnitude of stock price movements is often severe and difficult to predict. Thus, the distribution of stock price datasets is always skewed and the straightforward partitioning method is not well suited to these types of time series datasets. In this research, a novel fuzzy time series model is used to forecast stock market prices. The proposed model is based on the granular computing approach with binning-based partition and entropy-based discretization methods. The proposed model is verified using experimental datasets from the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX), Dow-Jones Industrial Average (DJIA), S&P 500 and IBOVESPA stock indexes, and results are compared against existing fuzzy time series models, three different SVM models, and three modern economic models - GARCH, GJR-GARCH, and Fuzzy GARCH. Compared to other current forecasting methods, the proposed models provide improved prediction accuracy and the results are verified by paired two-tailed t-tests. The experimental results clearly provide improvements for obtaining optimized linguistic intervals and ensuring the accuracy of the proposed model.

Approximation properties of ELM-fuzzy systems for smooth functions and their derivatives

In this paper, we utilize generalized Bernstein polynomials to construct fuzzy system. Different from traditional Bernstein polynomials, partition of interval on input variable can be chosen as non-equidistant division. We prove that generalized Bernstein fuzzy systems are universal approximators to a given continuous function and its high-order derivatives. Further, ELM method is used to tune the parameters of generalized Bernstein fuzzy system and Spline fuzzy system. It is proved that ELM-Spline fuzzy system can approximate a function and its derivative. Simulation examples show that the proposed ELM-Bernstein fuzzy system and ELM-spline fuzzy system can achieve high approximation capability for nonlinear model.

Existence results of stochastic impulsive systems with expectations‐dependent nonlinear terms

In this paper, sufficient conditions are established for the existence and uniqueness of global solutions to stochastic impulsive systems with expectations in the nonlinear terms. The maximal interval and the estimate of mild solutions are also discussed. These results are obtained by using the fixed point theorem, interval partition, and Lyapunov‐like technique. Finally, examples are given to illustrate the theory. Copyright © 2014 John Wiley & Sons, Ltd.