Partition Points Research Articles

Dynamic optimisation based fuzzy association rule mining method

Techniques of performance analysis, comprising of various metrics such as accuracy, efficiency and consuming time, have been conducted to evaluate the measures of properties and interestingness for the association rule mining method. Therefore, these metrics combined with different parameters (partitioning points, fuzzy sets) should be analysed thoroughly and balanced simultaneously to enhance the entire performance (effectiveness, accuracy and efficiency) for an algorithm. As a result, Most of the current algorithms face the pressure from the tradeoff of these metrics and parameters, which becomes even rougher when we employ it in different resources of data (discrete data, categorical data and continuous data). Specifically, serial data (i.e., sequences or transactions of floating point numbers), such as analysis of sensor streaming data, financial streaming data, medical streaming data and sentimental streaming data, are different from discrete variables, such as boolean data (e.g., sentiment: negative and positive represented as ‘0’ and ‘1’ separately) and categorical data (e.g., ‘young age’, ‘middle age’, ‘old age’). The main difference is that serial data face sharp boundary’s problem. That is, it is hard to decide the boundary values (i.e., the single points to partition data into different value groups), which is few to be solved in association rule mining methods. This paper aims to resolve the problem of sharp boundaries and balance multiple performances of our algorithm simultaneously by developing a novel dynamic optimisation (parameters and metrics) based fuzzy association rule mining (DOFARM) method. The proposed method can be applied in a wide range of classifying problems, such as the classification of sentiment strength (negative and positive). In our DOFARM method, instead of single partitioning points, we use a range of values to smoothly separate two consecutive partitions and develop a corresponding membership function to generate fuzzy sets for original data sets of physical and emotional diseases. Mainly, we design a dual compromise scheme: the first tradeoff balances better performance of out-putting association rules and more widely applicable fuzzy membership function while the second tradeoff reduces the time parameter as well as enhances the entire performance of our DOFARM method. The feasibility and accuracy of DOFARM we proposed have been certified theoretically and experimentally. Besides, we demonstrate the accuracy, effectiveness and efficiency for our DOFARM method by experiments according to both synthesis and real datasets.

Combining statistical techniques to predict postsurgical risk of 1-year mortality for patients with colon cancer.

IntroductionColorectal cancer is one of the most frequently diagnosed malignancies and a common cause of cancer-related mortality. The aim of this study was to develop and validate a clinical predictive model for 1-year mortality among patients with colon cancer who survive for at least 30 days after surgery.MethodsPatients diagnosed with colon cancer who had surgery for the first time and who survived 30 days after the surgery were selected prospectively. The outcome was mortality within 1 year. Random forest, genetic algorithms and classification and regression trees were combined in order to identify the variables and partition points that optimally classify patients by risk of mortality. The resulting decision tree was categorized into four risk categories. Split-sample and bootstrap validation were performed. ClinicalTrials.gov Identifier: NCT02488161.ResultsA total of 1945 patients were enrolled in the study. The variables identified as the main predictors of 1-year mortality were presence of residual tumor, American Society of Anesthesiologists Physical Status Classification System risk score, pathologic tumor staging, Charlson Comorbidity Index, intraoperative complications, adjuvant chemotherapy and recurrence of tumor. The model was internally validated; area under the receiver operating characteristic curve (AUC) was 0.896 in the derivation sample and 0.835 in the validation sample. Risk categorization leads to AUC values of 0.875 and 0.832 in the derivation and validation samples, respectively. Optimal cut-off point of estimated risk had a sensitivity of 0.889 and a specificity of 0.758.ConclusionThe decision tree was a simple, interpretable, valid and accurate prediction rule of 1-year mortality among colon cancer patients who survived for at least 30 days after surgery.

Phase-Change Partitions for Thermal Automation of Multistep Reactions.

Medical diagnostics and basic research in low-resource settings require automated reactions to be controlled in a simple, portable manner. Here, we present a novel platform that enables simple automation of multistep reactions to facilitate robust, hands-free assay operation without complex microfluidics or paperfluidics. We separate reagent zones in a conventional PCR tube via solid layers of purified higher alkanes. Reagents can be mixed on demand by simply raising the temperature above the melting point of the alkane partition that separates the two zones. We partitioned various reagents to enable hands-free thermally automated isothermal nucleic acid amplification, heavy metal ion detection, and β-lactamase detection with tandem antibiotic specificity characterization. We anticipate that this phase-change partition platform will find broad application in clinical diagnostics at the point-of-care and in low-resource settings.

A Comparison of Partitioning Strategies for Fixed Points Based Limited Preemptive Scheduling

The increasing industrial demand for handling complex functionalities has influenced the design of hardware architectures for time critical embedded systems, during the past decade. Multicore systems facilitate the inclusion of many complex functionalities, while, at the same time, inducing cache related overheads, as well as adding partitioning complexity to the overall system schedulability. One of the efficient paradigms for controlling and reducing the cache related costs in real-time systems is limited preemptive scheduling (LPS), with its particular instance fixed preemption points scheduling (LP-FPPS), which has been shown to outperform other alternatives as well as has been supported by and investigated in the automotive domain. With respect to the partitioning constraints, partitioned scheduling has been widely used to preruntime allocate tasks to specific cores, resulting in predictable cache-related preemption delays estimations. In this paper, we propose to integrate the LP-FPPS and partitioned scheduling on fixed-priority multicore real-time systems in order to increase the overall system schedulability. We define a new joint approach for task partitioning and preemption point selection, which is based on the computation of the maximum blocking tolerance upon each allocation, thus being able to quantify the schedulability of the taskset on each processor. Furthermore, we investigate the partitioning strategies based on different heuristics, i.e., first fit decreasing and worst fit decreasing, and priority and density taskset orderings. The evaluation performed on randomly generated tasksets shows that in the general case, no single partitioning strategy fully dominates the others. However, the evaluation results reveal that the certain partitioning strategies perform significantly better with respect to the overall schedulability for specific taskset characteristics. The results also reveal that the proposed partitioning strategies outperform fully preemptive and nonpreemptive partitioned scheduling in terms of successful partitioning.

Sampled-data synchronization of chaotic Lur’e systems via input-delay-dependent-free-matrix zero equality approach

This paper focuses on the sampled-data synchronization problem of chaotic Lur’e systems (CLSs) by using sampled output of the systems with variable sampling rates. One novel approach, input-delay-dependent-free-matrix zero equality (IDDFMZE) approach, is proposed for the first time. The IDDFMZE approach can not only fully capture the available information on the actual sampling pattern, but deploy more system information at the dynamic partitioning point. A new Lyapunov–Krasovskii functional (LKF) with some new terms is constructed, which can use more information of the activation function at the dynamic partitioning point. Based on the presented IDDFMZE approach and the constructed LKF, developed synchronization criterion is obtained in the form of linear matrix inequalities (LMIs). The desired sampled-data controller is designed under larger sampling period. Finally, the superiority of proposed results is shown by two numerical examples.

Conditional adaptive Bayesian spectral analysis of nonstationary biomedical time series.

Many studies of biomedical time series signals aim to measure the association between frequency-domain properties of time series and clinical and behavioral covariates. However, the time-varying dynamics of these associations are largely ignored due to a lack of methods that can assess the changing nature of the relationship through time. This article introduces a method for the simultaneous and automatic analysis of the association between the time-varying power spectrum and covariates, which we refer to as conditional adaptive Bayesian spectrum analysis (CABS). The procedure adaptively partitions the grid of time and covariate values into an unknown number of approximately stationary blocks and nonparametrically estimates local spectra within blocks through penalized splines. CABS is formulated in a fully Bayesian framework, in which the number and locations of partition points are random, and fit using reversible jump Markov chain Monte Carlo techniques. Estimation and inference averaged over the distribution of partitions allows for the accurate analysis of spectra with both smooth and abrupt changes. The proposed methodology is used to analyze the association between the time-varying spectrum of heart rate variability and self-reported sleep quality in a study of older adults serving as the primary caregiver for their ill spouse.

A note on improvement by iteration of approximate solutions of operator equations

Let T be a bounded linear operator on a Banach space X = C[0, 1]. Consider the operator equation $$\begin{aligned} u-Tu=f,\;u,f\in X. \end{aligned}$$ Collocation methods are a class of important methods to solve the above equation approximately We consider a modified projection method and an iterated modified projection for the solution of the above operator equation. Let \(\pi _n\) be an interpolatory projection onto the space \(X_n\) of piecewise polynomials of degree \(\le r-1.\) If the collocation points are the Gauss points, then the iterated collocation and iterated modified projection solution is an improvement on the collocation and the modified projection solution. Now let \(\pi _n: X\rightarrow X_n\) be the interpolatory projection with collocation points as the partition points of a uniform partition of [0, 1]. Then iteration fails to improve the order of convergence. But when the approximating space \(X_n\) is the space of continuous functions that are piecewise polynomials of even degree with respect to a uniform partition, then Atkinson (The numerical solutions of integral equations of the second kind, 1997) has shown that iterated collocation solution is an improvement on the collocation solution whereas we show that the iteration improves the order of convergence in the case of modified projection method.

Spline-based DQM for multi-dimensional PDEs: Application to biharmonic and Poisson equations in 2D and 3D

The idea of differential quadrature is used to construct a new algorithm for the solution of differential equations. To determine the weighting coefficients of DQM, B-spline basis functions of degree r are used as test functions. The method is constructed on a set of points mixed from grid points and mid points of a uniform partition. Using the definition of B-splines interpolation as alternative, some error bounds are obtained for DQM. The method is successfully implemented on nonlinear boundary value problems of order m. Also the application of the proposed method to approximate the solution of multi-dimensional elliptic PDEs is included in the paper. As test problem, some examples of biharmonic and Poisson equations are solved in 2D and 3D. The results are compared with some existing methods to show the efficiency and performance of the proposed algorithm. Also some examples of time dependent PDEs are solved to compare the results with other existing spline based DQ methods.

Lacunary Interpolation by Fractal Splines with Variable Scaling Parameters

AbstractFor a prescribed set of lacunary data with equally spaced knot sequence in the unit interval, we show the existence of a family of fractal splines satisfying for v = 0, 1, … ,N and suitable boundary conditions. To this end, the unique quintic spline introduced by A. Meir and A. Sharma [SIAM J. Numer. Anal. 10(3) 1973, pp. 433-442] is generalized by using fractal functions with variable scaling parameters. The presence of scaling parameters that add extra “degrees of freedom”, self-referentiality of the interpolant, and “fractality” of the third derivative of the interpolant are additional features in the fractal version, which may be advantageous in applications. If the lacunary data is generated from a function Φ satisfying certain smoothness condition, then for suitable choices of scaling factors, the corresponding fractal spline satisfies , as the number of partition points increases.

A novel delay partitioning method for stability analysis of interval time-varying delay systems

This paper investigates the problem of the delay-dependent stability for systems with interval time-varying delays. By using the idea of delay-partitioning approach, an appropriate delay partitioning point of h2−h1∈[0,h2] has been selected. Based on this delay partitioning point, a new augmented Lyapunov–Krasovskii functional is constructed. Then, the free-matrix-based integral inequality is employed to estimate the derivative of Lyapunov–Krasovskii functional. As a result, less conservative criteria are presented. Numerical examples are given to illustrate the improvement of the presented approach over the existing ones.

Partitioned log-rank tests for the overall homogeneity of hazard rate functions.

In survival analysis, it is routine to test equality of two survival curves, which is often conducted by using the log-rank test. Although it is optimal under the proportional hazards assumption, the log-rank test is known to have little power when the survival or hazard functions cross. To test the overall homogeneity of hazard rate functions, we propose a group of partitioned log-rank tests. By partitioning the time axis and taking the supremum of the sum of two partitioned log-rank statistics over different partitioning points, the proposed test gains enormous power for cases with crossing hazards. On the other hand, when the hazards are indeed proportional, our test still maintains high power close to that of the optimal log-rank test. Extensive simulation studies are conducted to compare the proposed test with existing methods, and three real data examples are used to illustrate the commonality of crossing hazards and the advantages of the partitioned log-rank tests.

Temporal characterization and regional contribution to O3 and NOx at an urban and a suburban site in Nanjing, China

To improve our understanding of the interplay among local and regional photochemical pollutants in the typical city of the Yangtze River Delta (YRD) region, the concurrent observation of O3 and NOx concentrations at an urban and a suburban site in Nanjing during 2008 is presented. In general, the annual mean O3 concentration is 2.35ppbv lower in the downtown than at suburban due to higher NOx pollution levels correlated with heavy traffic. At both sites, O3 shows a distinct seasonality with the spring maximum and the winter minimum, while the minimum concentration of NOx appears in summertime. Besides the chemical processes of O3 sensitivity in the daytime and the NOx titration at night, meteorological conditions also play an essential role in these monthly and diurnal variations. The ozone weekend effect that can be attributed to the weekly routine of human activities is observed in the urban atmosphere of Nanjing as well, with O3 concentrations 2.09ppbv higher and NOx concentrations 6.20ppbv lower on weekends than on weekdays. The chemical coupling of NO, NO2 and O3 is investigated to show that the OX-component (O3 and NO2) partitioning point occurs at about 35ppbv for NOx, with O3 being the dominant form at lower levels and NO2 dominating at higher levels. And it is also discovered that the level of OX is made up of two contributions, including the regional contribution affected by regional background O3 level and the local contribution correlated with the level of primary pollution. The diurnal peak of regional contribution appears 2–5h after the peak of local contribution, implying that OX in Nanjing might prominently affected by the pollutants from a short distance. The highest regional contribution and the second highest local contribution lead to the spring peak of O3 observed in Nanjing, whereas the highest local contribution and the moderate regional contribution make the O3 concentrations in summer higher than those in autumn and winter. Our results reveal the important environment impacts from meteorological conditions and human activities in the YRD region, and can help to understand O3 pollution in these polluted areas by just using the conventional observations.

The Cloud Point of Alkyl Ethoxylates and Its Prediction with the Hydrophilic-Lipophilic Difference (HLD) Framework.

The hydrophobicity of surfactants has been described through different concepts used to guide the formulation of surfactant-water (SW) and surfactant-oil-water (SOW) systems. An integrated framework of hydrophobicity indicators could provide a complete tool for surfactant characterization, and insights on how their relationship may influence the overall phase behavior of the system. The hydrophilic-lipophilic difference (HLD) and the characteristic curvature (Cc) parameter, included in the HLD, have been shown to correlate with different hydrophobicity indicators including the hydrophilic-lipophilic balance (HLB), packing factor (Pf), phase inversion temperature (PIT), spontaneous curvature (Ho), surfactant partition (K(o-w)), and the critical micelle concentration (CMC). This work aims to investigate whether the HLD can further describe a concomitant hydrophobicity parameter, the cloud point (CP) of alkyl ethoxylates. After applying group contribution models to calculate the Cc of monodisperse (pure) nonionic alkyl ethoxylates, a linear correlation between the calculated Cc and the CP was observed for pure surfactants with 8 ethylene oxide (EO) units or less. Furthermore, using an apparent equivalent alkane carbon number (EACN) to represent the hydrophobicity of the micelle core, the HLD equation was capable of predicting cloud point temperatures of pure alkyl ethoxylates, typically within 5 °C. Polydisperse surfactants did not follow the linear CP-Cc correlation found for pure surfactants. After treating polydisperse samples using a liquid-liquid extraction procedure used to remove the most hydrophobic components in the mixture, the resulting treated surfactants fell in the correlation line of pure alkyl ethoxylates. A closer look at the partition behavior of these treated surfactants showed that their partition, Cc and cloud point are dominated by the most abundant ethoxymers in the treated surfactant. The HLD also predicted the cloud point depression of treated surfactants with increasing sodium chloride concentration. This work shows how the HLD framework could be extended to predict the behavior of SW systems.

VLSI Circuit Partitioning Using Ant Colony Optimisation to Yield Fault Tolerant Testable Systems

As CMOS technology enters the nanometer regime, digital designs are becoming more susceptible to permanent, transient and delay faults. Due to higher probability of faults, there is a fundamental need for addressing reliability and design for testability (DFT) issues, while designing fault tolerant VLSI systems. In this paper, a simulation framework and optimisation technique are presented to guide partitioning of VLSI circuits in order to develop fault tolerant testable designs. This framework utilises ant colony optimisation (ACO) and a primary input primary output fan in fan out partitioning algorithm to determine the optimal DFT locations. The DFT cells are added at the partition points to apply pseudo-exhaustive test patterns for fault detection. The number of DFT cells to be inserted and its locations are critical as it affects the system reliability and performance. Hence, their selection is crucial in order to optimise system performance and reliability. In the present work, the design constraints of the partitioned circuit considered for optimisation include critical path delay, hardware overhead, reliability and test time. ACO uses the parameters of the circuit obtained after partitioning, to determine the optimal values of circuits maximum primary input cone size (N) and minimum fan-out value (F) to decide on the number of partitions and its locations. Experiments conducted using ISCAS85 benchmark circuits demonstrate that this novel approach significantly outperforms results of the state-of-the-art works. The effectiveness of proposed optimisation technique is verified using hardware implementation of the partitioned system in Virtex-6E field programmable gate array.

The recognition and localization of insulators adopting SURF and IFS based on correlation coefficient

The recognition and localization of insulators is a crucial process of insulators’ failure detection. Aiming to identify insulators in test aerial image under the complicated background with no template and segmentation, a novel method of the recognition and localization of insulators based on SURF (Speeded Up Robust Features) and IFS (Intuitionistic Fuzzy Set) based on correlation coefficient is proposed as following: SURF is used to extract a set of feature points of the test aerial image. Then use IFS based on correlation coefficient to partition points into k classes. Find all the connected regions for each class, and calculate minimum circumscribed rectangle and shape characteristic value for each region to identify insulators, and localize them by rectangular boxes. Thus we can detect all the insulators from test aerial image correctly. Experimental results show that the proposed approach can obtain high precision in the recognition and localization of insulators.

Chain transitive induced interval maps on continua

Let $f:I\rightarrow I$ be a continuous map of a compact interval $I$ and $C(I)$ be the space of all compact subintervals of $I$ with the Hausdorff metric. We investigate chain transitivity of induced maps on subcontinua of $C(I)$. In particular, we prove the following theorem: Let $\mathcal{M}$ be a subcontinuum of $C(I)$ having at most countably many partitioning points. Then, the induced map $\mathcal{F}:C(I)\to C(I)$ $($i.e. $\mathcal{F}(A):=\{f(x):x\in A\}$ for each $A \in C(I)$$)$ is chain transitive on $\mathcal{M}$ iff $\mathcal{F}^{2}\vert_{\mathcal{M}}=Id$.

Simple Piecewise Geodesic Interpolation of Simple and Jordan Curves with Applications

We explicitly construct simple, piecewise minimizing geodesic, arbitrarily fine interpolation of simple and Jordan curves on a Riemannian manifold. In particular, a finite sequence of partition points can be specified in advance to be included in our construction. Then we present two applications of our main results: the generalized Green’s theorem and the uniqueness of signature for planar Jordan curves with finite \(p\)-variation for \(1\leqslant p<2\).

An h-p Petrov-Galerkin finite element method for linear Volterra integro-differential equations

We analyze an h-p version Petrov-Galerkin finite element method for linear Volterra integrodifferential equations. We prove optimal a priori error bounds in the L2- and H1-norm that are explicit in the time steps, the approximation orders and in the regularity of the exact solution. Numerical experiments confirm the theoretical results. Moreover, we observe that the numerical scheme superconverges at the nodal points of the time partition.

Closure measures for coarse-graining of the tent map

We quantify the relationship between the dynamics of a time-discrete dynamical system, the tent map T and its iterations T(m), and the induced dynamics at a symbolical level in information theoretical terms. The symbol dynamics, given by a binary string s of length m, is obtained by choosing a partition point [Formula: see text] and lumping together the points [Formula: see text] s.t. T(i)(x) concurs with the i - 1th digit of s-i.e., we apply a so called threshold crossing technique. Interpreting the original dynamics and the symbolic one as different levels, this allows us to quantitatively evaluate and compare various closure measures that have been proposed for identifying emergent macro-levels of a dynamical system. In particular, we can see how these measures depend on the choice of the partition point α. As main benefit of this new information theoretical approach, we get all Markov partitions with full support of the time-discrete dynamical system induced by the tent map. Furthermore, we could derive an example of a Markovian symbol dynamics whose underlying partition is not Markovian at all, and even a whole hierarchy of Markovian symbol dynamics.

CUBIC SPLINE SUPER FRACTAL INTERPOLATION FUNCTIONS

In the present work, the notion of Cubic Spline Super Fractal Interpolation Function (SFIF) is introduced to simulate an object that depicts one structure embedded into another and its approximation properties are investigated. It is shown that, for an equidistant partition points of [x0, xN], the interpolating Cubic Spline SFIF[Formula: see text] and their derivatives [Formula: see text] converge respectively to the data generating function y(x) ≡ y(0)(x) and its derivatives y(j)(x) at the rate of h2-j+ϵ(0 &lt; ϵ &lt; 1), j = 0, 1, 2, as the norm h of the partition of [x0, xN] approaches zero. The convergence results for Cubic Spline SFIF found here show that any desired accuracy can be achieved in the approximation of a regular data generating function and its derivatives by a Cubic Spline SFIF and its corresponding derivatives.