Showing papers in "Fundamenta Informaticae in 2017"

Abnormal Breast Detection in Mammogram Images by Feed-forward Neural Network Trained by Jaya Algorithm

Abstract: (Aim) Abnormal breast can be diagnosed using the digital mammography. Traditional manual interpretation method cannot yield high accuracy. (Method) In this study, we proposed a novel computer-aided diagnosis system for detecting abnormal breasts in mammogram images. First, we segmented the region-of-interest. Next, the weighted-type fractional Fourier transform (WFRFT) was employed to obtain the unified time-frequency spectrum. Third, principal component analysis (PCA) was introduced and used to reduce the spectrum to only 18 principal components. Fourth, feed-forward neural network (FNN) was utilized to generate the classifier. Finally, a novel algorithm-specific parameter free approach, Jaya, was employed to train the classifier. (Results) Our proposed WFRFT + PCA + Jaya-FNN achieved sensitivity of 92.26%±3.44%, specificity of 92.28%±3.58%, and accuracy of 92.27%±3.49%. (Conclusions) The proposed CAD system is effective in detecting abnormal breasts and performs better than 5 state-of-the-art systems. Besides, Jaya is more effective in training FNN than BP, MBP, GA, SA, and PSO. ∗Address for correspondence: Jiangsu Key Laboratory of 3D, Printing Equipment and Manufacturing, Nanjing, Jiangsu 210042, China 192 S. Wang et al. / Abnormal Breast Detection in Mammogram Images by Feed-forward Neural Network Trained

Interval-valued Fuzzy Soft Decision Making Methods Based on MABAC, Similarity Measure and EDAS

Abstract: Interval-valued fuzzy soft decision making problems have obtained great popularity recently. Most of the current methods depend on level soft set that provide choice value of alternatives to be ranked. Such choice value always encounter the equal condition that the optimal alternative can’t be gained. Most important of all, the current decision making procedure is not in accordance with the way that the decision makers think about the decision making problems. In this paper, we initiate a new axiomatic definition of interval-valued fuzzy distance measure and similarity measure, which is expressed by interval-valued fuzzy number (IVFN) that will reduce the information loss and keep more original information. Later, the objective weights of various parameters are determined via grey system theory, meanwhile, we develop the combined weights, which can show both the subjective information and the objective information. Then, we present three algorithms to solve interval-valued fuzzy soft decision making problems by MultiAttributive Border Approximation area Comparison (MABAC), Evaluation based on Distance from Average Solution (EDAS) and new similarity measure. Three approaches solve some unreasonable conditions and promote the development of decision making methods. Finally, the effectiveness and feasibility of approaches are demonstrated by some numerical examples.

An Optimization Wavelet Method for Multi Variable-order Fractional Differential Equations

Abstract: In this paper, a new operational matrix of variable-order fractional derivative (OMVFD) is derived for the second kind Chebyshev wavelets (SKCWs). Moreover, a new optimization wavelet method based on SKCWs is proposed to solve multi variable-order fractional differential equations (MV-FDEs). In the proposed method, the solution of the problem under consideration is expanded in terms of SKCWs. Then, the residual function and its errors in 2-norm are employed for converting the problem under study to an optimization one, which optimally chooses the unknown coefficients. Finally, the method of constrained extremum is applied, which consists of adjoining the constraint equations obtained from the given initial conditions to the object function obtained from residual function by a set of unknown Lagrange multipliers. The main advantage of this approach is that it reduces such problems to those optimization problems, which greatly simplifies them and also leads to obtain a good approximate solution for them.

Semantics for Specialising Attack Trees based on Linear Logic

Abstract: Attack trees profile the sub-goals of the proponent of an attack. Attack trees have a variety of semantics depending on the kind of question posed about the attack, where questions are captured by an attribute domain. We observe that one of the most general semantics for attack trees, the multiset semantics, coincides with a semantics expressed using linear logic propositions. The semantics can be used to compare attack trees to determine whether one attack tree is a specialisation of another attack tree. Building on these observations, we propose two new semantics for an extension of attack trees named causal attack trees. Such attack trees are extended with an operator capturing the causal order of sub-goals in an attack. These two semantics extend the multiset semantics to sets of series-parallel graphs closed under certain graph homomorphisms, where each semantics respects a class of attribute domains. We define a sound logical system with respect to each of these semantics, by using a recently introduced extension of linear logic, called MAV, featuring a non-commutative operator. The non-commutative operator models causal dependencies in causal attack trees. Similarly to linear logic for attack trees, implication defines a decidable preorder for specialising causal attack trees that soundly respects a class of attribute domains.

Tea Category Identification using Computer Vision and Generalized Eigenvalue Proximal SVM

Abstract: (Objective) In order to increase classification accuracy of tea-category identification (TCI) system, this paper proposed a novel approach. (Method) The proposed methods first extracted 64 color histogram to obtain color information, and 16 wavelet packet entropy to obtain the texture information. With the aim of reducing the 80 features, principal component analysis was harnessed. The reduced features were used as input to generalized eigenvalue proximal support vector machine (GEPSVM). Winner-takes-all (WTA) was used to handle the multiclass problem. Two kernels were tested, linear kernel and Radial basis function (RBF) kernel. Ten repetitions of 10-fold stratified cross validation technique were used to estimate the out-of-sample errors. We named our method as GEPSVM + RBF + WTA and GEPSVM + WTA. (Result) The results showed that PCA reduced the 80 features to merely five with explaining 99.90% of total variance. The recall rate of GEPSVM + RBF + WTA achieved the highest overall recall rate of 97.9%. (Conclusion) This was higher than the result of GEPSVM + WTA and other five state-of-the-art algorithms: back propagation neural network, RBF support vector machine, genetic neural-network, linear discriminant analysis, and fitness-scaling chaotic artificial bee colony artificial neural network. ∗Address for correspondence: School of Electronic Science and Engineering, Nanjing University, Nanjing, Jiangsu 210046, China 326 S. Wang et al. / Tea Category Identification using CV and GEPSVM

A New Approach for Modeling with Discrete Fractional Equations

Abstract: In this paper, we introduce a new class of nonlinear discrete fractional equations to model tumor growth rates in mice. For the data fitting purpose, we develop a new method which can be considered as an improved version of the partial sum method for parameter estimations. We demonstrate the goodness of fit by comparing the models with three statistical measures.

CoCaml: Functional Programming with Regular Coinductive Types

Abstract: Functional languages offer a high level of abstraction, which results in programs that are elegant and easy to understand. Central to the development of functional programming are inductive and coinductive types and associated programming constructs, such as pattern-matching. Whereas inductive types have a long tradition and are well supported in most languages, coinductive types are subject of more recent research and are less mainstream. We present CoCaml, a functional programming language extending OCaml, which allows us to define recursive functions on regular coinductive datatypes. These functions are defined like usual recursive functions, but parameterized by an equation solver. We present a full implementation of all the constructs and solvers and show how these can be used in a variety of examples, including operations on infinite lists, infinitary γ-terms, and p-adic numbers.

Numeric Algorithms for Corank Two Edge-bipartite Graphs and their Mesh Geometries of Roots

Abstract: Following a Coxeter spectral analysis problems for positive edge-bipartite graphs (signed multigraphs with a separation property) introduced in [SIAM J. Discr. Math. 27(2013), 827-854] and [Fund. Inform. 123(2013), 447-490], we study analogous problems for loop-free corank two edge-bipartite graphs ∆ = (∆0,∆1). i.e. for edge-bipartite graphs ∆, with at least n = 3 vertices such that their rational symmetric Gram matrix G∆ ∈ Mn(Q) is positive semidefinite of rank n − 2. We study such connected edge-bipartite graphs by means of the nonsymmetric Gram matrix Ǧ∆ ∈ Mn(Z), the Coxeter matrix Cox∆ := −Ǧ∆ · Ǧ−tr ∆ , its complex spectrum specc∆ ⊆ C, and an associated simply laced Dynkin diagram Dyn∆, with n − 2 vertices. Here Z means the ring of integers. It is well-known that if ∆ ≈Z ∆′ (i.e., there exists B ∈ Mn(Z) such that detB = ±1 and Ǧ∆′ = B · Ǧ∆ · B) then specc∆ = specc∆′ and Dyn∆ = Dyn∆′ . A complete classification of connected non-negative loop-free edge-bipartite graphs ∆ with at most six vertices of corank two, up to the Z-congruence ∆ ≈Z ∆′, is also given. A complete list of representatives of the Z-congruence classes of all connected non-negative edge-bipartite graphs of corank two with with at most 6 vertices is constructed; it consists of 1, 2, 2 and 8 edge-bipartite graphs of corank two with 3, 4, 5 and 6 vertices, respectively.

Monitoring with Parametrized Extended Life Sequence Charts

Abstract: Runtime verification is a lightweight verification technique that checks whether an execution of a system satisfies a given property. A problem in monitoring specification languages is to express parametric properties, where the correctness of a property depends on both the temporal relations of events, and the data carried by events. In this paper, we introduce parametrized extended live sequence charts (PeLSCs) for monitoring sequences of data-carrying events. The language of PeLSCs is extended from life sequence charts by introducing condition and assignment structures. We develop a translation from PeLSCs into the hybrid logic HL, and prove that the word problem of the PeLSCs is linear with respect to the size of a parametrized event trace. Therefore, the formalism is feasible for on-line monitoring.

Naming a channel with beeps

Abstract: We consider a communication channel in which the only possible communication mode is transmitting beeps, which reach all the nodes instantaneously. Nodes are anonymous, in that they do not have any individual identifiers. The algorithmic goal is to randomly assign names to the nodes in such a manner that the names make a contiguous segment of positive integers starting from $1$. We give a Las Vegas naming algorithm for the case when the number of nodes $n$ is known, and a Monte Carlo algorithm for the case when the number of nodes $n$ is not known. The algorithms are provably optimal with respect to the expected time $O(n\log n)$, the number of used random bits $O(n\log n)$, and the probability of error.

Łukasiewicz μ-calculus

Abstract: The paper explores properties of Eukasiewicz μ-calculus, a version of the quantitative/probabilistic modal μ-calculus containing both weak and strong conjunctions and disjunctions from Eukasiewicz (fuzzy) logic. We show that this logic encodes the well-known probabilistic temporal logic PCTL. And we give a model-checking algorithm for computing the rational denotational value of a formula at any state in a finite rational probabilistic nondetermini stic transition system.

A Framework for the Verification of Parameterized Infinite-state Systems

Abstract: We present our tool, developed for the analysis and verification of parameterized infinite-state systems. The framework has been successfully applied in the verification of programs handling unbounded data-structures. In such application domain, being able to infer quantified invariants is a mandatory requirement for successful results. We will describe the techniques implemented in our system and discuss how they contribute in achieving important results in the analysis of parameterized distributed and timed systems, as well as of programs with arrays of unknown length.

Monotone Convergence of Extended Iterative Methods and Fractional Calculus with Applications

Abstract: We present monotone convergence results for general iterative methods in order to approximate a solution of a nonlinear equation defined on a partially ordered linear topological space. The main novelty of the paper is that the operators appearing in the iterative method are not necessarily linear. This way we expand of the applicability of iterative methods. Some applications are also provided from fractional calculus using Caputo and Canavati type fractional derivatives and other areas.

Interpretation of Fractional Derivatives as Reconstruction from Sequence of Integer Derivatives

Abstract: In this paper, we propose an ”informatic” interpretation of the Riemann-Liouville and Caputo derivatives of non-integer orders as reconstruction from infinite sequence of standard derivatives of integer orders. The reconstruction is considered with respect to orders of derivatives.

Dynamics of Commodities Prices: Integer and Fractional Models

Abstract: This paper examines the time series of four important agricultural commodities, namely the soybean, corn, coffee and sugar prices. Time series can exhibit long-range dependence and persistence in their observation. The long memory feature of data is a documented fact and there has been an increasing interest in studying such concepts in the perspective of economics and finance. In this work, we start by analyzing the time series of the four commodities by means of the Fractional Fourier Transform (FrFT) to unveil time-frequency patterns in the data. In a second phase, we apply Auto Regressive Integrated Moving Average (ARIMA) and Auto Regressive Fractionally Integrated Moving Average (ARFIMA) models for obtaining the spot price composition and predict future price. The ARFIMA process is a known class of long memory model, representing a generalization of the ARIMA algorithm. We compare the performances of the ARIMA and the ARFIMA models and we show that the ARFIMA has a superior performance for future price forecasting. ∗Address for correspondence: University of São Paulo, Av. Duque de Caxias Norte 225, 13635-900, Brazil 390 S.A. David et al. / Dynamics of Commodities Prices: Integer and Fractional Models

The Weighted Matching Approach to Maximum Cardinality Matching

Abstract: Several papers have achieved time $O(\sqrt n m)$ for cardinality matching, starting from first principles. This results in a long derivation. We simplify the task by employing well-known concepts for maximum weight matching. We use Edmonds' algorithm to derive the structure of shortest augmenting paths. We extend this to a complete algorithm for maximum cardinality matching in time $O(\sqrt n m)$.

Eigenvector method and rank reversal in group decision making revisited

Abstract: It has been shown recently that the Eigenvector Method may lead to strong rank reversal in group decision making, that is, the alternative with the highest priority according to all individual vectors may lose its position when evaluations are derived from the aggregated group comparison matrix. We give a minimal counterexample and prove that this negative result is a consequence of the difference of the rankings induced by the right and inverse left eigenvectors.

The RC Circuit Described by Local Fractional Differential Equations

Abstract: A non-differentiable resistor-capacitor circuit comprised of the capacitor and resistor in the fractal-time domain is first proposed in this article. The solution behavior of the corresponding local fractional ordinary differential equation is presented for the Mittag-Leffler decay defined on Cantor sets. The obtained results reveal the sufficiency of the local fractional calculus in the analysis of the fractal electrical systems.