Set Of Representations Research Articles

Set-based state estimation and fault diagnosis of linear discrete-time descriptor systems using constrained zonotopes

This paper presents new methods for set-valued state estimation and active fault diagnosis of linear descriptor systems. The algorithms are based on constrained zonotopes, a generalization of zonotopes capable of describing strongly asymmetric convex sets, while retaining the computational advantages of zonotopes. Additionally, unlike other set representations like intervals, zonotopes, ellipsoids, paralletopes, among others, linear static constraints on the state variables, typical of descriptor systems, can be directly incorporated in the mathematical description of constrained zonotopes. Therefore, the proposed methods lead to more accurate results in state estimation in comparison to existing methods based on the previous sets without requiring rank assumptions on the structure of the descriptor system and with a fair trade-off between accuracy and efficiency. These advantages are highlighted in two numerical examples.

A simple algorithm to compute link polynomials defined by using skein relations

Abstract We give a simple and practical algorithm to compute the link polynomials, which are defined according to the skein relations. Our method is based on a new total order on the set of all braid representatives. As by-product a new complete link invariant are obtained.

Some properties of E(G,W,F_TG) and an application in the theory of splittings of groups

Let us consider W a G-set and M a Z2G-module, where G is a group. In this paper we investigate some properties of the cohomological the theory of splittings of groups. Namely, we give a proof of the invariant E(G,W,M), defined in [5] and present related results with independence of E(G,W,M) with respect to the set of G-orbit representatives in W and properties of the invariant E(G,W,FTG) establishing a relation with the end of pairs of groups e˜(G,T), defined by Kropphller and Holler in [15]. The main results give necessary conditions for G to split over a subgroup T, in the cases where M=Z2(G/T) or M=FTG.

Extending UML Use Case Diagrams to Represent Non-Interactive Functional Requirements

Background: The comprehensive representation of functional requirements is a crucial activity in the analysis phase of the software development life cycle. Representation of a complete set of functional requirements helps in tracing business goals effectively throughout the development life cycle. Use case modelling is one of the most widely-used methods to represent and document functional requirements of the system. Practitioners exploit use case modelling to represent interactive functional requirements of the system while overlooking some of the non-interactive functional requirements. The non-interactive functional requirements are the ones which are performed by the system without an initiation by the user, for instance, notifying something to the user or creating an internal backup. Aim: This paper addresses the representation of non-interactive requirements along with interactive ones (use cases) in one model. This paper calls such requirements `operation cases’ and proposes a new set of graphical and textual notations to represent them. Method: The proposed notations have been applied on a case study and have also been empirically evaluated to demonstrate the effectiveness of the new notations in capturing non-interactive functional requirements. Results and Conclusion: The results of the evaluation indicate that the representation of operation cases helps in documenting a complete set of functional requirements, which ultimately results in a comprehensive translation of requirements into design.

Solving a class of multiobjective bilevel problems by DC programming

In this paper, we consider a class of multiobjective bilevel programming problems in which the first level objective function is assumed to be a vector valued DC function and the second level problem is a linear multiobjective program. The problem is transformed into a standard single optimisation problem by using a preference function. We give a characterisation to the induced region and reformulate the problem as a problem of optimising a function over the efficient set. Next, a well-known representation of the efficient set is used which will allow to transform the problem, using an exact penalisation, into a DC program. Finally, we apply the DC algorithm to solve the resulting DC program.

Fine-Tuning the Fuzziness of Strong Fuzzy Partitions through PSO

We study the influence of fuzziness of trapezoidal fuzzy sets in the strong fuzzy partitions (SFPs) that constitute the database of a fuzzy rule-based classifier. To this end, we develop a particular representation of the trapezoidal fuzzy sets that is based on the concept of cuts, which are the cross-points of fuzzy sets in a SFP and fix the position of the fuzzy sets in the Universe of Discourse. In this way, it is possible to isolate the parameters that characterize the fuzziness of the fuzzy sets, which are subject to fine-tuning through particle swarm optimization (PSO). In this paper, we propose a formulation of the parameter space that enables the exploration of all possible levels of fuzziness in a SFP. The experimental results show that the impact of fuzziness is strongly dependent on the defuzzification procedure used in fuzzy rule-based classifiers. Fuzziness has little influence in the case of winner-takes-all defuzzification, while it is more influential in weighted sum defuzzification, which however may pose some interpretation problems.

GGM-Net: Graph Geometric Moments Convolution Neural Network for Point Cloud Shape Classification

Geometric feature acts as an important role in point cloud shape classification tasks. Previous methods have proved that the geometric information of point clouds effectively improves the classification accuracy. Mo-Net firstly introduced geometric moments into point cloud shape classification, which, to fit the form of second order geometric moments, extends the number of input channels from three to nine. Unfortunately, similar to PointNet, Mo-Net cannot capture the local structures. To address this issue, we propose a graph geometric moments convolution neural network (GGM-Net), which learns local geometric features from geometric moments representation of a local point set. The core module of the GGM-Net is to learn features from geometric moments (termed as GGM convolution). Specifically, the GGM convolution learns point features and local features from the first and second order geometric moments of points and its local neighbors, respectively, and then combines these features by using an addition operation. In this way, a geometrical local representation about points is obtained, which leads to much surface geometry awareness and robustness. Equipped with the GGM convolution, GGM-Net, a simple end-to-end architecture, is developed to achieve a competitive accuracy on the benchmark dataset ModelNet40 and perform more efficiently in terms of memory and computational complexity.

Operatic Prisons: Carcerality on the Stage and in Music

article traces two lines of development in the dramatic and musical representation of carceral settings in the tradition of European opera. On the one hand, the tradition that runs from the Italian operas of the seventeenth century to what is called the romantic “opera of liberation” (Befreiungsoper), could be argued to reflect tragedy on the operatic stage, in which political issues dominate the plot, and the characters’ heroism, and villainy, provides focal thematic material. This article discusses three major instances of this genre: Beethoven’s Fidelio (1814), Puccini’s Tosca (1900), and Luigi Dallapiccola’s Il Prigioniero (1949). On the other hand, a counter-tradition reacts to the seriousness of operas, including the Befreiungsoper, and parodies its bathetic excesses with satirical inversion, as the villains become the heroes. Here we provide a bracket for the first tradition by beginning with John Gay’s Beggar’s Opera and closing with an appreciation of Bertolt Brecht’s 1928 masterpiece, the Dreigroschenoper (Threepenny Opera).

Intelligent approach for large-scale data mining

Large-scale data mining has become a very difficult issue using traditional methods because the data complexity is very high. In the proposed approach, an integration of three methods; Optimised Principal Component Analysis (OPCA), Optimised Enhanced Extreme Learning Machine (OEELM), and stratified sampling, called OPCA-EELM2SS, is presented to provide intelligent and enhanced large-scale data mining. OPCA provides a good representation of large-scale data sets by using the Stratified Sample (SS). By using OEELM, the optimal number of Hidden Nodes (HNs) in ELM is exploited to build a single hidden layer feedforward neural network (SLFN). The proposed approach is tested by using nineteen benchmark data sets. The experimental results demonstrate the effectiveness of the proposed approach by performing different experiments for classical PCA and Independent Component Analysis (ICA), which are integrated with the enhanced ELM using different evaluation criteria. For more reliability, the proposed approach is compared with many previous methods.

Алгоритмизация формирования и прагматической трансформации ограничений существования свойств предметной области

The research area of this article is data mining, specifically the direction "ontological data analysis" developed by the authors, which should be understood as the analysis of empirical data on an unexplored, unstructured knowledge domain in order to build its formal ontology. The research subject of this article is the formation of a set of properties which are supposed to characterize objects of the studied knowledge domain (and, therefore, are subject to measurement in the broadest sense of the word), but with restrictions on the combination of such characteristics in objects — properties "existence constraints". The objectives of the research are to develop algorithms for the step-by-step formation of a set of measured properties with existence constraints, algorithms for modifying such a set (replacing and deleting properties), an algorithm for transforming the "natural" description of this set as a set with relations specified on it into a form convenient for the subsequent constructive use of information about existence constraints in ontological data analysis. In the paper we use the methods of set theory, binary relations, models and methods of formal concept analysis and the methodology for applying the existence constraints to construct formal ontologies. The difference and novelty of the proposed algorithms for the formation of a set of properties with existence constraints lies, first of all, in the "natural" and efficient representation of such sets in the form of graphs and incidence matrices (from the point of view of machine implementation). The novelty of the algorithms for modifying a set of properties with existence constraints lies in performed for the first time algorithmization of unique methods for expanding the set of measured properties that address directly the fundamen tal laws of classical logic. The same is true for the algorithm for transforming a set of measured properties into a set of properties groups that are homogeneous in the form of existential conjugation of member properties. The significance of the results obtained lies in the algorithmic support of a number of stages of ontological data analysis.

STOCHASTIC SIMULATION IN THE FRAMEWORK OF VARIATIONAL-GRID METHOD OF GEOLOGICAL MAPPING

The need for stochastic modeling of the geological objects properties is due to their significant heterogeneity and the limited amount of data. The existing simulation methods, in their formulation, are largely based on the stochastic representation of the model settings laid down and implemented in kriging. Within the framework of other mapping methods that use other model conditions, developing of novel approaches to the problem formulation and to implementation of stochastic simulations methods is necessary. In this paper, we consider an approach based on the application of the variational-grid method of geological mapping. The method is based on minimizing the quadratic functional with ability taking into account a variety of heterogeneous data, including those of a stochastic nature. The direct stochastic simulation method is proposed and tested. It consists in application of the functionality, which includes three constituent elements responsible for: 1) the data approximation, 2) taking into account general spatial patterns, and 3) for the contribution of the random component to the model constructions. The main features of the method are as follows: 1) a small number of control parameters, 2) a predictable effect of their changing on the simulation results, 3) it provides an easy way to accurately mapping the mathematical expectation of the stochastic simulations options variety, and 4) it is applicable for modeling both continuous and categorical parameters. The mathematical implementation of the approach allows reducing the problem to solving a system of linear algebraic equations with a symmetric and positive definite matrix. This determines the multioptional calculations’ computational efficiency due to a single execution of matrix factorization. The calculations are presented for two groups of data with significantly different both quantitative and model parameters, demonstrating the possibilities and features of the proposed approach implementation under different conditions. The calculations testify that the variograms’ parameters of the stochastic solutions and of the actual data could be coordinated.

Self-Representation Based Unsupervised Exemplar Selection in a Union of Subspaces.

Finding a small set of representatives from an unlabeled dataset is a core problem in a broad range of applications such as dataset summarization and information extraction. Classical exemplar selection methods such as k-medoids work under the assumption that the data points are close to a few cluster centroids, and cannot handle the case where data lie close to a union of subspaces. This paper proposes a new exemplar selection model that searches for a subset that best reconstructs all data points as measured by the l1 norm of the representation coefficients. Geometrically, this subset best covers all the data points as measured by the Minkowski functional of the subset. To solve our model efficiently, we introduce a farthest first search algorithm that iteratively selects the worst represented point as an exemplar. When the dataset is drawn from a union of independent subspaces, our method is able to select sufficiently many representatives from each subspace. We further develop an exemplar based subspace clustering method that is robust to imbalanced data and efficient for large scale data. Moreover, we show that a classifier trained on the selected exemplars (when they are labeled) can correctly classify the rest of the data points.

Comparing Degenerate Strings

Uncertain sequences are compact representations of sets of similar strings. They highlight common segments by collapsing them, and explicitly represent varying segments by listing all possible options. A generalized degenerate string (GD string) is a type of uncertain sequence. Formally, a GD string Ŝ is a sequence of n sets of strings of total size N, where the ith set contains strings of the same length ki but this length can vary between different sets. We denote by W the sum of these lengths k0, k1, . . . , kn-1. Our main result is an 𝒪(N + M)-time algorithm for deciding whether two GD strings of total sizes N and M, respectively, over an integer alphabet, have a non-empty intersection. This result is based on a combinatorial result of independent interest: although the intersection of two GD strings can be exponential in the total size of the two strings, it can be represented in linear space. We then apply our string comparison tool to devise a simple algorithm for computing all palindromes in Ŝ in 𝒪(min{W, n2}N)-time. We complement this upper bound by showing a similar conditional lower bound for computing maximal palindromes in Ŝ. We also show that a result, which is essentially the same as our string comparison linear-time algorithm, can be obtained by employing an automata-based approach.

A Partial Differential Equation Obstacle Problem for the Level Set Approach to Visibility

In this article we consider the problem of finding the visibility set from a given point when the obstacles are represented as the level set of a given function. Although the visibility set can be computed efficiently by ray tracing, there are advantages to using a level set representation for the obstacles, and to characterizing the solution using a partial differential equation (PDE). A nonlocal PDE formulation was proposed in Tsai et al. (J Comput Phys 199(1):260–290. https://doi.org/10.1016/j.jcp.2004.02.015, 2004): in this article we propose a simpler PDE formulation, involving a nonlinear obstacle problem. We present a simple numerical scheme and show its convergence using the framework of Barles and Souganidis. Numerical examples in both two and three dimensions are presented.

Molecular Surface Estimation by Geometric Coupled Distance Functions

Estimating the surface from given atoms with location and size information is a fundamental task in many fields, such as molecular dynamics and protein analysis. In this paper, we present a novel method for such surface estimation. Our method is based on level set representations, which can efficiently handle complex geometries. The proposed method is analyzed from mathematical point of view and from computation point of view. The method does not require any prior information about the surface. This property is fundamentally important for the surface estimation task. The presented method is evaluated on both synthetic and real data. Several numerical experiments confirm that our method is effective and computationally efficient. Finally, the method is applied on protein surface estimation. This method is suitable for high performance molecular dynamics study, protein surface analysis, etc.

An information-theoretic graph-based approach for feature selection

Feature selection is a critical research problem in data science. The need for feature selection has become more critical with the advent of high-dimensional data sets especially related to text, image and micro-array data. In this paper, a graph-theoretic approach with step-by-step visualization is proposed in the context of supervised feature selection. Mutual information criterion is used to evaluate the relevance of the features with respect to the class. A graph-based representation of the input data set, named as feature information map (FIM) is created, highlighting the vertices representing the less informative features. Amongst the more informative features, the inter-feature similarity is measured to draw edges between features having high similarity. At the end, minimal vertex cover is applied on the connected vertices to identify a subset of features potentially having less similarity among each other. Results of the experiments conducted with standard data sets show that the proposed method gives better results than the competing algorithms for most of the data sets. The proposed algorithm also has a novel contribution of rendering a visualization of features in terms of relevance and redundancy.

Methods of forecasting technical and economic processes and the possibility of improving them

The article provides a brief overview of the methods for forecasting technical and economic processes, reveals their features. A method for estimating the parameters of models with a varying value of the degree of time is proposed, which can be used to implement the method of growth models and the method based on representations of fuzzy sets. The features of methods based on growth models are considered. The simplest methods are compared, the implementation of which can be represented in the form of the following steps: 1) a curve is selected heuristically (expertly), smoothing the initial statistical data and extrapolating to their perspective, while the degrees of the terms of the model are chosen constant; 2) the parameters of the models are estimated, most often by the least squares method; 3) the adequacy of the model by the initial data and the value of the predicted parameter are evaluated. As analysis has shown, the first two stages are decisive in the process of increasing the accuracy of the forecast, and therefore it is advisable to improve them. To do this, it is proposed to use an iterative process, which allows you to simultaneously vary the coefficients at various degrees of the time parameter, as well as its degree. The iterative process is presented in detail by analytical calculations that are convenient in engineering applications.

Visual attention-capture cue in depicted scenes fails to modulate online sentence processing

Everyday communication is enriched by the visual environment that listeners concomitantly link to the linguistic input. If and when visual cues are integrated into the mental meaning representation of the communicative setting, is still unclear. In our earlier findings, the integration of linguistic cues (i.e., topic-hood of a discourse referent) reduced discourse updating costs of the mental representation as indicated by reduced sentence-initial processing costs of the non-canonical word order in German. In the present study we tried to replicate our earlier findings by replacing the linguistic cue by a visual attention-capture cue presented below the threshold of perception in order to direct participant’s attention to a depicted referent. While this type of cue has previously been shown to modulate word order preferences in sentence production, we found no effects on sentence comprehension. We discuss possible theory-based reasons for the null effect of the implicit visual cue as well as methodological caveats and issues that should be considered in future research on multimodal meaning integration.

Collective viscosity model for shear thinning polymeric materials

This work presents a framework for collectively modeling shear viscosities of grouped polymeric materials. The viscosity model has been derived from the multi-modal White-Metzner constitutive equation. Simplification to the multi-modal viscosity has resulted in a viscosity model that controls gradual transition between two conventional viscosity models. It facilitates mathematical representation of multiple sets of viscosity data at the same time. A conventional shear viscosity function, which is common to the group, is multiplied by a material-specific function with one or two constants to form the collective viscosity model. The proposed framework has been applied to several polymeric systems such as polymers with varying molecular weight, polymer solutions with different concentrations, polymers with different filler loadings, and polymer blends with various composition ratios. It has been shown that the K-index in the proposed viscosity model and the variable in the material system such as concentration or compounding ratio can be correlated with each other to predict the viscosities of untested cases.

The Tandem Counting Bloom Filter - It Takes Two Counters to Tango

Set representation is a crucial functionality in various areas such as networking and databases. In many applications, memory and time constraints allow only an approximate representation where errors can appear for some queried elements. The Variable-Increment Counting Bloom Filter (VI-CBF) is a popular data structure for the representation of dynamically-changing sets, achieving a good tradeoff between memory efficiency and queries accuracy. For some applications, the required accuracy is higher than that enabled by the VI-CBF. In this paper, we present the Tandem Counting Bloom Filter (T-CBF), a new data structure that relies on the interaction among counters to describe sets with higher accuracy. We analyze its performance and show that by a joint consideration of counters, the T-CBF always performs better than the VI-CBF and it can for some configurations reduce its false positive probability by an order of magnitude. The overhead of such an approach is expressed upon an element insertion or query as read or write operations to a pair of counters rather than a single counter in each hash location. The operations themselves also require considering a larger number of scenarios.