Stabilizing region of PDμ controller for fractional order system with general interval uncertainties and an interval delay

This paper concentrates on computing the stabilizing region of PD^μ controller for fractional order system with general interval uncertainties and an interval delay. The stabilizing region means the complete/approximate set of PD^μ controllers that stabilize the given closed-loop control system. General interval uncertainties refer to both coefficients and orders of the fractional system suffer from interval uncertainties. Interval delay indicates that the delay also vary in a specified interval.Firstly, a method is presented to calculate the stabilizing region for general interval fractional system with an interval time-constant delay. Based on a novel mapping function and the concept of critical controller parameters, the stabilizing region can be determined numerically. Secondly, the stabilizing region computation problem for general interval fractional system with an interval time-varyingdelay is considered. By applying a revised small-gain theorem, the stabilizing region can be calculated like the time-constant delay case. Thirdly, two alternative methods are proposed to improve the computational efficiency of stabilizing region calculation. Both methods can reduce the number of polynomials which are used to determine the stabilizing region. Examples are followed to illustrate the proposed results.     

Routh-type table test for zero distribution of polynomials with commensurate fractional and integer degrees

This paper mainly presents Routh-type table test methods for zero distribution of polynomials with commensurate fractional degrees on the left-half plane, right-half plane and imaginary axis in the complex plane. The proposed tabular methods are derived for extension and generalization of the Routh test, which is widely used in controls for zero distribution of polynomials with integer degrees. Singular cases are discussed and handled efficiently and simply. Necessary and sufficient conditions for the second singular case are completely analyzed in terms of symmetric zeros. A particular property is revealed that a polynomial with commensurate fractional degrees without pure imaginary zero may still be stable in the presence of the second singular case, which is impossible for a real polynomial with integer degrees. Furthermore, we present a test to solve the zero distribution problem with respect to general sector region for polynomials with commensurate fractional degrees and real/complex coefficients. Finally, numerical examples are given to illustrate the correctness and effectiveness of the results. The proposed methods have broad application areas, including various systems, circuits and control.     

A simplified stability test for 1-D discrete systems

This paper shows that the stability tests for 1-D discrete systems using the transformation p=(z+z⁻¹) and properties of Chebyshev polynomials developed previously can be directly obtained from the z-domain continued fraction expansion based on the functions (z+1) and (z⁻¹+1) on an alternate basis. Furthermore, it is shown that the root distribution of a polynomial with real coefficient can be determined by the same algorithm.     

A test for robust Hurwitz stability of convex combinations of complex polynomials

In this paper we present a method for testing the Hurwitz property of a segment of polynomials (1−λ)p₀(s)+λp₁(s), where λ∈[0,1] and p₀(s) and p₁(s) are nth-degree polynomials with complex coefficients. The method consists in constructing a parametric Routh-like array with polynomial entries and generating Sturm sequences for checking the absence of zeros of two real λ-polynomials of degrees 2 and 2n in the interval (0,1). The presented method is easy to implement. Moreover, it accomplishes the test in a finite number of arithmetic operations because it does not invoke any numerical root-finding procedure.     

OpinionLink: Leveraging user opinions for product catalog enrichment

A vast number of user opinions are available from reviews posted on e-commerce websites. Although these opinions are a valuable source of knowledge for both manufacturers and customers, they provide volumes of information that exceeds the human cognitive processing capacity, which can be a major bottleneck for their effective use. To address this problem, a number of opinion-summarization methods have been proposed to organize these opinions by grouping them around aspects. However, these methods tend to generate an excessive number of aspect groups that are frequently overly generic and difficult to interpret. We argue that a superior alternative would be to organize opinions around product attributes as defined in a product catalog. Typically, product attributes correspond to the most important characteristics of the products. Furthermore, they are common to all products in a given category and thus, form a more stable set than aspects. In this paper, we propose a novel approach called OpinionLink to products in a catalog at the attribute granularity level with opinions extracted from product reviews. The proposed approach is divided into two phases. In the first phase, OpinionLink uses a classifier to identify opinionated sentences in the reviews on a particular product. In the second phase, another classifier is used to map the opinions that were previously extracted from the user reviews to the attributes of the products in the product catalog. We performed a series of experiments on these phases. For the first phase, our experiments indicated that using classifiers with the proposed features achieved an average of 0.87 in terms of F₁ measure for the task of identifying opinionated sentences. In the second phase, the method we proposed for the opinion-mapping task achieved an average of 0.85 in terms of F₁. Further, we verified the effectiveness of the proposed approach as a realistic end-to-end application, indicating that we can use OpinionLink in a real setting. Finally, we empirically demonstrate the feasibility of using the proposed approach with an extremely large volume of opinions available in a collection of more than 600,000 real reviews. We also set forth a number of directions for future research.     

Error Estimation in Numerical Inversion of Laplace Transforms Using Padé Approximation

Uniform asymptotic estimates for the error in the main diagonal and first two subdiagonal Padé approximants for exp(iz) in a sector covering the real z axis are derived. The results are applied to analyze the error in a cerain procedure for the numerical inversion of the Laplace transform.     

Parameter identification of a class of time-varying systems via orthogonal shifted legendre polynomials

A method of using orthogonal shifted Legendre polynomials for identifying the parameters of a process whose behaviour can be modelled by a linear differential equation with time-varying coefficients in the form of finite-order polynomials is presented. It is based on the repeated integration of the differential equation and the representations of $\text{∫}\text{0}\text{t}$s(τ) dτ = Ps(t) and ts(t) = Rs(t), where P and R are constant matrices and s(t) is a shifted Legendre vector whose elements are shifted Legendre polynomials. The differential input-output equation is converted into a set of overdetermined linear algebraic equations for a least squares solution. The results of simulation studies are included to illustrate the applicability of the method.     

On the Conditions for the Characteristic Roots of a Matrix in a Sector

Davison and Ramesh expressed equivalently the condition for the characteristic roots of a real matrix to lie within a sector by the condition for a matrixof doubled order to be Hurwitzian (1). A further generalization of their result is given in this note.     

Optimal tensegrity structures in bending: The discrete Michell truss

This paper provides the closed form analytical solution to the problem of minimizing the material volume required to support a given set of bending loads with a given number of discrete structural members, subject to material yield constraints. The solution is expressed in terms of two variables, the aspect ratio, ρ^-1, and complexity of the structure, q (the total number of members of the structure is equal to q(q+1)). The minimal material volume (normalized) is also given in closed form by a simple function of ρ and q, namely, V=q(ρ^-1/q-ρ^1/q). The forces for this nonlinear problem are shown to satisfy a linear recursive equation, from node-to-node of the structure. All member lengths are specified by a linear recursive equation, dependent only on the initial conditions involving a user specified length of the structure. The final optimal design is a class 2 tensegrity structure. Our results generate the 1904 results of Michell in the special case when the selected complexity q approaches infinity. Providing the optimum in terms of a given complexity has the obvious advantage of relating complexity q to other criteria, such as costs, fabrication issues, and control. If the structure is manufactured with perfect joints (no glue, welding material, etc.), the minimal mass complexity is infinite. But in the presence of any joint mass, the optimal structural complexity is finite, and indeed quite small. Hence, only simple structures (low complexity q) are needed for practical design.     

Special functions of circuits and systems

The polynomial solutions of the equation fy″ + gy′ + λy = 0 are obtained and classified for f, g, and λ certain second-degree, first-degree, and zero-degree polynomials, respectively. Applications are given illustrating the use of these polynomials in the construction of amplitude functions and system functions and in tree counting. In particular, all-pole and rational filter functions are considered which include as special cases the Chebyshev, Butterworth, elliptic, Bessel, and various transitional filter functions.     

Strong delay-independent stability of linear delay systems

This paper presents a new necessary and sufficient condition for testing the strong delay-independent stability of linear systems subject to a single delay. The proposed method follows from the use of matrix polynomials constraints and the Kalman–Yakubovich–Popov lemma. The resulting condition can be checked exactly by solving a feasibility problem in terms of a linear matrix inequality (LMI). Simple numerical examples are given to show the effectiveness of the proposed method.     

Accurate approximate solutions to oscillatory problems with perturbing singular damping

In this paper we attempt to obtain approximate solutions of improved accuracy for a class of differential equations of the form

$\text{d}{}^2\text{y}\text{d}\text{x}{}^2\text{+εμ(x)}\text{d}\text{y}\text{d}\text{x}\text{+ω}{}^2{}_{\mathrm{c}}\text{y = 0}$

, where ε is a real parameter less than unity, ω_c is a positive real constant of order unity and μ(x) is a singular function of x in the region of interest. It does not appear to be possible to find a general analytic expression for the error estimate of the approximate solution. For the case μ(x) = x^?2, however, it is shown that the approximate solution is accurate to 0(ε²), as x → 0^? from negative values, by comparing it with the numerically integrated solution. For the same case, the approximate solution is orders of magnitude more accurate than Poincaré's first-order perturbation solution, which is accurate to $\text{0(}\text{ε}{}^2\text{ln}\text{|x|}\text{|x|}\text{)}$ as x → 0^?. This work arose in search of analytic solutions to a linearized form of the restricted three-body problem.     

Towards effective document clustering: A constrained K-means based approach

Document clustering is an important tool for document collection organization and browsing. In real applications, some limited knowledge about cluster membership of a small number of documents is often available, such as some pairs of documents belonging to the same cluster. This kind of prior knowledge can be served as constraints for the clustering process. We integrate the constraints into the trace formulation of the sum of square Euclidean distance function of K-means. Then,the combined criterion function is transformed into trace maximization, which is further optimized by eigen-decomposition. Our experimental evaluation shows that the proposed semi-supervised clustering method can achieve better performance, compared to three existing methods.     

Low level of adherence to instructions for 24-hour urine collection among hospital outpatients

Introduction:

We hypothesized that patients are poorly informed about proper procedure for 24-hour urine specimen collection and its relevance in determination of biochemical analytes, despite availability of leaflets and webpage with instruction for collection. The aim of this survey was to question outpatients how well are they informed about procedure of 24-hour urine specimen collection.

Materials and methods:

The survey with 10 questions was done in outpatient laboratory of University Department of Chemistry, Medical School University Hospital Sestre Milosrdnice, Zagreb, Croatia. The study included 59 patients with collected 24-hour urine sample who have consented to participate in the survey.

Results:

Out of 59 participants, most of them (0.97) were older than 40 years. Internet was not recognized as a source of information (1/59). Almost one third of the patients have changed their drinking habits to collect more urine volume. Although most of the patients (0.60) were aware that the bottle of water is the best choice for the container, almost half of them were collected urine samples in the plastic soft drink bottle. Laboratory staff and physicians often have given information about proper collection procedure, but that information was insufficient.

Conclusions:

Patients are usually not aware of importance of proper preanalytical procedure for collecting urine specimen and how improper collection could affect results of requested tests. Education of outpatients, general practitioners and laboratory staff is needed in order to improve sample quality and trueness of results.     

Study on stability and stabilizability of discrete-time mean-field stochastic systems

This paper is to study the mean square stabilizability and regional stability of discrete-time mean-field stochastic systems. Firstly, a necessary and sufficient condition is presented via the spectrum of linear operator to illustrate the stabilizability of discrete-time mean-field stochastic systems. B(0, γ)-stabilizability is introduced and transformed into solving linear matrix inequalities (LMIs). Secondly, B_M-stability is characterized, especially, the stabilities of circular region, sector region and annulus regions are discussed extensively. Finally, as applications, it is shown that B(0, γ₁; γ₂)-stability has close relationship with the decay rate of the system state response and the Lyapunov exponent.     

Expert group formation using facility location analysis

In this paper, we propose an optimization framework to retrieve an optimal group of experts to perform a multi-aspect task. While a diverse set of skills are needed to perform a multi-aspect task, the group of assigned experts should be able to collectively cover all these required skills. We consider three types of multi-aspect expert group formation problems and propose a unified framework to solve these problems accurately and efficiently. The first problem is concerned with finding the top k experts for a given task, while the required skills of the task are implicitly described. In the second problem, the required skills of the tasks are explicitly described using some keywords but each expert has a limited capacity to perform these tasks and therefore should be assigned to a limited number of them. Finally, the third problem is the combination of the first and the second problems. Our proposed optimization framework is based on the Facility Location Analysis which is a well known branch of the Operation Research. In our experiments, we compare the accuracy and efficiency of the proposed framework with the state-of-the-art approaches for the group formation problems. The experiment results show the effectiveness of our proposed methods in comparison with state-of-the-art approaches.     

Binary matrices with specified properties

The binary matrices A which are circulant with one or more of the following properties: (1) A is symmetric, i.e. A = A^T, (2) A is orthogonal, i.e. AA^T = I (mod 2), (3) A has low multiplicative order, i.e. A^m = I, occur often in communication, control and network theory problems. In this paper we construct a number of such matrices. The results are based on the theory of power-residues modulo an odd prime p, and the fact that the algebra of all p × p circulant matrices is isomorphic to the algebra of polynomials modulo (x^p?1).     

Advancing innovation in the public sector: Aligning innovation measurement with policy goals

There is sufficient evidence, drawn from surveys of innovation in the public sector and cognitive testing interviews with public sector managers, to develop a framework for measuring public sector innovation. Although many questions that are covered in the Oslo Manual guidelines for measuring innovation in the private sector can be applied with some modifications to the public sector, public sector innovation surveys need to meet policy needs that require collecting additional types of data. Policy to support public sector innovation requires data on how public sector organizations innovate and how a strategic management approach to innovation can influence the types of innovations that are developed. Both issues require innovations surveys to delve deeply into the innovation processes and strategies that are used by public sector managers. Implementation of the measurement framework proposed in this paper would open up opportunities for a new, policy-relevant research program on public sector innovation.     

Interpolative coding of integer sequences supporting log-time random access

Sequences of integers are common data types, occurring either as primary data or ancillary structures. The sizes of sequences can be large, making compression an interesting option. Effective compression presupposes variable-length coding, which destroys the regular alignment of values. Yet it would often be desirable to access only a small subset of the entries, either by position (ordinal number) or by content (element value), without having to decode most of the sequence from the start. Here such a random access technique for compressed integers is described, with the special feature that no auxiliary index is needed. The solution applies a method called interpolative coding, which is one of the most efficient non-statistical codes for integers. Indexing is avoided by address calculation guaranteeing sufficient space for codes even in the worst case. The additional redundancy, compared to regular interpolative coding, is only about 1 bit per source integer for uniform distribution. The time complexity of random access is logarithmic with respect to the source size for both position-based and content-based retrieval. According to experiments, random access is faster than full decoding when the number of accessed integers is not more than approximately 0.75 · n/log₂n for sequence length n. The tests also confirm that the method is quite competitive with other approaches to random access coding, suggested in the literature.     

Design of 2-D stable analog and recursive digital filters using properties of the derivative of even or odd Parts of Hurwitz polynomials

In this paper, a method for the design of 2-D analog and recursive digital filters is presented. Starting from a structure in the analog domain, suitable even or odd parts of two-variable Hurwitz polynomials are generated. This enables 2-variable very strictly Hurwitz polynomials (VSHP) to be obtained,² thus avoiding non-essential singularities of the second kind. Thus it will ensure a stable 2-D recursive digital filter obtained by the use of bilinear transformations. Examples are given to illustrate the method.