Identification of a Wiener–Hammerstein system using the polynomial nonlinear state space approach

In this paper, the Polynomial NonLinear State Space (PNLSS) approach is applied to model a nonlinear system with a Wiener–Hammerstein structure. To obtain good initial estimates, the best linear approximation of the system under test is first identified. Next, this linear model is extended to a polynomial nonlinear state space model to capture also the system's nonlinear behavior. The identification procedure is applied to measurement data.     

Entanglement and Berry phase in a 9 × 9 Yang–Baxter system

A M-matrix which satisfies the Hecke algebraic relations is presented. Via the Yang–Baxterization approach, we obtain a unitary solution \breveR(q,j₁,j₂){\breve{R}(\theta,\varphi_{1},\varphi_{2})} of Yang–Baxter equation. It is shown that any pure two-qutrit entangled states can be generated via the universal \breveR{\breve{R}}-matrix assisted by local unitary transformations. A Hamiltonian is constructed from the \breveR{\breve{R}}-matrix, and Berry phase of the Yang–Baxter system is investigated. Specifically, for j₁ = j₂{\varphi_{1}\,{=}\,\varphi_{2}}, the Hamiltonian can be represented based on three sets of SU(2) operators, and three oscillator Hamiltonians can be obtained. Under this framework, the Berry phase can be interpreted.     

Entanglement of the quantum system with spin–spin coupling created by optical excitation

In this paper, we investigate the quantum entanglement characteristics of the system consisting an intermediary molecule with an optically excited triplet and two bilateral spin-1/2 nucleons. The two nuclear spins both couple to the excitation state which is caused by a pulsed laser. We study the linear entropy and entangling power of the evolution operator acting on the product state of the system. We deduce the entangling power when the energy state has a uniform distribution, and we find that the entanglement of the system shows a certain stability. In this paper, several standard expressions are analyzed and calculated in detail, including the detailed solution for the quantum entropy as well as the calculation of the linear entropy and entangling power, which are based on this solution. In comparing the linear entropy and entangling power, we find that the latter is the average of the former. Subsequently, we present an alternative derivation of the evolution operator and find that the result is consistent with that of the traditional method. When the evolution operator acts on the average of the product states, the entangling power of the evolution operator presents a distinct changing trend.     

Testing the link when the index is semiparametric—a comparative study

Generalized structured models are popular in applied statistics. They can circumvent the curse of dimensionality and provide results that are easy to interpret. However, there are two major concerns that need to be addressed before they are applied. Firstly, the credibility of the specified structure, such as additivity, and secondly, the specification of the link function need to be assessed. The focus is on the latter issue. In many cases it is feasible to estimate a nonparametric link, but the effort is often not justified. In contrast parametric links enable the use of likelihood-based estimates, which are asymptotically efficient, and which perform excellently in practice, particularly for small samples. Several statistics for testing the credibility of parametric link specifications are introduced. Estimation and implementation are discussed, and the performance of the statistics is compared in an intensive simulation study. Applications to real data are also described.     

Adaptive music retrieval–a state of the art

With the development of more and more sophisticated Music Information Retrieval approaches, aspects of adaptivity are becoming an increasingly important research topic. Even though, adaptive techniques have already found their way into Music Information Retrieval systems and contribute to robustness or user satisfaction they are not always identified as such. This paper attempts a structured view on the last decade of Music Information Retrieval research from the perspective of adaptivity in order to increase awareness and promote the application and further development of adaptive techniques. To this end, different approaches from a wide range of application areas that share the common aspect of adaptivity are identified and systematically categorized.     

Computing the regularization of a linear differential–algebraic system

We study the regularization problem for linear differential–algebraic systems. As an improvement of former results we show that any system can be regularized by a combination of state-space and input-space transformations, behavioral equivalence transformations and a reorganization of variables. The additional state feedback which is needed in earlier publications is shown to be superfluous. We provide an algorithmic procedure for the construction of the regularization and discuss computational aspects.     

A continuous-time reduced-order filter for estimating the state vector of a linear stochastic system†

A design procedure for a, reduced-order filter is suggested and the differential equation obeyed by the estimate error covariance matrix is obtained. The problem of optimizing the filter within the design framework is partially solved.     

A desired state can not be found with certainty for Grover��s algorithm in a possible three-dimensional complex subspace

Using an accurate method, we prove that no matter what the initial superposition may be, neither a superposition of desired states nor a unique desired state can be found with certainty in a possible three-dimensional complex subspace, provided that the deflection angle Φ is not exactly equal to zero. By this method, we derive such a result that, if N is sufficiently large (where N denotes the total number of the desired and undesired states in an unsorted database), then corresponding to the case of identical rotation angles, the maximum success probability of finding a unique desired state is approximately equal to cos² Φ for any given F ? [0,p/2){\Phi\in\left[0,\pi/2\right)}.     

Trade credit financing in the vendor–buyer inventory system with ordering cost reduction,transportation cost and backorder price discount when the received quantity is uncertain

Previous ordering cost reduction vendor–buyer inventory models with backorder price discount usually assumed that the buyer must pay to the vendor for the ordered items as soon as the items are received, the received quantity is same as the ordered quantity and the transportation cost is independent of the shipment lot-size. In practice, however, the vendor is willing to offer the buyer a certain credit period without interest to promote market competition as well as the buyer's quantity received may not match with the ordered quantity due to unavailability of the raw material, worker's strike, human errors in counting, transcribing, etc. Furthermore, the discounts are offered for the transportation cost of large ordered quantities. This paper derives a single-vendor single-buyer supply chain model for the ordering cost reduction inventory system with backorder price discount, taking into consideration the effect of transportation cost discount and the condition of permissible delay in payments include the case where the buyer's received quantity does not necessarily match the quantity requisitioned. We take the transportation cost as a function of the shipment lot-size and it is taken to be in an all-unit-discount cost format. Thus we incorporate transportation cost explicitly into the model and develop optimal solution procedures for solving the proposed inventory problem. Numerical example and sensitivity analyses are given to demonstrate the applications and performance of the proposed methodology.     

Towards a parallel component in a GPU–CUDA environment: a case study with the L-BFGS Harwell routine

Modern graphics processing units (GPUs) have been at the leading edge of increasing parallelism over the last 10 years. This fact has encouraged the use of GPUs in a broader range of applications, where developers are required to lever age this technology with new programming models which ease the task of writing programs to run efficiently on GPUs. In this paper, we discuss the main guidelines to assist the developer when porting sequential scientific code on modern GPUs. These guidelines were carried out by porting the L-BFGS, the (Limited memory-) BFGS algorithm for large scale optimization, available as Harwell routine VA15. The specific interest in the L-BFGS algorithm arises from the fact that this is the computational module with the longest running time of a Oceanographic Data Assimilation application software, on which some of the authors are working.     

When is the discretization of a spatially distributed system good enough for control?

This paper describes a new and straightforward method for controlling spatially distributed plants based on low-order models obtained from spatial discretization techniques. A suitable level of discretization is determined by computing the sequence of ν-gaps between weighted models of successively finer spatial resolution, and bounding this by another sequence with an analytic series. It is proved that such a series forms an upper bound on the ν-gap between a weighted model in the initial sequence and the spatially distributed weighted plant. This enables the synthesis, on low-order models, of robust controllers that are guaranteed to stabilize the actual plant, a feature not shared by most model reduction methods where the gap between the high-order model and plant is often not known, and where the gap between high-order and reduced models may be too expensive to compute. Since the calculation of the current bound is based on weighted models of small state-dimension, the new method avoids the numerical problems inherent in large-scale model reduction based approaches. The ideas presented in this paper are demonstrated on a disturbance rejection problem for a 1D heat equation.     

The Deceptive Safety of RTF Files: A breach in a system’s safety is not the biggest threat posed by RTF files

RTF (Rich Text Format), as presented to many users, is considered to be a so-called universal remedy against obtrusive macro-viruses and any other sort of malicious code. Numerous anti-virus companies categorically recommend not accepting any standard MS Word (DOC) files. It is true that RTF files cannot contain a macro-program (macros) in basic form — in the instance of conversion by standard means from other formats, the macros are automatically deleted — however, this same RTF feature has a flip side to it: users are lulled into a false sense of security, ignoring the basic principles of safety when working with RTF documents.     

Relaxation oscillations in a system with delays modeling the predator–prey problem

A new asymptotic method for investigating complex relaxation oscillations in a system with delay is offered. By applying it, we can reduce the problem of predator–prey system dynamics to that of one-dimensional maps analysis. Some conclusions of a biological nature based on asymptotic analysis are made.     

Shaking the usability tree: why usability is not a dead end,and a constructive way forward

A recent contribution to the ongoing debate concerning the concept of usability and its measures proposed that usability reached a dead end – i.e. a construct unable to provide stable results and to unify scientific knowledge. Extensive commentaries rejected the conclusion that researchers need to look for alternative constructs to measure the quality of interaction. Nevertheless, several practitioners involved in this international debate asked for a constructive way to move forward the usability practice. In fact, two key issues of the usability field were identified in this debate: (i) knowledge fragmentation in the scientific community, and (ii) the unstable relationship among the usability metrics. We recognise both the importance and impact of these key issues, although, in line with others, we may not agree with the conclusion that the usability is a dead end. Under the light of the international debate, this work discusses the strengths and weaknesses of usability construct and its application. Our discussion focuses on identifying alternative explanations to the issues and to suggest mitigation strategies, which may be considered the starting point to move forward the usability field. However, scientific community actions will be needed to implement these mitigation strategies and to harmonise the usability practice.     

Dynamics of quantum correlation for a qubit–qutrit system in the presence of the dephasing environments

We analytically study the dynamic behaviors of quantum correlation measured by three kinds of measures including quantum discord (QD), geometric quantum discord (GQD) and one-norm GQD for a qubit–qutrit system under the influence of dephasing environments with Ohmic-like spectral densities at nonzero temperature. It is shown that the similar evolution behaviors may be obtained for sub-Ohmic and Ohmic reservoirs. By properly choosing the system’s initial states and reservoir temperature, quantum correlation can take on some interesting results, such as the frozen and double sudden transition as well as the “revival” phenomenon, etc. Meanwhile, the remarkable similarities and differences among these correlation measures are also analyzed in detail and some significant results are presented. Our results provide some important information for the application of quantum correlation in hybrid qubit–qutrit systems in quantum information.     

Existence and uniqueness of a transient state for the coupled radiative–conductive heat transfer problem

This paper deals with existence and uniqueness results for a transient nonlinear radiative–conductive system in three-dimensional case. This system describes the heat transfer for a grey, semi-transparent and non-scattering medium with general boundary conditions. We reformulate the full transient state system as a fixed-point problem. The existence and uniqueness proof is based on Banach fixed point theorem.     

On the validity of the arithmetic–geometric mean method to locate the optimal solution in a supply chain system

Cardenas-Barron [Cardenas-Barron, L.E. (2010) ‘A Simple Method to Compute Economic order Quantities: Some Observations’, Applied Mathematical Modelling, 34, 1684–1688] indicates that there are several functions in which the arithmetic–geometric mean method (AGM) does not give the minimum. This article presents another situation to reveal that the AGM inequality to locate the optimal solution may be invalid for Teng, Chen, and Goyal [Teng, J.T., Chen, J., and Goyal S.K. (2009), ‘A Comprehensive Note on: An Inventory Model under Two Levels of Trade Credit and Limited Storage Space Derived without Derivatives’, Applied Mathematical Modelling, 33, 4388–4396], Teng and Goyal [Teng, J.T., and Goyal S.K. (2009), ‘Comment on ‘Optimal Inventory Replenishment Policy for the EPQ Model under Trade Credit Derived without Derivatives’, International Journal of Systems Science, 40, 1095–1098] and Hsieh, Chang, Weng, and Dye [Hsieh, T.P., Chang, H.J., Weng, M.W., and Dye, C.Y. (2008), ‘A Simple Approach to an Integrated Single-vendor Single-buyer Inventory System with Shortage’, Production Planning and Control, 19, 601–604]. So, the main purpose of this article is to adopt the calculus approach not only to overcome shortcomings of the arithmetic–geometric mean method of Teng et al. (2009), Teng and Goyal (2009 Teng, JT, Chen, J and Goyal, SK. 2009. A Comprehensive Note on: An Inventory Model under Two Levels of Trade Credit and Limited Storage Space Derived without Derivatives. Applied Mathematical Modelling, 33: 4388–4396. [Crossref], [Web of Science ®] , [Google Scholar]) and Hsieh et al. (2008), but also to develop the complete solution procedures for them.     

Why ‘GSA: a gravitational search algorithm’ is not genuinely based on the law of gravity

This letter highlights a fundamental inconsistency in the formulation of the Gravitational search algorithm (GSA) (Rashedi et al., Inf Sci 2232?C48, 2009). GSA is said to be based on the law of gravity, that is, candidate solutions attract each other in the search space based on their relative distances and ??masses?? (qualities). We show that, contrary to what is claimed, GSA does not take the distances between solutions into account, and therefore cannot be considered to be based on the law of gravity.     

Analysis and solution of a predator–protector–prey multi-robot system by a high-level reinforcement learning architecture and the adaptive systems theory

The area of competitive robotic systems usually leads to highly complicated strategies that must be achieved by complex learning architectures since analytic solutions are unpractical or completely unfeasible. In this work we design an experiment in order to study and validate a model about the complex phenomena of adaptation. In particular, we study a reinforcement learning problem that comprises a complex predator–protector–prey system composed by three different robots: a pure bio-mimetic reactive (in Brook’s sense, i.e. without reasoning and representation) predator-like robot, a protector-like robot with reinforcement learning capabilities and a pure bio-mimetic reactive prey-like robot. From the high-level point of view, we are interested in studying whether the Law of Adaptation is useful enough to model and explain the whole learning process occurring in this multi-robot system. From a low-level point of view, our interest is in the design of a learning system capable of solving such a complex competitive predator–protector–prey system optimally. We show how this learning problem can be addressed and solved effectively by means of a reinforcement learning setup that uses abstract actions to select a goal or target towards which a pure bio-mimetic reactive robot must navigate. The experimental results clearly show how the Law of Adaptation fits this complex learning system and that the proposed Reinforcement Learning setup is able to find an optimal policy to control the defender robot in its role of protecting the prey against the predator robot.