An Augmented Lagrangian Method for <Emphasis Type=Italic>TV</Emphasis><Subscript><Emphasis Type=Italic>g</Emphasis></Subscript>+<Emphasis Type=Italic>L</Emphasis><Superscript>1</Superscript>-norm Minimization

In this paper, the minimization of a weighted total variation regularization term (denoted TV _g ) with L ¹ norm as the data fidelity term is addressed using the Uzawa block relaxation method. The unconstrained minimization problem is transformed into a saddle-point problem by introducing a suitable auxiliary unknown. Applying a Uzawa block relaxation method to the corresponding augmented Lagrangian functional, we obtain a new numerical algorithm in which the main unknown is computed using Chambolle projection algorithm. The auxiliary unknown is computed explicitly. Numerical experiments show the availability of our algorithm for salt and pepper noise removal or shape retrieval and also its robustness against the choice of the penalty parameter. This last property is useful to attain the convergence in a reduced number of iterations leading to efficient numerical schemes. The specific role of the function g in TV _g is also investigated and we highlight the fact that an appropriate choice leads to a significant improvement of the denoising results. Using this property, we propose a whole algorithm for salt and pepper noise removal (denoted UBR-EDGE) that is able to handle high noise levels at a low computational cost. Shape retrieval and geometric filtering are also investigated by taking into account the geometric properties of the model.     

Some light-traffic and heavy-traffic results for the <Emphasis Type=Italic>GI</Emphasis>/<Emphasis Type=Italic>G</Emphasis>/<Emphasis Type=Italic>n</Emphasis>/0 queue using the <Emphasis Type=Italic>GM Heuristic</Emphasis>

In this paper we carry out both light-traffic and heavy-traffic analyses for the calculation of steady-state loss probabilities in the general multi-server queuing loss system, the GI/G/n/0 queue. The analysis makes use of a heuristic approach called the GM Heuristic, for which a detailed analysis in normal traffic has previously been published. Sufficient conditions are given for the GM Heuristic to be asymptotically exact in light traffic. The heuristic is also shown to be asymptotically exact in heavy-traffic when the number of servers n tends to infinity. These results are illustrated numerically using two-phase Coxian distributions for both the inter-arrival time and service time.     

Solution of the problem of <Emphasis Type=Italic>L</Emphasis>-optimal experiment design with a skeleton algorithm

For the solution of the problem of L-optimal design of an experiment use is made of a skeleton algorithm [1]. This algorithm is modified for the solution of a multiparameter problem of linear programming, to which the initial problem reduces. The algorithm ensures the lack of almost degenerate iterations and does not require operations of the matrix inversion.     

Stochastic <Emphasis Type=Italic>Ceteris Paribus</Emphasis> Simulations

Common random numbers (CRN) is a general variance reducing technique for comparing stochastic models via simulations. By inducing positive correlation between different simulations, CRN are likely to reduce the experimental or sampling variance of the difference between the simulations. However, in this paper my motivation for and interpretations of CRN go beyond the statistical design of a simulation experiment, and into the core of economic and econometric reasoning. In a counterfactual-, scenario- or policy analysis based on stochastic simulation, CRN implement the qualifier in partial analysis known as the ceteris paribus clause. In addition, CRN are consistent with the requirement of super exogeneity for valid policy analysis.      

Packing <Emphasis Type=Italic>n</Emphasis>-dimensional parallelepipeds with the feasibility of changing their orthogonal orientation in an <Emphasis Type=Italic>n</Emphasis>-dimensional parallelepiped

A mathematical model is constructed and a method is developed for the solution of the packing problem for n-dimensional parallelepipeds with the feasibility of changing their orthogonal orientation in an n-dimensional parallelepiped. To search for an approximation to the global minimum, a combination of the sequentially-single placement method and a modification of the decremental neighborhood method is used. The offered approach contributes to the improvement of the results of packing oriented n-dimensional parallelepipeds.     

Testing for refinement in <Emphasis FontCategory=SansSerif Type=Italic>Circus</Emphasis>

Circus combines constructs to define complex data operations and interactions; it integrates Z and CSP, and, distinctively, it is a language for refinement that can describe programs as well as specification and design models. The semantics is based on the unifying theories of programming (UTP). Most importantly, Circus is representative of a class of refinement-oriented languages that combines facilities to specify abstract data types in a model-based style and patterns of interaction. What we present here is the Circus testing theory; this work is relevant as a foundation for sound test-generation techniques for a plethora of state-rich reactive languages. To cater for data operations, we define symbolic tests and exhaustive test sets. They are the basis for test-generation techniques that can combine coverage criteria for data and transition models. The notion of correctness is Circus refinement, a UTP-based generalisation of failures-divergences refinement that considers data modelling. Proof of exhaustivity exploits the correspondence between the operational and denotational semantics.     

The Approximation and Computation of a Basis of the Trace Space <Emphasis Type="Italic">H</Emphasis><Superscript>1/2</Superscript>

We present a method for construction of an approximate basis of the trace space H ^1/2 based on a combination of the Steklov spectral method and a finite element approximation. Specifically, we approximate the Steklov eigenfunctions with respect to a particular finite element basis. Then solutions of elliptic boundary value problems with Dirichlet boundary conditions can be efficiently and accurately expanded in the discrete Steklov basis. We provide a reformulation of the discrete Steklov eigenproblem as a generalized eigenproblem that we solve by the implicitly restarted Arnoldi method of ARPACK. We include examples highlighting the computational properties of the proposed method for the solution of elliptic problems on bounded domains using both a conforming bilinear finite element and a non-conforming harmonic finite element. In addition, we document the efficiency of the proposed method by solving a Dirichlet problem for the Laplace equation on a densely perforated domain.     

Programmable reconfiguration of <Emphasis Type=Italic>Physarum</Emphasis> machines

Plasmodium of Physarum polycephalum is a large cell capable of solving graph-theoretic, optimization and computational geometry problems due to its unique foraging behavior. Also the plasmodium is a unique biological substrate that mimics universal storage modification machines, namely the Kolmogorov–Uspensky machine. In the plasmodium implementation of the storage modification machine data are represented by sources of nutrients and memory structure by protoplasmic tubes connecting the sources. In laboratory experiments and simulation we demonstrate how the plasmodium-based storage modification machine can be programmed. We show execution of the following operations with the active zone (where computation occurs): merge two active zones, multiply active zone, translate active zone from one data site to another, direct active zone. Results of the paper bear two-fold value: they provide a basis for programming unconventional devices based on biological substrates and also shed light on behavioral patterns of the plasmodium.     

On the eigenvectors of <Emphasis Type=Italic>p</Emphasis>-Laplacian

Spectral analysis approaches have been actively studied in machine learning and data mining areas, due to their generality, efficiency, and rich theoretical foundations. As a natural non-linear generalization of Graph Laplacian, p-Laplacian has recently been proposed, which interpolates between a relaxation of normalized cut and the Cheeger cut. However, the relaxation can only be applied to two-class cases. In this paper, we propose full eigenvector analysis of p-Laplacian and obtain a natural global embedding for multi-class clustering problems, instead of using greedy search strategy implemented by previous researchers. An efficient gradient descend optimization approach is introduced to obtain the p-Laplacian embedding space, which is guaranteed to converge to feasible local solutions. Empirical results suggest that the greedy search method often fails in many real-world applications with non-trivial data structures, but our approach consistently gets robust clustering results. Visualizations of experimental results also indicate our embedding space preserves the local smooth manifold structures existing in real-world data.     

A Simple Fractionally Integrated Model with a Time-varying Long Memory Parameter <Emphasis Type=Italic>d</Emphasis><Subscript><Emphasis Type=Italic>t</Emphasis></Subscript>

This paper generalizes the standard long memory modeling by assuming that the long memory parameter d is stochastic and time-varying: we introduce a STAR process on this parameter characterized by a logistic function. We propose an estimation method of this model. Some simulation experiments are conducted. The empirical results suggest that this new model offers an interesting alternative competing framework to describe the persistent dynamics in modeling some financial series.      

Combinations of <Emphasis Type=Italic>Stit</Emphasis> and Actions

We present a simple theory of actions against the background of branching time, based on which we propose two versions of an extended stit theory, one equipped with particular actions and the other with sets of such actions. After reporting some basic results of a formal development of such a theory, we briefly explore its connection to a version of branching ETL.     

<Emphasis Type="Italic">H</Emphasis><Superscript>1</Superscript>-interpolation on quadrilateral and hexahedral meshes with hanging nodes

We propose a Scott-Zhang type finite element interpolation operator of first order for the approximation of H ¹-functions by means of continuous piecewise mapped bilinear or trilinear polynomials. The novelty of the proposed interpolation operator is that it is defined for general non-affine equivalent quadrilateral and hexahedral elements and so-called 1-irregular meshes with hanging nodes. We prove optimal local approximation properties of this interpolation operator for functions in H ¹. As necessary ingredients we provide a definition of a hanging node and a rigorous analysis of the issue of constrained approximation which cover both the two- and three-dimensional case in a unified fashion.      

Roughly <Emphasis Type=Italic>B</Emphasis>-invex programming problems

In this paper, a new class of functions, called roughly B-invex functions, and generalized roughly B-invex functions are defined. We discuss some their properties and obtain sufficient optimality criteria for nonlinear programming problems involving these functions.     

<Emphasis Type=Italic>H</Emphasis><Subscript>2</Subscript>-optimization of time-delayed sampled-data systems on the basis of the parametric transfer matrix method

A solution to the H ₂-optimization problem for multi-input-multi-output sampled-data system with delay is presented on the basis of the parametric transfer matrix concept. A procedure is developed for design of the optimal controller by means of factorization and separation of real rational matrices. Some qualitative properties of the H ₂-optimal system are established, which are useful for applications. In particular, it is proved that there is a set of fixing poles of continuous-time elements of the system, and performance of the optimal system is limited because of them. A constructive algorithm is given for determination of the set of fixing poles.     

On the Long-Time <Emphasis Type="Italic">H</Emphasis><Superscript>2</Superscript>-Stability of the Implicit Euler Scheme for the 2D Magnetohydrodynamics Equations

Pursuing our work in Tone (Asymptot. Analysis 51:231–245, 2007) and Tone and Wirosoetisno (SIAM J. Number. Analysis 44:29–40, 2006), we consider in this article the two-dimensional magnetohydrodynamics equations, we discretize these equations in time using the implicit Euler scheme and with the aid of the classical and uniform discrete Gronwall lemma, we prove that the scheme is H ²-uniformly stable in time.     

Synthesis of <Emphasis Type=Italic>n</Emphasis>-operand modulo-three adders

A method of synthesis of modulo-three adders for the case of data representation in positional codes is presented. The method is oriented to the construction of two-level circuits consisting of OR elements and exclusive OR elements with given thresholds. The method is generalized to the realization of the operation ±X ₁ ±X ₂ ... ±X _n = S (mod 3). A logical circuit of an adder with a controlled input is suggested such that the value of one of the digits of the result of the summation is realized on its single output.