Iterant recombination with one-norm minimization for multilevel Markov chain algorithms via the ellipsoid method

Recently, it was shown how the convergence of a class of multigrid methods for computing the stationary distribution of sparse, irreducible Markov chains can be accelerated by the addition of an outer iteration based on iterant recombination. The acceleration was performed by selecting a linear combination of previous fine-level iterates with probability constraints to minimize the two-norm of the residual using a quadratic programming method. In this paper we investigate the alternative of minimizing the one-norm of the residual. This gives rise to a nonlinear convex program which must be solved at each acceleration step. To solve this minimization problem we propose to use a deep-cuts ellipsoid method for nonlinear convex programs. The main purpose of this paper is to investigate whether an iterant recombination approach can be obtained in this way that is competitive in terms of execution time and robustness. We derive formulas for subgradients of the one-norm objective function and the constraint functions, and show how an initial ellipsoid can be constructed that is guaranteed to contain the exact solution and give conditions for its existence. We also investigate using the ellipsoid method to minimize the two-norm. Numerical tests show that the one-norm and two-norm acceleration procedures yield a similar reduction in the number of multigrid cycles. The tests also indicate that one-norm ellipsoid acceleration is competitive with two-norm quadratic programming acceleration in terms of running time with improved robustness.     

Optimization problems in contracted tensor networks

We discuss the calculus of variations in tensor representations with a special focus on tensor networks and apply it to functionals of practical interest. The survey provides all necessary ingredients for applying minimization methods in a general setting. The important cases of target functionals which are linear and quadratic with respect to the tensor product are discussed, and combinations of these functionals are presented in detail. As an example, we consider the representation rank compression in tensor networks. For the numerical treatment, we use the nonlinear block Gauss?CSeidel method. We demonstrate the rate of convergence in numerical tests.     

Automated Flaw Detection in Algebraic Specifications

In interactive theorem proving practice a significant amount of time is spent on unsuccessful proof attempts of wrong conjectures. An automatic method that reveals them by generating finite counter examples would offer an extremely valuable support for a proof engineer by saving his time and effort. In practice, such counter examples tend to be small, so usually there is no need to search for big instances. Most definitions of functions or predicates on infinite structures do not preserve the semantics if a transition to arbitrary finite substructures is made. We propose constraints which guarantee a correct axiomatization on finite structures and present an approach which uses the Alloy Analyzer to generate finite instances of theories in the theorem prover KIV. It is evaluated on the library of basic data types as well as on some challenging case studies in KIV. The technique is implemented using the Kodkod constraint solver which is a successor of Alloy.     

Method development for epoxy resin analysis

Epoxy resin based negative photo resists are showing interesting properties which are useful for a series of applications in electronic industries (Mark et al. in Encyclopedia of polymer science and engineering, Wiley, New York, 1986; Potter in Epoxide resins, Springer, New York, 1970; May and Tanka in Epoxy resin chemistry and technology, Marcel Dekker, New York, 1973; Bauer in Epoxy resin chemistry, vol 114, American Chemical Society, Washington, 1979; Hood in RAPRA Rev Rep 38:4, 1990). Especially in micro system technologies they promise a high potential. To adjust the properties for the particular application modification of the chemical composition and crosslinker system must be performed. An actual problem is the constancy in behaviour during the LIGA-process of the resist mixture. In this work analytical techniques are used to get a detailed insight into the chemical composition of a commercial available epoxy novolac resin. Methods like size exclusion chromatography (SEC), matrix assisted laser desorption-time of flight (MALDI-ToF) and fourier transform infrared spectroscopy (FTIR) offer information about the molecular weight and functionality. The results reveal a distribution in molecular weight and functionality. Due this the resin was chemically modified. After processing a dependency of molecular weight and therefore the amount of epoxy groups existent was obtained.     

Understanding cost drivers of software evolution: a quantitative and qualitative investigation of change effort in two evolving software systems

Making changes to software systems can prove costly and it remains a challenge to understand the factors that affect the costs of software evolution. This study sought to identify such factors by investigating the effort expended by developers to perform 336 change tasks in two different software organizations. We quantitatively analyzed data from version control systems and change trackers to identify factors that correlated with change effort. In-depth interviews with the developers about a subset of the change tasks further refined the analysis. Two central quantitative results found that dispersion of changed code and volatility of the requirements for the change task correlated with change effort. The analysis of the qualitative interviews pointed to two important, underlying cost drivers: Difficulties in comprehending dispersed code and difficulties in anticipating side effects of changes. This study demonstrates a novel method for combining qualitative and quantitative analysis to assess cost drivers of software evolution. Given our findings, we propose improvements to practices and development tools to manage and reduce the costs.     

Protected subspaces in quantum information

In certain situations the state of a quantum system, after transmission through a quantum channel, can be perfectly restored. This can be done by “coding” the state space of the system before transmission into a “protected” part of a larger state space, and by applying a proper “decoding” map afterwards. By a version of the Heisenberg Principle, which we prove, such a protected space must be “dark” in the sense that no information leaks out during the transmission. We explain the role of the Knill–Laflamme condition in relation to protection and darkness, and we analyze several degrees of protection, whether related to error correction, or to state restauration after a measurement. Recent results on higher rank numerical ranges of operators are used to construct examples. In particular, dark spaces are constructed for any map of rank 2, for a biased permutations channel and for certain separable maps acting on multipartite systems. Furthermore, error correction subspaces are provided for a class of tri-unitary noise models.     

Neue Unabhängigkeit für den betrieblichen Datenschutzbeauftragten?

Der betriebliche Datenschutzbeauftragte dient der Selbstkontrolle der verantwortlichen Stelle. Wirksam ist solch eine Selbstkontrolle aber nur dann, wenn der Datenschutzbeauftragte auch Unabh?gigkeit genie?t. Welche Voraussetzungen hierfür erfüllt sein müssen, erl?utert der folgende Beitrag.     

A two-layer architecture for economically optimal process control and operation

A two-layer architecture for dynamic real-time optimization (or nonlinear modelpredictive control (NMPC) with an economic objective) is presented, where the solution of the dynamic optimization problem is computed on two time-scales. On the upper layer, a rigorous optimization problem is solved with an economic objective function at a slow time-scale, which captures slow trends in process uncertainties. On the lower layer, a fast neighboring-extremal controller is tracking the trajectory in order to deal with fast disturbances acting on the process. Compared to a single-layer architecture, the two-layer architecture is able to address control systems with complex models leading to high computational load, since the rigorous optimization problem can be solved at a slower rate than the process sampling time. Furthermore, solving a new rigorous optimization problem is not necessary at each sampling time if the process has rather slow dynamics compared to the disturbance dynamics. The two-layer control strategy is illustrated with a simulated case study of an industrial polymerization process.     

The double-edged effects of explanation prompts

Explanation prompts usually foster conceptual understanding. However, it has been claimed within cognitive load theory that prompts can take cognitive load to the upper limit when learning complex contents. Under such circumstances, prompts focusing the learners’ attention on specific aspects (e.g., conceptual aspects such as elaborations on domain principles) might have some costs: Other important aspects (e.g., procedural aspects such as how to calculate) cannot be processed deeply. Thus, we expected that conceptually-oriented explanation prompts would foster the detailedness of explanations, the number of elaborations on domain principles, and conceptual knowledge. In addition, we tested the influence of such prompts on the number of calculations performed during learning and procedural knowledge. We conducted an experiment in which we employed conceptually-oriented explanation prompts in a complex e-learning module on tax law. Tax law university students (N = 40) worked on this e-learning module under two conditions: (a) conceptually-oriented explanation prompts, (b) no prompts. The prompts led to double-edged effects: positive effects on the detailedness of explanations and on the number of elaborations on domain principles, as well as on conceptual knowledge and simultaneously negative effects on the number of calculations performed during learning as well as on procedural knowledge.