Playing with parameters: structural parameterization in graphs

When considering a graph problem from a parameterized point of view, the parameter chosen is often the size of an optimal solution of this problem (the "standard" parameter). A natural subject for investigation is what happens when we parameterize such a problem by various other parameters, some of which may be the values of optimal solutions to different problems. Such research is known as parameterized ecology. In this paper, we investigate seven natural vertex problems, along with their respective parameters: the size of a maximum independent set, the size of a minimum vertex cover, the size of a maximum clique, the chromatic number, the size of a minimum dominating set, the size of a minimum independent dominating set and the size of a minimum feedback vertex set. We study the parameterized complexity of each of these problems with respect to the standard parameter of the others.Comment: 17 page

Bayesian long-run prediction in time series models

This paper considers Bayesian long-run prediction in time series models. We allow time series to exhibit stationary or non-stationary behavior and show how differences between prior structures which have little effect on posterior inferences can have a large effect in a prediction exercise. In particular, the Jeffreys' prior given in Phillips (1991) is seen to prevent the existence of one-period ahead predictive moments. A Bayesian counterpart is provided to Sampson (1991) who takes parameter uncertainty into account in a classical framework. An empirical example illustrates our results

Bayesian long-run prediction in time series models.

This paper considers Bayesian long-run prediction in time series models. We allow time series to exhibit stationary or non-stationary behavior and show how differences between prior structures which have little effect on posterior inferences can have a large effect in a prediction exercise. In particular, the Jeffreys' prior given in Phillips (1991) is seen to prevent the existence of one-period ahead predictive moments. A Bayesian counterpart is provided to Sampson (1991) who takes parameter uncertainty into account in a classical framework. An empirical example illustrates our results.Forecasting; Predictive moments; Unit root; Parameter uncertainty;

Parametric design and optimization of engine disc

With the development of science and technology, traditional design methods can no longer meet the needs of modern design and production development. Parametric and optimal design has become one of the most popular application technologies in CAD. Parametric and optimal design was studied based on VB.net language for secondary development of AutoCAD and MATLAB language for secondary development of ANSYS Apdl for disc of aero-engine. The structural parameterization technology was used to realize the rapid forming, and genetic algorithm retains elite was used to optimal design. The optimal design was carried out by using the developed software in this paper, and the optimal results shown that the disc weight was reduced by 34.48 %, the reduction effect of weight was obvious

Parameterized (in)approximability of subset problems

We discuss approximability and inapproximability in FPT-time for a large class of subset problems where a feasible solution $S$ is a subset of the input data and the value of $S$ is $|S|$. The class handled encompasses many well-known graph, set, or satisfiability problems such as Dominating Set, Vertex Cover, Set Cover, Independent Set, Feedback Vertex Set, etc. In a first time, we introduce the notion of intersective approximability that generalizes the one of safe approximability and show strong parameterized inapproximability results for many of the subset problems handled. Then, we study approximability of these problems with respect to the dual parameter $n-k$ where $n$ is the size of the instance and $k$ the standard parameter. More precisely, we show that under such a parameterization, many of these problems, while W[$\cdot$]-hard, admit parameterized approximation schemata.Comment: 7 page

Statistical Methodology for Optimal Sensor Locations for Damage Detection in Structures

A Bayesian statistical methodology is presented for optimally locating the sensors in a structure for the purpose of extracting the most information about the model parameters which can be used in model updating and in damage detection and localization. This statistical approach properly handles the unavoidable uncertainties in the measured data as well as the uncertainties in the mathematical model used to represent the structural behavior. The optimality criterion for the sensor locations is based on information entropy which is a measure of the uncertainty in the model parameters. The uncertainty in these parameters is computed by the Bayesian statistical methodology and then the entropy measure is minimized over the set of possible sensor configurations using a genetic algorithm. Results presented illustrate how both the minimum entropy of the parameters and the optimal sensor configuration depend on the location of sensors, number of sensors, number and type of contributing modes and the structural parameterization (substructuring) scheme used

Continuous Structural Parameterization: A Proposed Method for Representing Different Model Parameterizations Within One Structure Demonstrated for Atmospheric Convection

Continuous structural parameterization (CSP) is a proposed method for approximating different numerical model parameterizations of the same process as functions of the same grid‐scale variables. This allows systematic comparison of parameterizations with each other and observations or resolved simulations of the same process. Using the example of two convection schemes running in the Met Office Unified Model (UM), we show that a CSP is able to capture concisely the broad behavior of the two schemes, and differences between the parameterizations and resolved convection simulated by a high resolution simulation. When the original convection schemes are replaced with their CSP emulators within the UM, basic features of the original model climate and some features of climate change are reproduced, demonstrating that CSP can capture much of the important behavior of the schemes. Our results open the possibility that future work will estimate uncertainty in model projections of climate change from estimates of uncertainty in simulation of the relevant physical processes. Plain Language Summary Numerical models are used to provide estimates of future weather and climate change. The models contain “parameterizations,” which are algorithms that simulate the effect of processes too small or poorly understood to represent using physical equations. Although they are based as much as possible on physics, parameterizations are a large source of modeling uncertainty because there can be large disagreements on how to best represent a given process. The method and even the variables used by two different parameterizations may differ. It is therefore very difficult to know how different parameterizations cause numerical models to produce different results and whether the parameterizations we have are adequate and span the range of uncertainty concerning our knowledge of the processes they represent. Using the example of small‐scale atmospheric convection linked to rain and thunderstorms, this paper describes a mathematical method for expressing different parameterizations within the same framework. This allows easy but formal mathematical comparison of different parameterizations and gives future work the potential to understand whether our parameterizations perform as they should in conjunction with future observations

Do Job, Age, and Place of Residence Matter for Gaming Activity? A Study of the Mid-Colorado River Communities

A household survey in the mid-Colorado River communities of Laughlin, Nevada and Bullhead City, Arizona examined local residents\u27 gaming activities. A censored regression analysis distinguished between factors affecting gaming participation versus expenditures. Results suggest that gaming behavior can often be predicted with knowledge of individuals\u27 residence, workplace, and other household demographic characteristics. Both local government agencies and casino managers can use the results to make better-informed decisions