The ski-rental problem with multiple discount options

We propose the ski-rental problem with multiple discount options in which there are n options to rent an equipment. Every option has a rental duration; the longer the duration, the more the discount. This generalizes the standard ski-rental problem where one can only rent or buy. We present a 4-competitive on-line algorithm for our problem and show that no deterministic algorithm can have a smaller competitive ratio when n is large enough. Comparing with the original ski-rental problem, the competitive ratio becomes larger when there are more options.     

Universal instability modes in internal and external flows

Two prototypical external and internal flows have been studied which display linear temporal instability followed by nonlinear saturation taking the flows to a new equilibrium state. Direct simulation results are obtained using a specific formulation and numerical methods with very high accuracy. These results are analyzed via proper orthogonal decomposition (POD), which reveal similar modes for flow past a circular cylinder and flow inside a lid-driven cavity, indicating universality of such modes. Unlike many other efforts on reduced order modeling via POD, here the emphasis has been on understanding the physical aspect of the flow instability which requires very high accuracy of the simulation. Then, the obtained POD modes are related to the instability modes (in the classical sense of defining the latter) and new generic types of instability modes are identified in the studied external and internal flows. These new modes have been reported for flow past a circular cylinder [Sengupta TK, Singh N, Suman VK. Dynamical system approach to instability of flow past a circular cylinder. J Fluid Mech 2010;656:82–115] which help one in understanding the instability sequence and the relative importance of these modes in the flow evolution starting from an impulsive start. Present comparative study, furthermore, reveals universality of such instability modes by showing their presence for the flow inside a lid-driven cavity as well. Despite seeming dissimilarities between these two flows, similarities between the instability portrait of these two flows suggest universality of such modes. From the equilibrium amplitude of vorticity time-series, we establish the presence of multiple modes and multiple bifurcation sequences for these flows in parameter space. Existing theory due to Landau and Stuart that considers only a single dominant mode and its self-interaction does not explain all these features. We invoke a multi-modal interaction model in the cited reference above, termed as Landau–Stuart–Eckhaus (LSE) equation in recognition of Eckhaus’ work in modifying the classical Stuart–Landau equation. We also show that the new instability modes do not follow either the classical Stuart–Landau or the newly proposed LSE model equations and for this reason we call these as anomalous modes. Two specific classes of anomalous modes are identified and classified in the present work. Empirical expressions for the evolution of these anomalous modes are presented and their unambiguous role during instabilities is discussed.     

Automatic camera control in virtual environments augmented using multiple sparse videos

Automated virtual camera control has been widely used in animation and interactive virtual environments. We have developed a multiple sparse camera based free view video system prototype that allows users to control the position and orientation of a virtual camera, enabling the observation of a real scene in three dimensions (3D) from any desired viewpoint. Automatic camera control can be activated to follow selected objects by the user. Our method combines a simple geometric model of the scene composed of planes (virtual environment), augmented with visual information from the cameras and pre-computed tracking information of moving targets to generate novel perspective corrected 3D views of the virtual camera and moving objects. To achieve real-time rendering performance, view-dependent textured mapped billboards are used to render the moving objects at their correct locations and foreground masks are used to remove the moving objects from the projected video streams. The current prototype runs on a PC with a common graphics card and can generate virtual 2D views from three cameras of resolution 768×576 with several moving objects at about 11 fps.     

Model reduction of multi-scale chemical Langevin equations

This paper addresses the model reduction problem for a class of stiff chemical Langevin equations that arise as models of biomolecular networks with fast and slow reactions and can be described as continuous Markov processes. Initially, a coordinate transformation is sought that allows the decoupling of fast and slow variables in the model equations. Necessary and sufficient conditions are derived for such a linear transformation to exist, along with an explicit change of variables which achieves the desired decoupling. For the systems for which this step is applicable, the method of adiabatic elimination is applied to determine a representation of the slow dynamics. Theoretical concepts and results are illustrated with simple examples.     

Design of experiments for bivariate binary responses modelled by Copula functions

Optimal design for generalized linear models has primarily focused on univariate data. Often experiments are performed that have multiple dependent responses described by regression type models, and it is of interest and of value to design the experiment for all these responses. This requires a multivariate distribution underlying a pre-chosen model for the data. Here, we consider the design of experiments for bivariate binary data which are dependent. We explore Copula functions which provide a rich and flexible class of structures to derive joint distributions for bivariate binary data. We present methods for deriving optimal experimental designs for dependent bivariate binary data using Copulas, and demonstrate that, by including the dependence between responses in the design process, more efficient parameter estimates are obtained than by the usual practice of simply designing for a single variable only. Further, we investigate the robustness of designs with respect to initial parameter estimates and Copula function, and also show the performance of compound criteria within this bivariate binary setting.     

TimeLapseAnalyzer: multi-target analysis for live-cell imaging and time-lapse microscopy

The direct observation of cells over time using time-lapse microscopy can provide deep insights into many important biological processes. Reliable analyses of motility, proliferation, invasive potential or mortality of cells are essential to many studies involving live cell imaging and can aid in biomarker discovery and diagnostic decisions. Given the vast amount of image- and time-series data produced by modern microscopes, automated analysis is a key feature to capitalize the potential of time-lapse imaging devices. To provide fast and reproducible analyses of multiple aspects of cell behaviour, we developed TimeLapseAnalyzer. Apart from general purpose image enhancements and segmentation procedures, this extensible, self-contained, modular cross-platform package provides dedicated modalities for fast and reliable analysis of multi-target cell tracking, scratch wound healing analysis, cell counting and tube formation analysis in high throughput screening of live-cell experiments. TimeLapseAnalyzer is freely available (MATLAB, Open Source) at http://www.informatik.uni-ulm.de/ni/mitarbeiter/HKestler/tla.     

Comparison of multiple linear regression and artificial neural network in developing the objective functions of the orthopaedic screws

Optimizing the orthopaedic screws can greatly improve their biomechanical performances. However, a methodical design optimization approach requires a long time to search the best design. Thus, the surrogate objective functions of the orthopaedic screws should be accurately developed. To our knowledge, there is no study to evaluate the strengths and limitations of the surrogate methods in developing the objective functions of the orthopaedic screws. Three-dimensional finite element models for both the tibial locking screws and the spinal pedicle screws were constructed and analyzed. Then, the learning data were prepared according to the arrangement of the Taguchi orthogonal array, and the verification data were selected with use of a randomized selection. Finally, the surrogate objective functions were developed by using either the multiple linear regression or the artificial neural network. The applicability and accuracy of those surrogate methods were evaluated and discussed. The multiple linear regression method could successfully construct the objective function of the tibial locking screws, but it failed to develop the objective function of the spinal pedicle screws. The artificial neural network method showed a greater capacity of prediction in developing the objective functions for the tibial locking screws and the spinal pedicle screws than the multiple linear regression method. The artificial neural network method may be a useful option for developing the objective functions of the orthopaedic screws with a greater structural complexity. The surrogate objective functions of the orthopaedic screws could effectively decrease the time and effort required for the design optimization process.     

A SAS(®) macro implementation of a multiple comparison post hoc test for a Kruskal-Wallis analysis

The Kruskal-Wallis (KW) nonparametric analysis of variance is often used instead of a standard one-way ANOVA when data are from a suspected non-normal population. The KW omnibus procedure tests for some differences between groups, but provides no specific post hoc pair wise comparisons. This paper provides a SAS^® macro implementation of a multiple comparison test based on significant Kruskal-Wallis results from the SAS NPAR1WAY procedure. The implementation is designed for up to 20 groups at a user-specified alpha significance level. A Monte-Carlo simulation compared this nonparametric procedure to commonly used parametric multiple comparison tests.     

Multiple piecewise constant with geodesic active contours (MPC-GAC) framework for interactive image segmentation using graph cut optimization

This paper proposes an improved variational model, multiple piecewise constant with geodesic active contour (MPC-GAC) model, which generalizes the region-based active contour model by Chan and Vese, 2001 [11] and merges the edge-based active contour by Caselles et al., 1997 [7] to inherit the advantages of region-based and edge-based image segmentation models. We show that the new MPC-GAC energy functional can be iteratively minimized by graph cut algorithms with high computational efficiency compared with the level set framework. This iterative algorithm alternates between the piecewise constant functional learning and the foreground and background updating so that the energy value gradually decreases to the minimum of the energy functional. The k-means method is used to compute the piecewise constant values of the foreground and background of image. We use a graph cut method to detect and update the foreground and background. Numerical experiments show that the proposed interactive segmentation method based on the MPC-GAC model by graph cut optimization can effectively segment images with inhomogeneous objects and background.