Sharp estimation of local convergence radius for the Picard iteration

We investigate the local convergence radius of a general Picard iteration in the frame of a real Hilbert space. We propose a new algorithm to estimate the local convergence radius. Numerical experiments show that the proposed procedure gives sharp estimation (i.e., close to or even identical with the best one) for several well known or recent iterative methods and for various nonlinear mappings. Particularly, we applied the proposed algorithm for classical Newton method, for multi-step Newton method (in particular for third-order Potra-Ptak method) and for fifth-order "M5" method. We present also a new formula to estimate the local convergence radius for multi-step Newton method

Local convergence of generalized Mann iteration

The local convergence of generalized Mann iteration is investigated in the setting of a real Hilbert space. As application, we obtain an algorithm for estimating the local radius of convergence for some known iterative methods. Numerical experiments are presented showing the performances of the proposed algorithm. For a particular case of the Ezquerro-Hernandez method (Ezquerro and Hernandez, J. Complex., 25:343-361: 2009), the proposed procedure gives radii which are very close to or even identical with the best possible ones

Tailoring the Engineering Design Process Through Data and Process Mining

Engineering changes (ECs) are new product development activities addressing external or internal challenges, such as market demand, governmental regulations, and competitive reasons. The corresponding EC processes, although perceived as standard, can be very complex and inefficient. There seem to be significant differences between what is the “officially” documented and the executed process. To better understand this complexity, we propose a data-driven approach, based on advanced text analytics and process and data mining techniques. Our approach sets the first steps toward an automatic analysis, extracting detailed events from an unstructured event log, which is necessary for an in-depth understanding of the EC process. The results show that the predictive accuracy associated with certain EC types is high, which assures the method applicability. The contribution of this article is threefold: 1) a detailed model representation of the actual EC process is developed, revealing problematic process steps (such as bottleneck departments); 2) homogeneous, complexity-based EC types are determined (ranging from “standard” to “complex” processes); and 3) process characteristics serving as predictors for EC types are identified (e.g., the sequence of initial process steps determines a “complex” process). The proposed approach facilitates process and product innovation, and efficient design process management in future projects

Ensemble similarity measures for clustering terms

Clustering semantically related terms is crucial for many applications such as document categorization, and word sense disambiguation. However, automatically identifying semantically similar terms is challenging. We present a novel approach for automatically determining the degree of relatedness between terms to facilitate their subsequent clustering. Using the analogy of ensemble classifiers in Machine Learning, we combine multiple techniques like contextual similarity and semantic relatedness to boost the accuracy of our computations. A new method, based on Yarowsky's [9] word sense disambiguation approach, to generate high-quality topic signatures for contextual similarity computations, is presented. A technique to measure semantic relatedness between multi-word terms, based on the work of Hirst and St. Onge [2] is also proposed. Experimental evaluation reveals that our method outperforms similar related works. We also investigate the effects of assigning different importance levels to the different similarity measures based on the corpus characteristics.</p

Identifying Frequent Health Care Users and Care Consumption Patterns:Process Mining of Emergency Medical Services Data

Background: Tracing frequent users of health care services is highly relevant to policymakers and clinicians, enabling them to avoid wasting scarce resources. Data collection on frequent users from all possible health care providers may be cumbersome due to patient privacy, competition, incompatible information systems, and the efforts involved. Objective: This study explored the use of a single key source, emergency medical services (EMS) records, to trace and reveal frequent users’ health care consumption patterns. Methods: A retrospective study was performed analyzing EMS calls from the province of Drenthe in the Netherlands between 2012 and 2017. Process mining was applied to identify the structure of patient routings (ie, their consecutive visits to hospitals, nursing homes, and EMS). Routings are used to identify and quantify frequent users, recognizing frail elderly users as a focal group. The structure of these routes was analyzed at the patient and group levels, aiming to gain insight into regional coordination issues and workload distributions among health care providers. Results: Frail elderly users aged 70 years or more represented over 50% of frequent users, making 4 or more calls per year. Over the period of observation, their annual number and the number of calls increased from 395 to 628 and 2607 to 3615, respectively. Structural analysis based on process mining revealed two categories of frail elderly users: low-complexity patients who need dialysis, radiation therapy, or hyperbaric medicine, involving a few health care providers, and high-complexity patients for whom routings appear chaotic. Conclusions: This efficient approach exploits the role of EMS as the unique regional “ferryman,” while the combined use of EMS data and process mining allows for the effective and efficient tracing of frequent users’ utilization of health care services. The approach informs regional policymakers and clinicians by quantifying and detailing frequent user consumption patterns to support subsequent policy adaptations

Process mining beyond workflows

After two decades of research and development, process mining techniques are now recognized as essential analysis tools, as they have their own Gartner Magic Quadrant. The development of process mining techniques is rooted in process-related research fields such as Business Process Management and fueled by increasing data availability. To cope with the complexity of business processes, the focus of process mining techniques needs to go beyond workflow-like processes, that represent the life-cycle of a single case and enable multiple object types and events. This can only be accomplished by capitalizing on essential concepts from production and logistics domains, such as Bills-of-Materials (BOMs), and Customer Order Decoupling Points (CODPs). Pioneer researchers, e.g. Hans Wortmann contributed to the development of Enterprise Resource Planning, enterprise modeling, product models, and lean manufacturing. Experiences from these fields help to lift the process mining domain from case-based (i.e. workflow mining) to object-centered process mining. These contributions could be realized by conducting insightful case studies at company sites, one of them being discussed in this paper. The evaluation of process mining techniques is elaborated by proposing an “evaluation ladder”, and its application is shown in the case study under consideration