On the Convex Feasibility Problem

The convergence of the projection algorithm for solving the convex feasibility problem for a family of closed convex sets, is in connection with the regularity properties of the family. In the paper [18] are pointed out four cases of such a family depending of the two characteristics: the emptiness and boudedness of the intersection of the family. The case four (the interior of the intersection is empty and the intersection itself is bounded) is unsolved. In this paper we give a (partial) answer for the case four: in the case of two closed convex sets in R3 the regularity property holds.Comment: 14 pages, exposed on 5th International Conference "Actualities and Perspectives on Hardware and Software" - APHS2009, Timisoara, Romani

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

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

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

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

Tracing frequent users of regional care services using emergency medical services data:a networked approach

Objectives: This study shows how a networked approach relying on ‘real-world’ emergency medical services (EMS) records might contribute to tracing frequent users of care services on a regional scale. Their tracing is considered of importance for policy-makers and clinicians, since they represent a considerable workload and use of scarce resources. While existing approaches for data collection on frequent users tend to limit scope to individual or associated care providers, the proposed approach exploits the role of EMS as the network’s ‘ferryman’ overseeing and recording patient calls made to an entire network of care providers. Design: A retrospective study was performed analysing 2012–2017 EMS calls in the province of Drenthe, the Netherlands. Using EMS data, benefits of the networked approach versus existing approaches are assessed by quantifying the number of frequent users and their associated calls for various categories of care providers. Main categories considered are hospitals, nursing homes and EMS. Setting: EMS in the province of Drenthe, the Netherlands, serving a population of 491 867. Participants: Analyses are based on secondary patient data from EMS records, entailing 212 967 transports and 126 758 patients, over 6 years (2012–2017). Results: Use of the networked approach for analysing calls made to hospitals in Drenthe resulted in a 20% average increase of frequent users traced. Extending the analysis by including hospitals outside Drenthe increased ascertainment by 28%. Extending to all categories of care providers, inside Drenthe, and subsequently, irrespective of their location, resulted in an average increase of 132% and 152% of frequent users identified, respectively. Conclusions: Many frequent users of care services are network users relying on multiple regional care providers, possibly representing inefficient use of scarce resources. Network users are effectively and efficiently traced by using EMS records offering high coverage of calls made to regional care provider