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Fiaschi A.,CNR Institute for Applied Mathematics and Information Technologies
Networks and Heterogeneous Media | Year: 2010

A quasistatic evolution problem for a phase transition model with nonconvex energy density is considered in terms of Young measures. We focus on the particular case of a finite number of phases. The new feature consists in the usage of suitable regularity arguments in order to prove an existence result for a notion of evolution presenting some improvements with respect to the one defined in [13], for infinitely many phases. © American Institute of Mathematical Sciences.

Patane G.,CNR Institute for Applied Mathematics and Information Technologies
Fuzzy Sets and Systems | Year: 2011

Investigating the relations between the least-squares approximation techniques and the Fuzzy Transform, in this paper we show that the Discrete Fuzzy Transform is invariant with respect to the interpolating and least-squares approximation. Additionally, the Fuzzy Transform is evaluated at any point by simply resampling the continuous approximation underlying the input data. Using numerical linear algebra, we also derive new properties (e.g., stability to noise, additivity with respect to the input data) and characterizations (e.g., radial and dual membership maps) of the Discrete Fuzzy Transform. Finally, we define the geometry- and confidence-driven Discrete Fuzzy Transforms, which take into account the intrinsic geometry and the confidence weights associated to the data. © 2010 Elsevier B.V. All rights reserved.

Lanzarone E.,CNR Institute for Applied Mathematics and Information Technologies | Matta A.,Polytechnic of Milan
Operations Research for Health Care | Year: 2014

Home Care (HC) providers are complex organizations that manage a large number of patients, different categories of operators, support staff and material resources in a context affected by high variability. Hence, robust resource planning is crucial for operations in HC organizations, in order to avoid process inefficiencies, treatment delays, and low quality of service. Under continuity of care, one of the main issues in HC planning is the assignment of a reference nurse to each assisted patient, because this decision has an impact on the workload assigned to the nurse for the entire patient's length of stay. In this paper, we derive an analytical structural policy for solving the nurse-to-patient assignment problem in the HC context under continuity of care. This policy accounts for randomness related to both the demands from patients already assigned to nurses and the demands from new patients who need assignments. The policy is compared to other previously developed approaches, and applied to a relevant real case. © 2014 Elsevier Ltd.

Schillinger D.,University of Texas at Austin | Evans J.A.,University of Texas at Austin | Reali A.,CNR Institute for Applied Mathematics and Information Technologies | Scott M.A.,Brigham Young University | Hughes T.J.R.,University of Texas at Austin
Computer Methods in Applied Mechanics and Engineering | Year: 2013

We compare isogeometric collocation with isogeometric Galerkin and standard C0 finite element methods with respect to the cost of forming the matrix and residual vector, the cost of direct and iterative solvers, the accuracy versus degrees of freedom and the accuracy versus computing time. On this basis, we show that isogeometric collocation has the potential to increase the computational efficiency of isogeometric analysis and to outperform both isogeometric Galerkin and standard C0 finite element methods, when a specified level of accuracy is to be achieved with minimum computational cost. We then explore an adaptive isogeometric collocation method that is based on local hierarchical refinement of NURBS basis functions and collocation points derived from the corresponding multi-level Greville abscissae. We introduce the concept of weighted collocation that can be consistently developed from the weighted residual form and the two-scale relation of B-splines. Using weighted collocation in the transition regions between hierarchical levels, we are able to reliably handle coincident collocation points that naturally occur for multi-level Greville abscissae. The resulting method combines the favorable properties of isogeometric collocation and hierarchical refinement in terms of computational efficiency, local adaptivity, robustness and straightforward implementation, which we illustrate by numerical examples in one, two and three dimensions. © 2013 Elsevier B.V.

Lanzarone E.,CNR Institute for Applied Mathematics and Information Technologies | Matta A.,Polytechnic of Milan | Sahin E.,Ecole Centrale Paris
IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans | Year: 2012

In recent years, home care (HC) service systems have been developed as alternatives to conventional hospitalization. Many resources are involved in delivering HC service, including different categories of human resources, support staff, and material resources. One of the main issues encountered while planning human HC resources is the patient assignment problem, i.e., deciding which operator(s) will take care of which admitted patient given some sets of constraints (e.g., the continuity of care). This paper addresses the resource assignment problem for HC systems. A set of mathematical programming models to balance the workloads of the operators within specific categories are proposed. The models consider several peculiarities of HC services, such as the continuity of care constraint, operators' skills, and the geographical areas which patients and operators belong to. Given the high variability of patient demands, models are developed under the assumption that patients' demands are either deterministic or stochastic. The analysis of the results obtained from a real case study demonstrates the applicability of the proposed models as well as the benefits that stem from applying them. Moreover, the obtained results show that an acceptable level of continuity of care cannot be obtained without modeling the continuity of care as a hard constraint. The analysis under continuity of care also shows the high value of information and the difficulties of fully balancing workloads with the application of standard techniques. © 2012 IEEE.

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