The bivariate Shepard operator of Bernoulli type

Abstract The method of Shepard is an efficient method for interpolation of very large scattered data sets; unfortunately, it has poor reproduction qualities and high computational cost. In this paper we introduce a new operator which diminishes these drawbacks. This operator results from the combination of the Shepard operator with a new interpolation operator, recently proposed by Costabile and Dell’Accio, and generalizes to two variate functions the Shepard-Bernoulli operator introduced in [2]. We study this combined operator and give error bounds in terms of the modulus of continuity of high order and of the mesh length. We improve the accuracy and computational efficiency using a method introduced by Franke and Nielson. Keywords: Shepard operator, Bernoulli operator, interpolation of scattered data, error estimations. Mathematics Subject Classification (2000): 41A05, 41A25, 41A80.     

Knowledge networks across Europe: which distance matters?

In this paper, we address the manifold nature of knowledge through the analysis of four distinct but complementary phenomena (Internet hyperlinks, EPO co-patent applications, Erasmus students mobility and European research networks) which characterise knowledge as an intrinsic relational structure (directly) connecting people, institutions and (indirectly) regions across five European countries. We study the structure (in terms of density, centralisation, clustering, assortativity, centre-periphery and resilience) of these international knowledge flows through network analysis techniques and we test the influence of geographical distance as opposed to sectoral (based on the industrial distribution of innovative activity) and functional (based on the value of the European technological index) distances in shaping the strength of knowledge relations through a gravitational model. Network Analysis techniques applied to the configuration of international knowledge flows between European regions highlight the existence of a polarised hierarchical structure. By estimating a “gravity equation” model we demonstrate that, far from the claim of the “death of distance”, geographic distance is still relevant for determining the structure of inter-regional knowledge flows. Functional and, above all, sectoral distances play also a relevant role suggesting that knowledge flows easier between similar regions (according to their technological level and the industrial distribution of their innovation system).     

Principles and methods for automatic and semi-automatic tissue segmentation in MRI data

The development of magnetic resonance imaging (MRI) revolutionized both the medical and scientific worlds. A large variety of MRI options have generated a huge amount of image data to interpret. The investigation of a specific tissue in 3D or 4D MR images can be facilitated by image processing techniques, such as segmentation and registration. In this work, we provide a brief review of the principles and methods that are commonly applied to achieve superior tissue segmentation results in MRI. The impacts of MR image acquisition on segmentation outcome and the principles of selecting and exploiting segmentation techniques tailored for specific tissue identification tasks are discussed. In the end, two exemplary applications, breast and fibroglandular tissue segmentation in MRI and myocardium segmentation in short-axis cine and real-time MRI, are discussed to explain the typical challenges that can be posed in practical segmentation tasks in MRI data. The corresponding solutions that are adopted to deal with these challenges of the two practical segmentation tasks are thoroughly reviewed.     

Gene Mutation Profiles in Primary Diffuse Large B Cell Lymphoma of Central Nervous System: Next Generation Sequencing Analyses

The existence of a potential primary central nervous system lymphoma-specific genomic signature that differs from the systemic form of diffuse large B cell lymphoma (DLBCL) has been suggested, but is still controversial. We investigated 19 patients with primary DLBCL of central nervous system (DLBCL CNS) using the TruSeq Amplicon Cancer Panel (TSACP) for 48 cancer-related genes. Next generation sequencing (NGS) analyses have revealed that over 80% of potentially protein-changing mutations were located in eight genes (CTNNB1, PIK3CA, PTEN, ATM, KRAS, PTPN11, TP53 and JAK3), pointing to the potential role of these genes in lymphomagenesis. TP53 was the only gene harboring mutations in all 19 patients. In addition, the presence of mutated TP53 and ATM genes correlated with a higher total number of mutations in other analyzed genes. Furthermore, the presence of mutated ATM correlated with poorer event-free survival (EFS) (p = 0.036). The presence of the mutated SMO gene correlated with earlier disease relapse (p = 0.023), inferior event-free survival (p = 0.011) and overall survival (OS) (p = 0.017), while mutations in the PTEN gene were associated with inferior OS (p = 0.048). Our findings suggest that the TP53 and ATM genes could be involved in the molecular pathophysiology of primary DLBCL CNS, whereas mutations in the PTEN and SMO genes could affect survival regardless of the initial treatment approach.     

Machine learning as a service for enabling Internet of Things and People

The future Internet is expected to connect billions of people, things and services having the potential to deliver a new set of applications by deriving new insights from the data generated from these diverse data sources. This highly interconnected global network brings new types of challenges in analysing and making sense of data. This is why machine learning is expected to be a crucial technology in the future, in making sense of data, in improving business and decision making, and in doing so, providing the potential to solve a wide range of problems in health care, telecommunications, urban computing, and others. Machine learning algorithms can learn how to perform certain tasks by generalizing examples from a range of sampling. This is a totally different paradigm than traditional programming language approaches, which are based on writing programs that process data to produce an output. However, choosing a suitable machine learning algorithm for a particular application requires a substantial amount of time and effort that is hard to undertake even with excellent research papers and textbooks. In order to reduce the time and effort, this paper introduces the TCDC (train, compare, decide, and change) approach, which can be thought as a ‘Machine Learning as a Service’ approach, to aid machine learning researchers and practitioners to choose the optimum machine learning model to use for achieving the best trade-off between accuracy and interpretability, computational complexity, and ease of implementation. The paper includes the results of testing and evaluating the recommenders based on the TCDC approach (in comparison with the traditional default approach) applied to 12 datasets that are available as open-source datasets drawn from diverse domains including health care, agriculture, aerodynamics and others. Our results indicate that the proposed approach selects the best model in terms of predictive accuracy in 62.5 % for regression tests performed and 75 % for classification tests.