Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT

In this paper, we develop a shape optimization-based algorithm for the electrical impedance tomography (EIT) problem of determining a piecewise constant conductivity on a polygonal partition from boundary measurements. The key tool is to use a distributed shape derivative of a suitable cost functional with respect to movements of the partition. Numerical simulations showing the robustness and accuracy of the method are presented for simulated test cases in two dimensions

Learning the structure of Bayesian Networks: A quantitative assessment of the effect of different algorithmic schemes

One of the most challenging tasks when adopting Bayesian Networks (BNs) is the one of learning their structure from data. This task is complicated by the huge search space of possible solutions, and by the fact that the problem is NP-hard. Hence, full enumeration of all the possible solutions is not always feasible and approximations are often required. However, to the best of our knowledge, a quantitative analysis of the performance and characteristics of the different heuristics to solve this problem has never been done before. For this reason, in this work, we provide a detailed comparison of many different state-of-the-arts methods for structural learning on simulated data considering both BNs with discrete and continuous variables, and with different rates of noise in the data. In particular, we investigate the performance of different widespread scores and algorithmic approaches proposed for the inference and the statistical pitfalls within them

Correcting Gene Trees by Leaf Insertions: Complexity and Approximation

Abstract Gene tree correction has recently gained interest in phylogenomics, as it gives insights in understanding the evolution of gene families. Following some recent approaches based on leaf edit operations, we consider a variant of the problem where a gene tree is corrected by inserting leaves with labels in a multiset M. We show that the problem of deciding whether a gene tree can be corrected by inserting leaves with labels in M is NP-complete. Then, we consider an optimization variant of the problem that asks for the correction of a gene tree with leaves labeled by a multiset M ′ , with M ′ ⊇ M , having minimum size. For this optimization variant of the problem, we present a factor 2 approximation algorithm

Combining Bayesian Approaches and Evolutionary Techniques for the Inference of Breast Cancer Networks

Gene and protein networks are very important to model complex large-scale systems in molecular biology. Inferring or reverseengineering such networks can be defined as the process of identifying gene/protein interactions from experimental data through computational analysis. However, this task is typically complicated by the enormously large scale of the unknowns in a rather small sample size. Furthermore, when the goal is to study causal relationships within the network, tools capable of overcoming the limitations of correlation networks are required. In this work, we make use of Bayesian Graphical Models to attach this problem and, specifically, we perform a comparative study of different state-of-the-art heuristics, analyzing their performance in inferring the structure of the Bayesian Network from breast cancer data

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Fatigue crack growth in low cycle fatigue: an analysis of crack closure based on image correlation

n this paper, the effects of crack closure on the propagation of short cracks is investigated. An experimental campaign, performed in the low cycle fatigue regime, was performed on specimens with micro-defects, considering two different strain ratios: initially, tests were performed under fully reversed straining, whereas the effect of an applied mean strain were studied by considering a strain ratio equal to 0.5. Crack closure was characterized with an innovative technique based on digital image correlation: crack opening and closing levels were measured starting from the experimental crack tip displacement fields. Finally, experimental results were compared to those computed with the analytical model proposed by Newman

Covering Pairs in Directed Acyclic Graphs†

The Minimum Path Cover (MinPC) problem on directed acyclic graphs (DAGs) is a classical problem in graph theory that provides a clear and simple mathematical formulation for several applications in computational biology. In this paper, we study the computational complexity of three constrained variants of MinPC motivated by the recent introduction of Next-Generation Sequencing technologies. The first variant (MinRPC), given a DAG and a set of pairs of vertices, asks for a minimum-cardinality set of (not necessarily disjoint) paths such that both vertices of each pair belong to the same path. For this problem, we establish a sharp tractability borderline depending on the ‘overlapping degree' of the instance, a natural parameter in some applications of the problem. The second variant we consider (MinPCRP), given a DAG and a set of pairs of vertices, asks for a minimum-cardinality set of (not necessarily disjoint) paths ‘covering' all the vertices of the graph and such that both vertices of each pair belong to the same path. For this problem, we show that, while it is NP-hard to compute if there exists a solution consisting of at most three paths, it is possible to decide in polynomial time whether a solution consisting of at most two paths exists. The third variant (MaxRPSP), given a DAG and a set of pairs of vertices, asks for a single path containing the maximum number of the given pairs of vertices. We show that MaxRPSP is W[1]-hard when parameterized by the number of covered pairs and we give a fixed-parameter algorithm when the parameter is the maximum overlapping degre

A comparison of fatigue strength sensitivity to defects for materials manufactured by AM or traditional processes

The fatigue behavior of metallic materials fabricated via additive manufacturing processes is currently not well understood and it has been the subject of many experimental investigations in recent years. In this paper we carried out a literature review about the fatigue strength of additively manufactured AlSi10Mg and Ti6Al4V, especially in terms of sensitivity to defects and inhomogeneities. The analysis shows that fatigue properties and key variables (heat treatment, defect size) are very similar to the ones of parts obtained with traditional manufacturing processes. These results confirm that defect tolerant design concepts can be adopted also for AM components