Dipartimento di Informatica, Sistemistica e Comunicazione

This dataset contains images of five 3D models that can be used to evaluate pipelines for 3D reconstruction from images. Each model is placed in a reference scene and is rendered under different lighting and camera conditions. For each of the five models, 8 scenes are created and for each scene 100 images are taken from different points of view.

We present a MATLAB function to compute the subdivision matrices of semi-regular univariate interpolatory RBF-based binary subdivision schemes. The construction is the adaptation of the one presented in "Stationary binary subdivision schemes using radial basis function interpolation", B.-G. Lee, Y. J. Lee, J. Yoon (Adv. Comput. Math, 2006) and "Analysis of stationary subdivision schemes for curve design based on radial basis function interpolation", Y. J. Lee, J. Yoon (Appl. Math. Comput., 2010), to the semi-regular case, i.e. when the starting mesh is formed by two different uniform mesh that meet eachother at 0. The main function, RBFs_semi.m, given the stepsizes of the two uniform mesh, the family of radial basis function, the number of points used for the local computation, the required polynomial reproduction and, eventually, further parameters, determines the subdivision matrix of the scheme in the form of the regular mask on the left, the regular mask on the right and the irregular part of the matrix around 0. The supported families of RBFs are (inverse) multi-quadric, Gaussian, Wendland's functions, Wu's functions, Buhmann's functions, polyharmonic functions and Euclid's hat functions (see e.g. "Meshfree approximation methods with MATLAB", G. E. Fasshauer). For further information about how to choose the parameters for each family see the files in the Aux folder.

We present filters for the irregular framelets of semi-regular Dubuc-Deslauriers 2n-point wavelet tight frames with mesh parameters h_\ell = 1 and h_r > 0 for the cases: n = 2, h_r = 1.5, 2, 2.5, 3 n = 3, h_r = 1.5, 2, 2.25, 2.5 n = 4, h_r = 1.5, 2, 2.15, 2.3 n = 5, h_r = 1.5, 2, 2.1, 2.2 These filters have been computed using the method described in "Semi-regular Dubuc-Deslaurier wavelet tight frames" submitted to Journal of Computational and Applied Mathematics Special Issue for SMART 2017. The filters are the columns of the matrix Q_irr where R_irr = Q_irr * transpose(Q_irr). To avoid numerical fluctuations Q_irr is computed via singular value decomposition, with threshold on the singular values set to 10^-8. The filters depend only on the ratio h_\ell over h_r and, when this ratio is inverted, it is sufficient to flip the filters. Therefore there is no loss of generality in considering h_\ell = 1 and h_r greater than or equal to 1 only. Moreover, for any fixed natural number n and h_\ell = 1, there is an interval of availability for h_r of the form ( 1/c, c ), where h_r = 1 reduces to the regular case. For n = 2, the exact value of c is 3.5 while for the other values of n the approximated values of c are 2.6225, 2.3591 and 2.2346 respectively for n = 3, 4 and 5. For the examples presented we choose two common values of h_r working for all n=2,...,5 and two values specifically chosen for each n spreaded out between 2 and c.

Abstract Background A large number of algorithms is being developed to reconstruct evolutionary models of individual tumours from genome sequencing data. Most methods can analyze multiple samples collected either through bulk multi-region sequencing experiments or the sequencing of individual cancer cells. However, rarely the same method can support both data types. Results We introduce TRaIT, a computational framework to infer mutational graphs that model the accumulation of multiple types of somatic alterations driving tumour evolution. Compared to other tools, TRaIT supports multi-region and single-cell sequencing data within the same statistical framework, and delivers expressive models that capture many complex evolutionary phenomena. TRaIT improves accuracy, robustness to data-specific errors and computational complexity compared to competing methods. Conclusions We show that the application of TRaIT to single-cell and multi-region cancer datasets can produce accurate and reliable models of single-tumour evolution, quantify the extent of intra-tumour heterogeneity and generate new testable experimental hypotheses.

Given a directed graph with non-negative arc lengths, the Constrained Shortest Path Tour Problem (CSPTP) is aimed at finding a shortest path from a single-origin to a single-destination, such that a sequence of disjoint and possibly different-sized node subsets are crossed in a given fixed order. Moreover, the optimal path must not include repeated arcs. In this paper, for the CSPTP we propose a new mathematical model and a new efficient Branch & Bound method. Extensive computational experiments have been carried out on a significant set of test problems in order to evaluate empirically the performance of the proposed approach.

Additional file 1: Data.Extensive description of all the methods and experiments ran with TRaIT, both on simulated data and on real data. In-depth description of the simulated data generation algorithms and table summaries of ⠟140.00 simulations. (PDF 4507 kb)

Supplementary Information. Supplementary Material, Figures and Tables. (DOCX 1859Â kb)

LASSIE Graphical User Interface. (PDF 397 kb)

In silico dataset and accuracy assessment results. The excel table reports the list of all IS (in rows) and the corresponding output returned by the different tools (divided by colors in the following order: VISPA, VISPA2, MAVRIC, SEQMAP, QUICKMAP). For each read (identified by its “ID” in column “header”), we reported the source genomic coordinates (in columns chromosome “chr”, integration point “locus”, and orientation “strand”), the source of annotation as described in VISPA [22] and the nucleotide sequence. Then we reported the output of IS for each tool: the first set of columns report the returned IS genomic coordinates (columns “header”, “chr”, “locus” and “strand”), whereas the other columns label each IS for statistical assessment as true positive (TP), false positive (FP), and false negative (FN) based on the genomic distance (“IS distance”) from the ground truth. Precision and recall are then derived by the columns of TP, FP, and FN. (XLSX 233 kb)

LASSIE input files and command line arguments. (PDF 221 kb)