On the power of the semi-separated pair decomposition

A Semi-Separated Pair Decomposition (SSPD), with parameter s > 1, of a set is a set {(A i ,B i )} of pairs of subsets of S such that for each i, there are balls and containing A i and B i respectively such that min ( radius ) , radius ), and for any two points p, q S there is a unique index i such that p A i and q B i or vice-versa. In this paper, we use the SSPD to obtain the following results: First, we consider the construction of geometric t-spanners in the context of imprecise points and we prove that any set of n imprecise points, modeled as pairwise disjoint balls, admits a t-spanner with edges which can be computed in time. If all balls have the same radius, the number of edges reduces to . Secondly, for a set of n points in the plane, we design a query data structure for half-plane closest-pair queries that can be built in time using space and answers a query in time, for any ε> 0. By reducing the preprocessing time to and using space, the query can be answered in time. Moreover, we improve the preprocessing time of an existing axis-parallel rectangle closest-pair query data structure from quadratic to near-linear. Finally, we revisit some previously studied problems, namely spanners for complete k-partite graphs and l

Computing the greedy spanner in near-quadratic time

It is well-known that the greedy algorithm produces high quality spanners and therefore is used in several applications. However, for points in d-dimensional Euclidean space, the greedy algorithm has cubic running time. In this paper we present an algorithm that computes the greedy spanner (spanner computed by the greedy algorithm) for a set of n points from a metric space with bounded doubling dimension in time using space. Since the lower bound for computing such spanners is Ω(n 2), the time complexity of our algorithm is optimal to within a logarithmic factor

Comprehensive evaluation of methods to assess overall and cell-specific immune infiltrates in breast cancer

Background: Breast cancer (BC) immune infiltrates play a critical role in tumor progression and response to treatment. Besides stromal tumor infiltrating lymphocytes (sTILs) which have recently reached level 1B evidence as a prognostic marker in triple negative BC, a plethora of methods to assess immune infiltration exists, and it is unclear how these compare to each other and if they can be used interchangeably. Methods: Two experienced pathologists scored sTIL, intra-tumoral TIL (itTIL), and 6 immune cell types (CD3+, CD4+, CD8+, CD20+, CD68+, FOXP3+) in the International Cancer Genomics Consortium breast cancer cohort using hematoxylin and eosin-stained (n = 243) and immunohistochemistry-stained tissue microarrays (n = 254) and whole slides (n = 82). The same traits were evaluated using transcriptomic- and methylomic-based deconvolution methods or signatures. Results: The concordance correlation coefficient (CCC) between pathologists for sTIL was very good (0.84) and for cell-specific immune infiltrates slightly lower (0.63-0.66). Comparison between tissue microarray and whole slide pathology scores revealed systematically higher values in whole slides (ratio 2.60-5.98). The Spearman correlations between microscopic sTIL and transcriptomic- or methylomic-based assessment of immune infilt

Uncovering the Signaling Landscape Controlling Breast Cancer Cell Migration Identifies Novel Metastasis Driver Genes

Ttriple-negative breast cancer (TNBC) is an aggressive and highly metastatic breast cancer subtype. Enhanced TNBC cell motility is a prerequisite of TNBC cell dissemination. Here, we apply an imaging-based RNAi phenotypic cell migration screen using two highly motile TNBC cell lines (Hs578T and MDA-MB-231) to provide a repository of signaling determinants that functionally drive TNBC cell motility. We have screened ~4,200 target genes individually and discovered 133 and 113 migratory modulators of Hs578T and MDA-MB-231, respectively, which are linked to signaling networks predictive for breast cancer progression. The splicing factors PRPF4B and BUD31 and the transcription factor BPTF are essential for cancer cell migration, amplified in human primary breast tumors and associated with metastasis-free survival. Depletion of PRPF4B, BUD31 and BPTF causes primarily down regulation of genes involved in focal adhesion and ECM-interaction pathways. PRPF4B is essential for TNBC metastasis formation in vivo, making PRPF4B a candidate for further drug developmen

Uncovering the signaling landscape controlling breast cancer cell migration identifies novel metastasis driver genes

Ttriple-negative breast cancer (TNBC) is an aggressive and highly metastatic breast cancer subtype. Enhanced TNBC cell motility is a prerequisite of TNBC cell dissemination. Here, we apply an imaging-based RNAi phenotypic cell migration screen using two highly motile TNBC cell lines (Hs578T and MDA-MB-231) to provide a repository of signaling determinants that functionally drive TNBC cell motility. We have screened ~4,200 target genes individually and discovered 133 and 113 migratory modulators of Hs578T and MDA-MB-231, respectively, which are linked to signaling networks predictive for breast cancer progression. The splicing factors PRPF4B and BUD31 and the transcription factor BPTF are essential for cancer cell migration, amplified in human primary breast tumors and associated with metastasis-free survival. Depletion of PRPF4B, BUD31 and BPTF causes primarily down regulation of genes involved in focal adhesion and ECM-interaction pathways. PRPF4B is essential for TNBC metastasis formation in vivo, making PRPF4B a candidate for further drug development

An improved construction for spanners of disks

Let D be a set of n pairwise disjoint disks in the plane. Consider the metric space in which the distance between any two disks D and D′ in D is the length of the shortest line segment that connects D and D′. For any real number ε>0, we show how to obtain a (1+ε)-spanner for this metric space that has at most (2π/ε)⋅n edges. The previously best known result is by Bose et al. (2011) [1]. Their (1+ε)-spanner is a variant of the Yao graph and has at most (8π/ε)⋅n edges. Our new spanner is also a variant of the Yao graph

On Duadic Codes

We define a class of q-ary cyclic codes, the so-called duadic codes. These codes are a direct generalization of QR codes. The results of Leon, Masley and Pless on binary duadic codes are generalized. Duadic codes of composite length and a low minimum distance are constructed. We consider duadic codes of length a prime power, and we give an existence test for cyclic projective planes. Furthermore, we give bounds for the minimum distance of all binary duadic codes of length <=241

On spanners of geometric graphs

Given a connected geometric graph G, we consider the problem of constructing a t-spanner of G having the minimum number of edges. We prove that for every real number t with $1 < t < {1 \over 4}{\rm{log }}\,n$, there exists a connected geometric graph G with n vertices, such that every t-spanner of G contains Ω(n1+1/t) edges. This bound almost matches the known upper bound, which states that every connected weighted graph with n vertices contains a t-spanner with O(n1+2/(t-1)) edges. We also prove that the problem of deciding whether a given geometric graph contains a t-spanner with at most K edges is NP-hard. Previously, this NP-hardness result was only known for non-geometric graphs