A Randomly Weighted Minimum Spanning Tree with a Random Cost Constraint

We study the minimum spanning tree problem on the complete graph $K_n$ where an edge $e$ has a weight $W_e$ and a cost $C_e$, each of which is an independent copy of the random variable $U^\gamma$ where $\gamma\leq 1$ and $U$ is the uniform $[0,1]$ random variable. There is also a constraint that the spanning tree $T$ must satisfy $C(T)\leq c_0$. We establish, for a range of values for $c_0,\gamma$, the asymptotic value of the optimum weight via the consideration of a dual problem.

FastClone is a probabilistic tool for deconvoluting tumor heterogeneity in bulk-sequencing samples

Dissecting tumor heterogeneity is a key to understanding the complex mechanisms underlying drug resistance in cancers. The rich literature of pioneering studies on tumor heterogeneity analysis spurred a recent community-wide benchmark study that compares diverse modeling algorithms. Here we present FastClone, a top-performing algorithm in accuracy in this benchmark. FastClone improves over existing methods by allowing the deconvolution of subclones that have independent copy number variation events within the same chromosome regions. We characterize the behavior of FastClone in identifying subclones using stage III colon cancer primary tumor samples as well as simulated data. It achieves approximately 100-fold acceleration in computation for both simulated and patient data. The efficacy of FastClone will allow its application to large-scale data and clinical data, and facilitate personalized medicine in cancers.

Reconstructing directed graphs from generalized gauge actions on their Toeplitz algebras

We show how to reconstruct a finite directed graph E from its Toeplitz algebra, its gauge action, and the canonical finite-dimensional abelian subalgebra generated by the vertex projections. We also show that if E has no sinks, then we can recover E from its Toeplitz algebra and the generalized gauge action that has, for each vertex, an independent copy of the circle acting on the generators corresponding to edges emanating from that vertex. We show by example that it is not possible to recover E from its Toeplitz algebra and gauge action alone.

Generating surrogates from recurrences

In this paper, we present an approach to recover the dynamics from recurrences of a system and then generate (multivariate) twin surrogate (TS) trajectories. In contrast to other approaches, such as the linear-like surrogates, this technique produces surrogates which correspond to an independent copy of the underlying system, i.e. they induce a trajectory of the underlying system visiting the attractor in a different way. We show that these surrogates are well suited to test for complex synchronization, which makes it possible to systematically assess the reliability of synchronization analyses. We then apply the TS to study binocular fixational movements and find strong indications that the fixational movements of the left and right eye are phase synchronized. This result indicates that there might be only one centre in the brain that produces the fixational movements in both eyes or a close link between the two centres.

A minimal c-fes cassette directs myeloid-specific expression in transgenic mice

The c-fes proto-oncogene encodes a 92-kd protein tyrosine kinase whose expression is restricted largely to myeloid and endothelial cells in adult mammals. A 13.2-kilobase (kb) humanc-fes genomic fragment was previously shown to containcis-acting element(s) sufficient for a locus control function in bone marrow macrophages. Locus control regions (LCRs) confer transgene expression in mice that is integration site independent, copy number dependent, and similar to endogenous murine messenger RNA levels. To identify sequences required for this LCR,c-fes transgenes were analyzed in mice. Myeloid-cell–specific, deoxyribonuclease-I–hypersensitive sites localized to the 3′ boundary of exon 1 and intron 3 are required to confer high-level transgene expression comparable to endogenous c-fes, independent of integration site. We define a minimal LCR element as DNA sequences (nucleotides +28 to +2523 relative to the transcription start site) located within intron 1 to intron 3 of the human locus. When this 2.5-kb DNA fragment was linked to a c-fes complementary DNA regulated by its own 446–base-pair promoter, integration-site–independent, copy-number–dependent transcription was observed in myeloid cells in transgenic mice. Furthermore, this 2.5-kb cassette directed expression of a heterologous gene (enhanced green fluorescent protein) exclusively in myeloid cells. The c-fes regulatory unit represents a novel reagent for targeting gene expression to macrophages and neutrophils in transgenic mice.

A minimal c-fes cassette directs myeloid-specific expression in transgenic mice

The c-fes proto-oncogene encodes a 92-kd protein tyrosine kinase whose expression is restricted largely to myeloid and endothelial cells in adult mammals. A 13.2-kilobase (kb) humanc-fes genomic fragment was previously shown to containcis-acting element(s) sufficient for a locus control function in bone marrow macrophages. Locus control regions (LCRs) confer transgene expression in mice that is integration site independent, copy number dependent, and similar to endogenous murine messenger RNA levels. To identify sequences required for this LCR,c-fes transgenes were analyzed in mice. Myeloid-cell–specific, deoxyribonuclease-I–hypersensitive sites localized to the 3′ boundary of exon 1 and intron 3 are required to confer high-level transgene expression comparable to endogenous c-fes, independent of integration site. We define a minimal LCR element as DNA sequences (nucleotides +28 to +2523 relative to the transcription start site) located within intron 1 to intron 3 of the human locus. When this 2.5-kb DNA fragment was linked to a c-fes complementary DNA regulated by its own 446–base-pair promoter, integration-site–independent, copy-number–dependent transcription was observed in myeloid cells in transgenic mice. Furthermore, this 2.5-kb cassette directed expression of a heterologous gene (enhanced green fluorescent protein) exclusively in myeloid cells. The c-fes regulatory unit represents a novel reagent for targeting gene expression to macrophages and neutrophils in transgenic mice.