We introduce a new dissimilarity measure between a pair of “clonal trees”, each representing the progression and mutational heterogeneity of a tumor sample, constructed by the use of single cell or bulk high throughput sequencing data. In a clonal tree, each vertex represents a specific tumor clone, and is labeled with one or more mutations in a way that each mutation is assigned to the oldest clone that harbors it. Given two clonal trees, our multi-labeled tree dissimilarity (MLTD) measure is defined as the minimum number of mutation/label deletions, (empty) leaf deletions, and vertex (clonal) expansions, applied in any order, to convert each of the two trees to the maximum common tree. We show that the MLTD measure can be computed efficiently in polynomial time and it captures the similarity between trees of different clonal granularity well.

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Current practices in collaborative genomic data analysis (e.g. PCAWG [1]) necessitate all involved parties to exchange individual patient data and perform all analysis locally, or use a trusted server for maintaining all data to perform analysis in a single site (e.g. the Cancer Genome Collaboratory). Since both approaches involve sharing genomic sequence data -which is typically not feasible due to privacy issues, collaborative data analysis remains to be a rarity in genomic medicine.In order to facilitate efficient and effective collaborative or remote genomic computation we introduce SkSES (Sketching algorithms for Secure Enclave based genomic data analysiS), a computational framework for performing data analysis and querying on multiple, individually encrypted genomes from several institutions in an untrusted cloud environment. Unlike other techniques for secure/privacy preserving genomic data analysis, which typically rely on sophisticated cryptographic techniques with prohibitively large computational overheads, SkSES utilizes the secure enclaves supported by current generation microprocessor architectures such as Intel's SGX. The key conceptual contribution of SkSES is its use of sketching data structures that can fit in the limited memory available in a secure enclave.While streaming/sketching algorithms have been developed for many applications in computer science, their feasibility in genomics has remained largely unexplored. On the other hand, even though privacy and security issues are becoming critical in genomic medicine, available cryptographic techniques based on, e.g. homomorphic encryption or garbled circuits, fail to address the performance demands of this rapidly growing field. The alternative offered by Intel's SGX, a combination of hardware and software solutions for secure data analysis, is severely limited by the relatively small size of a secure enclave, a private region of the memory protected from other processes. SkSES addresses this limitation through the use of sketching data structures to support efficient secure and privacy preserving SNP analysis across individually encrypted VCF files from multiple institutions. In particular SkSES provides the users the ability to query for the "k most significant SNPs" among any set of user specified SNPs and any value of k -even when the total number of SNPs to be maintained is far beyond the memory capacity of the secure enclave. Results: We tested SkSES on the complete iDASH-2017 competition data set comprised of 1000 case and 1000 control samples related to an unknown phenotype. SkSES was able to identify the top SNPs with respect to the χ 2 statistic, among any user specified subset of SNPs across this data set of 2000 individually encrypted complete human genomes quickly and accurately -demonstrating the feasibility of secure and privacy preserving computation for genomic medicine via Intel's SGX.

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This paper is dedicated to a long-standing problem of the shape of the negative branch of polarization (NBP) for Jupiter's moon Europa, determination of which is crucial for the characterization of the icy regolith on this satellite and similar objects, as well as for further progress in understanding light scattering by particulate surfaces. To establish the shape of Europa's NBP, in 2018–2021 we accomplished high-precision disk-integrated polarimetry of Europa in the UBVR I bands using the identical two-channel photoelectric polarimeters mounted on the 2.6 m Shajn reflector of the Crimean Astrophysical Observatory and the 2 m telescope of the Peak Terskol Observatory. We found that the polarization dependence on the phase angle in each filter is an asymmetric curve with a sharp polarization minimum P min ≈ − 0.3 % at phase angle α min ≤ 0 .° 4 , after which the polarization degree gradually increases to positive values, passing the inversion angle at α inv ≈ 6° − 7°. Within the error limits, the parameters P min, α min , and α inv of the NPB are independent of the wavelength in the visible spectrum. The polarization curve clearly demonstrates the so-called polarization opposition effect (POE). Our analysis of the previous and new polarimetric observations of Europa allows us to conclude that the POE is caused by coherent backscattering of sunlight on microscopic icy grains covering Europa’s surface. Computer modeling with the numerical radiative transfer coherent backscattering method demonstrates that the best fit to the polarimetric observations and geometric albedo of Europa is provided by a regolith layer of elementary single-scattering albedo ∼0.985 and extinction mean free path length 2π l/λ eff ≈ 150, λ eff representing the effective wavelength in the UBVR I spectral bands.

Given an edge-weighted graph G with a set Q of k terminals, a mimicking network is a graph with the same set of terminals that exactly preserves the sizes of minimum cuts between any partition of the terminals. A natural question in the area of graph compression is to provide as small mimicking networks as possible for input graph G being either an arbitrary graph or coming from a specific graph class.In this note we show an exponential lower bound for cut mimicking networks in planar graphs: there are edge-weighted planar graphs with k terminals that require 2 k−2 edges in any mimicking network. This nearly matches an upper bound of O(k2 2k ) of Rika [SODA 2013, arXiv:1702.05951] and is in sharp contrast with the O(k 2 ) upper bound under the assumption that all terminals lie on a single face [Goranci, Henzinger, Peng, arXiv:1702.01136]. As a side result we show a hard instance for double-