Hard Instances of the Constrained Discrete Logarithm Problem

The discrete logarithm problem (DLP) generalizes to the constrained DLP, where the secret exponent $x$ belongs to a set known to the attacker. The complexity of generic algorithms for solving the constrained DLP depends on the choice of the set. Motivated by cryptographic applications, we study sets with succinct representation for which the constrained DLP is hard. We draw on earlier results due to Erd\"os et al. and Schnorr, develop geometric tools such as generalized Menelaus' theorem for proving lower bounds on the complexity of the constrained DLP, and construct sets with succinct representation with provable non-trivial lower bounds

Proteogenomic landscape of breast cancer tumorigenesis and targeted therapy

The integration of mass spectrometry-based proteomics with next-generation DNA and RNA sequencing profiles tumors more comprehensively. Here this "proteogenomics" approach was applied to 122 treatment-naive primary breast cancers accrued to preserve post-translational modifications, including protein phosphorylation and acetylation. Proteogenomics challenged standard breast cancer diagnoses, provided detailed analysis of the ERBB2 amplicon, defined tumor subsets that could benefit from immune checkpoint therapy, and allowed more accurate assessment of Rb status for prediction of CDK4/6 inhibitor responsiveness. Phosphoproteomics profiles uncovered novel associations between tumor suppressor loss and targetable kinases. Acetylproteome analysis highlighted acetylation on key nuclear proteins involved in the DNA damage response and revealed cross-talk between cytoplasmic and mitochondrial acetylation and metabolism. Our results underscore the potential of proteogenomics for clinical investigation of breast cancer through more accurate annotation of targetable pathways and biological features of this remarkably heterogeneous malignancy

Integrated Molecular Characterization of Testicular Germ Cell Tumors

We studied 137 primary testicular germ cell tumors (TGCTs) using high-dimensional assays of genomic, epigenomic, transcriptomic, and proteomic features. These tumors exhibited high aneuploidy and a paucity of somatic mutations. Somatic mutation of only three genes achieved significance—KIT, KRAS, and NRAS—exclusively in samples with seminoma components. Integrated analyses identified distinct molecular patterns that characterized the major recognized histologic subtypes of TGCT: seminoma, embryonal carcinoma, yolk sac tumor, and teratoma. Striking differences in global DNA methylation and microRNA expression between histology subtypes highlight a likely role of epigenomic processes in determining histologic fates in TGCTs. We also identified a subset of pure seminomas defined by KIT mutations, increased immune infiltration, globally demethylated DNA, and decreased KRAS copy number. We report potential biomarkers for risk stratification, such as miRNA specifically expressed in teratoma, and others with molecular diagnostic potential, such as CpH (CpA/CpC/CpT) methylation identifying embryonal carcinomas. Shen et al. identify molecular characteristics that classify testicular germ cell tumor types, including a separate subset of seminomas defined by KIT mutations. This provides a set of candidate biomarkers for risk stratification and potential therapeutic targeting