A logarithmic approximation for unsplittable flow on line graphs

We consider the unsplittable flow problem on a line. In this problem, we are given a set of n tasks, each specified by a start time s_i, an end time t_i, a demand d_i > 0, and a profit p_i > 0. A task, if accepted, requires di units of bandwidth from time s_i to t_i and accrues a profit of p_i. For every time t, we are also specified the available bandwidth c_t, and the goal is to find a subset of tasks with maximum profit subject to the bandwidth constraints. We present the first polynomial time O(log n) approximation algorithm for this problem. This significantly advances the state of the art, as no polynomial time o(n) approximation was known previously. Previous results for this problem were known only in more restrictive settings; in particular, either the instance satisfies the so-called no-bottleneck assumption: max_i d_i = min_t c_t, or the ratio of both maximum to minimum demands and maximum to minimum capacities are polynomially (or quasi-polynomially) bounded in n. Our result, on the other hand, does not require these assumptions. Our algorithm is based on a combination of dynamic programming and rounding a natural linear programming relaxation for the problem. While there is an O(n) integrality gap known for this LP relaxation, our key idea is to exploit certain structural properties of the problem to show that instances that are bad for the LP can in fact be handled using dynamic programming

Near Resonant Spatial Images of Confined Bose-Einstein Condensates in the '4D' Magnetic Bottle

We present quantitative measurements of the spatial density profile of Bose-Einstein condensates of sodium atoms confined in a new '4D' magnetic bottle. The condensates are imaged in transmission with near resonant laser light. We demonstrate that the Thomas-Fermi surface of a condensate can be determined to better than 1%. More generally, we obtain excellent agreement with mean-field theory. We conclude that precision measurements of atomic scattering lengths and interactions between phase separated cold atoms in a harmonic trap can be measured with high precision using this method.Comment: 15 pages, 3 figures. Submitted 10/30/97, accepted for publication in Phys. Rev. A Rapid Com

Pan-cancer Alterations of the MYC Oncogene and Its Proximal Network across the Cancer Genome Atlas

Although theMYConcogene has been implicated incancer, a systematic assessment of alterations ofMYC, related transcription factors, and co-regulatoryproteins, forming the proximal MYC network (PMN),across human cancers is lacking. Using computa-tional approaches, we define genomic and proteo-mic features associated with MYC and the PMNacross the 33 cancers of The Cancer Genome Atlas.Pan-cancer, 28% of all samples had at least one ofthe MYC paralogs amplified. In contrast, the MYCantagonists MGA and MNT were the most frequentlymutated or deleted members, proposing a roleas tumor suppressors.MYCalterations were mutu-ally exclusive withPIK3CA,PTEN,APC,orBRAFalterations, suggesting that MYC is a distinct onco-genic driver. Expression analysis revealed MYC-associated pathways in tumor subtypes, such asimmune response and growth factor signaling; chro-matin, translation, and DNA replication/repair wereconserved pan-cancer. This analysis reveals insightsinto MYC biology and is a reference for biomarkersand therapeutics for cancers with alterations ofMYC or the PMN

Genomic, Pathway Network, and Immunologic Features Distinguishing Squamous Carcinomas

This integrated, multiplatform PanCancer Atlas study co-mapped and identified distinguishing molecular features of squamous cell carcinomas (SCCs) from five sites associated with smokin

Pan-Cancer Analysis of lncRNA Regulation Supports Their Targeting of Cancer Genes in Each Tumor Context

Long noncoding RNAs (lncRNAs) are commonly dys-regulated in tumors, but only a handful are known toplay pathophysiological roles in cancer. We inferredlncRNAs that dysregulate cancer pathways, onco-genes, and tumor suppressors (cancer genes) bymodeling their effects on the activity of transcriptionfactors, RNA-binding proteins, and microRNAs in5,185 TCGA tumors and 1,019 ENCODE assays.Our predictions included hundreds of candidateonco- and tumor-suppressor lncRNAs (cancerlncRNAs) whose somatic alterations account for thedysregulation of dozens of cancer genes and path-ways in each of 14 tumor contexts. To demonstrateproof of concept, we showed that perturbations tar-geting OIP5-AS1 (an inferred tumor suppressor) andTUG1 and WT1-AS (inferred onco-lncRNAs) dysre-gulated cancer genes and altered proliferation ofbreast and gynecologic cancer cells. Our analysis in-dicates that, although most lncRNAs are dysregu-lated in a tumor-specific manner, some, includingOIP5-AS1, TUG1, NEAT1, MEG3, and TSIX, synergis-tically dysregulate cancer pathways in multiple tumorcontexts

Spatial Organization and Molecular Correlation of Tumor-Infiltrating Lymphocytes Using Deep Learning on Pathology Images

Beyond sample curation and basic pathologic characterization, the digitized H&E-stained images of TCGA samples remain underutilized. To highlight this resource, we present mappings of tumorinfiltrating lymphocytes (TILs) based on H&E images from 13 TCGA tumor types. These TIL maps are derived through computational staining using a convolutional neural network trained to classify patches of images. Affinity propagation revealed local spatial structure in TIL patterns and correlation with overall survival. TIL map structural patterns were grouped using standard histopathological parameters. These patterns are enriched in particular T cell subpopulations derived from molecular measures. TIL densities and spatial structure were differentially enriched among tumor types, immune subtypes, and tumor molecular subtypes, implying that spatial infiltrate state could reflect particular tumor cell aberration states. Obtaining spatial lymphocytic patterns linked to the rich genomic characterization of TCGA samples demonstrates one use for the TCGA image archives with insights into the tumor-immune microenvironment

Dysregulation of PRMT5 in chronic lymphocytic leukemia promotes progression with high risk of Richter's transformation

: Richter's Transformation (RT) is a poorly understood and fatal progression of chronic lymphocytic leukemia (CLL) manifesting histologically as diffuse large B-cell lymphoma. Protein arginine methyltransferase 5 (PRMT5) is implicated in lymphomagenesis, but its role in CLL or RT progression is unknown. We demonstrate herein that tumors uniformly overexpress PRMT5 in patients with progression to RT. Furthermore, mice with B-specific overexpression of hPRMT5 develop a B-lymphoid expansion with increased risk of death, and Eµ-PRMT5/TCL1 double transgenic mice develop a highly aggressive disease with transformation that histologically resembles RT; where large-scale transcriptional profiling identifies oncogenic pathways mediating PRMT5-driven disease progression. Lastly, we report the development of a SAM-competitive PRMT5 inhibitor, PRT382, with exclusive selectivity and optimal in vitro and in vivo activity compared to available PRMT5 inhibitors. Taken together, the discovery that PRMT5 drives oncogenic pathways promoting RT provides a compelling rationale for clinical investigation of PRMT5 inhibitors such as PRT382 in aggressive CLL/RT cases

Demographic, clinical, biomarker, and neuropathological correlates of posterior cortical atrophy: an international cohort study and individual participant data meta-analysis

Background: Posterior cortical atrophy is a rare syndrome characterised by early, prominent, and progressive impairment in visuoperceptual and visuospatial processing. The disorder has been associated with underlying neuropathological features of Alzheimer's disease, but large-scale biomarker and neuropathological studies are scarce. We aimed to describe demographic, clinical, biomarker, and neuropathological correlates of posterior cortical atrophy in a large international cohort.// Methods: We searched PubMed between database inception and Aug 1, 2021, for all published research studies on posterior cortical atrophy and related terms. We identified research centres from these studies and requested deidentified, individual participant data (published and unpublished) that had been obtained at the first diagnostic visit from the corresponding authors of the studies or heads of the research centres. Inclusion criteria were a clinical diagnosis of posterior cortical atrophy as defined by the local centre and availability of Alzheimer's disease biomarkers (PET or CSF), or a diagnosis made at autopsy. Not all individuals with posterior cortical atrophy fulfilled consensus criteria, being diagnosed using centre-specific procedures or before development of consensus criteria. We obtained demographic, clinical, biofluid, neuroimaging, and neuropathological data. Mean values for continuous variables were combined using the inverse variance meta-analysis method; only research centres with more than one participant for a variable were included. Pooled proportions were calculated for binary variables using a restricted maximum likelihood model. Heterogeneity was quantified using I2.// Findings: We identified 55 research centres from 1353 papers, with 29 centres responding to our request. An additional seven centres were recruited by advertising via the Alzheimer's Association. We obtained data for 1092 individuals who were evaluated at 36 research centres in 16 countries, the other sites having not responded to our initial invitation to participate to the study. Mean age at symptom onset was 59·4 years (95% CI 58·9–59·8; I2=77%), 60% (56–64; I2=35%) were women, and 80% (72–89; I2=98%) presented with posterior cortical atrophy pure syndrome. Amyloid β in CSF (536 participants from 28 centres) was positive in 81% (95% CI 75–87; I2=78%), whereas phosphorylated tau in CSF (503 participants from 29 centres) was positive in 65% (56–75; I2=87%). Amyloid-PET (299 participants from 24 centres) was positive in 94% (95% CI 90–97; I2=15%), whereas tau-PET (170 participants from 13 centres) was positive in 97% (93–100; I2=12%). At autopsy (145 participants from 13 centres), the most frequent neuropathological diagnosis was Alzheimer's disease (94%, 95% CI 90–97; I2=0%), with common co-pathologies of cerebral amyloid angiopathy (71%, 54–88; I2=89%), Lewy body disease (44%, 25–62; I2=77%), and cerebrovascular injury (42%, 24–60; I2=88%).// Interpretation: These data indicate that posterior cortical atrophy typically presents as a pure, young-onset dementia syndrome that is highly specific for underlying Alzheimer's disease pathology. Further work is needed to understand what drives cognitive vulnerability and progression rates by investigating the contribution of sex, genetics, premorbid cognitive strengths and weaknesses, and brain network integrity