Analysing Lyapunov spectra of chaotic dynamical systems

It is shown that the asymptotic spectra of finite-time Lyapunov exponents of a variety of fully chaotic dynamical systems can be understood in terms of a statistical analysis. Using random matrix theory we derive numerical and in particular analytical results which provide insights into the overall behaviour of the Lyapunov exponents particularly for strange attractors. The corresponding distributions for the unstable periodic orbits are investigated for comparison.Comment: 4 pages, 4 figure

Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape

Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems. While the former approach studies how regions of phase space are transported by reducing the flow to a two-dimensional map, the latter approach studies the phase space structures that lead to critical events by crossing periodic orbit around saddles. Both of these frameworks require computation with curves represented by millions of points-computing intersection points between these curves and area bounded by the segments of these curves-for quantifying the transport and escape rate. We present a theory for computing these intersection points and the area bounded between the segments of these curves based on a classification of the intersection points using equivalence class. We also present an alternate theory for curves with nontransverse intersections and a method to increase the density of points on the curves for locating the intersection points accurately.The numerical implementation of the theory presented herein is available as an open source software called Lober. We used this package to demonstrate the application of the theory to lobe dynamics that arises in fluid mechanics, and rate of escape from a potential well that arises in ship dynamics.Comment: 33 pages, 17 figure

Integration of mutational signature analysis with 3D chromatin data unveils differential AID-related mutagenesis in indolent lymphomas

Activation-induced deaminase (AID) is required for somatic hypermutation in immunoglobulin genes, but also induces off-target mutations. Follicular lymphoma (FL) and chronic lymphocytic leukemia (CLL), the most frequent types of indolent B-cell tumors, are exposed to AID activity during lymphomagenesis. We designed a workflow integrating de novo mutational signatures extraction and fitting of COSMIC (Catalogue Of Somatic Mutations In Cancer) signatures, with tridimensional chromatin conformation data (Hi-C). We applied the workflow to exome sequencing data from lymphoma samples. In 33 FL and 30 CLL samples, 42% and 34% of the contextual mutations could be traced to a known AID motif. We demonstrate that both CLL and FL share mutational processes dominated by spontaneous deamination, failures in DNA repair, and AID activity. The processes had equiproportional distribution across active and nonactive chromatin compartments in CLL. In contrast, canonical AID activity and failures in DNA repair pathways in FL were significantly higher within the active chromatin compartment. Analysis of DNA repair genes revealed a higher prevalence of base excision repair gene mutations (p = 0.02) in FL than CLL. These data indicate that AID activity drives the genetic landscapes of FL and CLL. However, the final result of AID-induced mutagenesis differs between these lymphomas depending on chromatin compartmentalization and mutations in DNA repair pathways.Immunobiology of allogeneic stem cell transplantation and immunotherapy of hematological disease

Approach to ergodicity in quantum wave functions

According to theorems of Shnirelman and followers, in the semiclassical limit the quantum wavefunctions of classically ergodic systems tend to the microcanonical density on the energy shell. We here develop a semiclassical theory that relates the rate of approach to the decay of certain classical fluctuations. For uniformly hyperbolic systems we find that the variance of the quantum matrix elements is proportional to the variance of the integral of the associated classical operator over trajectory segments of length $T_H$, and inversely proportional to $T_H^2$, where $T_H=h\bar\rho$ is the Heisenberg time, $\bar\rho$ being the mean density of states. Since for these systems the classical variance increases linearly with $T_H$, the variance of the matrix elements decays like $1/T_H$. For non-hyperbolic systems, like Hamiltonians with a mixed phase space and the stadium billiard, our results predict a slower decay due to sticking in marginally unstable regions. Numerical computations supporting these conclusions are presented for the bakers map and the hydrogen atom in a magnetic field.Comment: 11 pages postscript and 4 figures in two files, tar-compressed and uuencoded using uufiles, to appear in Phys Rev E. For related papers, see http://www.icbm.uni-oldenburg.de/icbm/kosy/ag.htm

An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics

For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types

Assessment of plasma chitotriosidase activity, CCL18/PARC concentration and NP-C suspicion index in the diagnosis of Niemann-Pick disease type C: A prospective observational study

Background: Niemann-Pick disease type C (NP-C) is a rare, autosomal recessive neurodegenerative disease caused by mutations in either the NPC1 or NPC2 genes. The diagnosis of NP-C remains challenging due to the non-specific, heterogeneous nature of signs/symptoms. This study assessed the utility of plasma chitotriosidase (ChT) and Chemokine (C-C motif) ligand 18 (CCL18)/pulmonary and activation-regulated chemokine (PARC) in conjunction with the NP-C suspicion index (NP-C SI) for guiding confirmatory laboratory testing in patients with suspected NP-C. Methods: In a prospective observational cohort study, incorporating a retrospective determination of NP-C SI scores, two different diagnostic approaches were applied in two separate groups of unrelated patients from 51 Spanish medical centers (n = 118 in both groups). From Jan 2010 to Apr 2012 (Period 1), patients with =2 clinical signs/symptoms of NP-C were considered ''suspected NP-C'' cases, and NPC1/NPC2 sequencing, plasma chitotriosidase (ChT), CCL18/PARC and sphingomyelinase levels were assessed. Based on findings in Period 1, plasma ChT and CCL18/PARC, and NP-C SI prediction scores were determined in a second group of patients between May 2012 and Apr 2014 (Period 2), and NPC1 and NPC2 were sequenced only in those with elevated ChT and/or elevated CCL18/PARC and/or NP-C SI =70. Filipin staining and 7-ketocholesterol (7-KC) measurements were performed in all patients with NP-C gene mutations, where possible. Results: In total across Periods 1 and 2, 10/236 (4%) patients had a confirmed diagnosis o NP-C based on gene sequencing (5/118 4.2%] in each Period): all of these patients had two causal NPC1 mutations. Single mutant NPC1 alleles were detected in 8/236 (3%) patients, overall. Positive filipin staining results comprised three classical and five variant biochemical phenotypes. No NPC2 mutations were detected. All patients with NPC1 mutations had high ChT activity, high CCL18/PARC concentrations and/or NP-C SI scores =70. Plasma 7-KC was higher than control cut-off values in all patients with two NPC1 mutations, and in the majority of patients with single mutations. Family studies identified three further NP-C patients. Conclusion: This approach may be very useful for laboratories that do not have mass spectrometry facilities and therefore, they cannot use other NP-C biomarkers for diagnosis

Driver Fusions and Their Implications in the Development and Treatment of Human Cancers.

Gene fusions represent an important class of somatic alterations in cancer. We systematically investigated fusions in 9,624 tumors across 33 cancer types using multiple fusion calling tools. We identified a total of 25,664 fusions, with a 63% validation rate. Integration of gene expression, copy number, and fusion annotation data revealed that fusions involving oncogenes tend to exhibit increased expression, whereas fusions involving tumor suppressors have the opposite effect. For fusions involving kinases, we found 1,275 with an intact kinase domain, the proportion of which varied significantly across cancer types. Our study suggests that fusions drive the development of 16.5% of cancer cases and function as the sole driver in more than 1% of them. Finally, we identified druggable fusions involving genes such as TMPRSS2, RET, FGFR3, ALK, and ESR1 in 6.0% of cases, and we predicted immunogenic peptides, suggesting that fusions may provide leads for targeted drug and immune therapy

Perspective on Oncogenic Processes at the End of the Beginning of Cancer Genomics

The Cancer Genome Atlas (TCGA) has catalyzed systematic characterization of diverse genomic alterations underlying human cancers. At this historic junction marking the completion of genomic characterization of over 11,000 tumors from 33 cancer types, we present our current understanding of the molecular processes governing oncogenesis. We illustrate our insights into cancer through synthesis of the findings of the TCGA PanCancer Atlas project on three facets of oncogenesis: (1) somatic driver mutations, germline pathogenic variants, and their interactions in the tumor; (2) the influence of the tumor genome and epigenome on transcriptome and proteome; and (3) the relationship between tumor and the microenvironment, including implications for drugs targeting driver events and immunotherapies. These results will anchor future characterization of rare and common tumor types, primary and relapsed tumors, and cancers across ancestry groups and will guide the deployment of clinical genomic sequencing

Pathogenic Germline Variants in 10,389 Adult Cancers

We conducted the largest investigation of predisposition variants in cancer to date, discovering 853 pathogenic or likely pathogenic variants in 8% of 10,389 cases from 33 cancer types. Twenty-one genes showed single or cross-cancer associations, including novel associations of SDHA in melanoma and PALB2 in stomach adenocarcinoma. The 659 predisposition variants and 18 additional large deletions in tumor suppressors, including ATM, BRCA1, and NF1, showed low gene expression and frequent (43%) loss of heterozygosity or biallelic two-hit events. We also discovered 33 such variants in oncogenes, including missenses in MET, RET, and PTPN11 associated with high gene expression. We nominated 47 additional predisposition variants from prioritized VUSs supported by multiple evidences involving case-control frequency, loss of heterozygosity, expression effect, and co-localization with mutations and modified residues. Our integrative approach links rare predisposition variants to functional consequences, informing future guidelines of variant classification and germline genetic testing in cancer. A pan-cancer analysis identifies hundreds of predisposing germline variants