Ergodicity, Decisions, and Partial Information

In the simplest sequential decision problem for an ergodic stochastic process X, at each time n a decision u_n is made as a function of past observations X_0,...,X_{n-1}, and a loss l(u_n,X_n) is incurred. In this setting, it is known that one may choose (under a mild integrability assumption) a decision strategy whose pathwise time-average loss is asymptotically smaller than that of any other strategy. The corresponding problem in the case of partial information proves to be much more delicate, however: if the process X is not observable, but decisions must be based on the observation of a different process Y, the existence of pathwise optimal strategies is not guaranteed. The aim of this paper is to exhibit connections between pathwise optimal strategies and notions from ergodic theory. The sequential decision problem is developed in the general setting of an ergodic dynamical system (\Omega,B,P,T) with partial information Y\subseteq B. The existence of pathwise optimal strategies grounded in two basic properties: the conditional ergodic theory of the dynamical system, and the complexity of the loss function. When the loss function is not too complex, a general sufficient condition for the existence of pathwise optimal strategies is that the dynamical system is a conditional K-automorphism relative to the past observations \bigvee_n T^n Y. If the conditional ergodicity assumption is strengthened, the complexity assumption can be weakened. Several examples demonstrate the interplay between complexity and ergodicity, which does not arise in the case of full information. Our results also yield a decision-theoretic characterization of weak mixing in ergodic theory, and establish pathwise optimality of ergodic nonlinear filters.Comment: 45 page

On the exchange of intersection and supremum of sigma-fields in filtering theory

We construct a stationary Markov process with trivial tail sigma-field and a nondegenerate observation process such that the corresponding nonlinear filtering process is not uniquely ergodic. This settles in the negative a conjecture of the author in the ergodic theory of nonlinear filters arising from an erroneous proof in the classic paper of H. Kunita (1971), wherein an exchange of intersection and supremum of sigma-fields is taken for granted.Comment: 20 page

(Non)Invariance of dynamical quantities for orbit equivalent flows

We study how dynamical quantities such as Lyapunov exponents, metric entropy, topological pressure, recurrence rates, and dimension-like characteristics change under a time reparameterization of a dynamical system. These quantities are shown to either remain invariant, transform according to a multiplicative factor or transform through a convoluted dependence that may take the form of an integral over the initial local values. We discuss the significance of these results for the apparent non-invariance of chaos in general relativity and explore applications to the synchronization of equilibrium states and the elimination of expansions

Low temperature magneto-morphological characterisation of coronene and the resolution of previously observed unexplained phenomena

The polyaromatic hydrocarbon coronene has been the molecule of choice for understanding the physical properties of graphene for over a decade. The modelling of the latter by the former was considered to be valid, as since it was first synthesised in 1932, the physical behaviour of coronene has been determined extremely accurately. We recently discovered however, an unforeseen polymorph of coronene, which exists as an enantiotrope with the previously observed crystal structure. Using low-temperature magnetisation and crystallographic measurements, we show here for the first time that the electronic and magnetic properties of coronene depend directly on the temperature at which it is observed, with hysteretic behaviour exhibited between 300 K and 100 K. Furthermore we determine that this behaviour is a direct result of the appearance and disappearance of the newly-discovered polymorph during thermal cycling. Our results not only highlight the need for theoretical models of graphene to take into account this anomalous behaviour at low temperatures, but also explain puzzling experimental observations of coronene dating back over 40 years

FRA2 is a STAT5 target gene regulated by IL-2 in human CD4 T cells

Signal transducers and activators of transcription 5(STAT5) are cytokine induced signaling proteins, which regulate key immunological processes, such as tolerance induction, maintenance of homeostasis, and CD4 T-effector cell differentiation. In this study, transcriptional targets of STAT5 in CD4 T cells were studied by Chromatin Immunoprecipitation (ChIP). Genomic mapping of the sites cloned and identified in this study revealed the striking observation that the majority of STAT5-binding sites mapped to intergenic (>50 kb upstream) or intronic, rather than promoter proximal regions. Of the 105 STAT5 responsive binding sites identified, 94% contained the canonical (IFN-γ activation site) GAS motifs. A number of putative target genes identified here are associated with tumor biology. Here, we identified Fos-related antigen 2 (FRA2) as a transcriptional target of IL-2 regulated STAT5. FRA2 is a basic -leucine zipper (bZIP) motif 'Fos' family transcription factor that is part of the AP-1 transcription factor complex and is also known to play a critical role in the progression of human tumours and more recently as a determinant of T cell plasticity. The binding site mapped to an internal intron within the FRA2 gene. The epigenetic architecture of FRA2, characterizes a transcriptionally active promoter as indicated by enrichment for histone methylation marks H3K4me1, H3K4me2, H3K4me3, and transcription/elongation associated marks H2BK5me1 and H4K20me1. FRA2 is regulated by IL-2 in activated CD4 T cells. Consistently, STAT5 bound to GAS sequence in the internal intron of FRA2 and reporter gene assays confirmed IL-2 induced STAT5 binding and transcriptional activation. Furthermore, addition of JAK3 inhibitor (R333) or Daclizumab inhibited the induction in TCR stimulated cells. Taken together, our data suggest that FRA2 is a novel STAT5 target gene, regulated by IL-2 in activated CD4 T cells

Sequencing and Analysis of Approximately 40 000 Soybean cDNA Clones from a Full-Length-Enriched cDNA Library

A large collection of full-length cDNAs is essential for the correct annotation of genomic sequences and for the functional analysis of genes and their products. We obtained a total of 39 936 soybean cDNA clones (GMFL01 and GMFL02 clone sets) in a full-length-enriched cDNA library which was constructed from soybean plants that were grown under various developmental and environmental conditions. Sequencing from 5′ and 3′ ends of the clones generated 68 661 expressed sequence tags (ESTs). The EST sequences were clustered into 22 674 scaffolds involving 2580 full-length sequences. In addition, we sequenced 4712 full-length cDNAs. After removing overlaps, we obtained 6570 new full-length sequences of soybean cDNAs so far. Our data indicated that 87.7% of the soybean cDNA clones contain complete coding sequences in addition to 5′- and 3′-untranslated regions. All of the obtained data confirmed that our collection of soybean full-length cDNAs covers a wide variety of genes. Comparative analysis between the derived sequences from soybean and Arabidopsis, rice or other legumes data revealed that some specific genes were involved in our collection and a large part of them could be annotated to unknown functions. A large set of soybean full-length cDNA clones reported in this study will serve as a useful resource for gene discovery from soybean and will also aid a precise annotation of the soybean genome

Initial sequencing and analysis of the human genome

The human genome holds an extraordinary trove of information about human development, physiology, medicine and evolution. Here we report the results of an international collaboration to produce and make freely available a draft sequence of the human genome. We also present an initial analysis of the data, describing some of the insights that can be gleaned from the sequence.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62798/1/409860a0.pd

Signatures of mutational processes in human cancer.

All cancers are caused by somatic mutations; however, understanding of the biological processes generating these mutations is limited. The catalogue of somatic mutations from a cancer genome bears the signatures of the mutational processes that have been operative. Here we analysed 4,938,362 mutations from 7,042 cancers and extracted more than 20 distinct mutational signatures. Some are present in many cancer types, notably a signature attributed to the APOBEC family of cytidine deaminases, whereas others are confined to a single cancer class. Certain signatures are associated with age of the patient at cancer diagnosis, known mutagenic exposures or defects in DNA maintenance, but many are of cryptic origin. In addition to these genome-wide mutational signatures, hypermutation localized to small genomic regions, 'kataegis', is found in many cancer types. The results reveal the diversity of mutational processes underlying the development of cancer, with potential implications for understanding of cancer aetiology, prevention and therapy

Deep sequencing analysis of the heterogeneity of seed and commercial lots of the bacillus Calmette-Guerin (BCG) tuberculosis vaccine substrain Tokyo-172

BCG, only vaccine available to prevent tuberculosis, was established in the early 20th century by prolonged passaging of a virulent clinical strain of Mycobacterium bovis. BCG Tokyo-172, originally distributed within Japan in 1924, is one of the currently used reference substrains for the vaccine. Recently, this substrain was reported to contain two spontaneously arising, heterogeneous subpopulations (Types I and II). The proportions of the subpopulations changed over time in both distributed seed lots and commercial lots. To maintain the homogeneity of live vaccines, such variations and subpopulational mutations in lots should be restrained and monitored. We incorporated deep sequencing techniques to validate such heterogeneity in lots of the BCG Tokyo-172 substrain without cloning. By bioinformatics analysis, we not only detected the two subpopulations but also detected two intrinsic variations within these populations. The intrinsic variants could be isolated from respective lots as colonies cultured on plate media, suggesting analyses incorporating deep sequencing techniques are powerful, valid tools to detect mutations in live bacterial vaccine lots. Our data showed that spontaneous mutations in BCG vaccines could be easily monitored by deep sequencing without direct isolation of variants, revealing the complex heterogeneity of BCG Tokyo-172 and its daughter lots currently in use

Pan-cancer analysis of whole genomes

Cancer is driven by genetic change, and the advent of massively parallel sequencing has enabled systematic documentation of this variation at the whole-genome scale(1-3). Here we report the integrative analysis of 2,658 whole-cancer genomes and their matching normal tissues across 38 tumour types from the Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium of the International Cancer Genome Consortium (ICGC) and The Cancer Genome Atlas (TCGA). We describe the generation of the PCAWG resource, facilitated by international data sharing using compute clouds. On average, cancer genomes contained 4-5 driver mutations when combining coding and non-coding genomic elements; however, in around 5% of cases no drivers were identified, suggesting that cancer driver discovery is not yet complete. Chromothripsis, in which many clustered structural variants arise in a single catastrophic event, is frequently an early event in tumour evolution; in acral melanoma, for example, these events precede most somatic point mutations and affect several cancer-associated genes simultaneously. Cancers with abnormal telomere maintenance often originate from tissues with low replicative activity and show several mechanisms of preventing telomere attrition to critical levels. Common and rare germline variants affect patterns of somatic mutation, including point mutations, structural variants and somatic retrotransposition. A collection of papers from the PCAWG Consortium describes non-coding mutations that drive cancer beyond those in the TERT promoter(4); identifies new signatures of mutational processes that cause base substitutions, small insertions and deletions and structural variation(5,6); analyses timings and patterns of tumour evolution(7); describes the diverse transcriptional consequences of somatic mutation on splicing, expression levels, fusion genes and promoter activity(8,9); and evaluates a range of more-specialized features of cancer genomes(8,10-18).Peer reviewe