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Regulated transcription controls the diversity, developmental pathways and spatial organization of the hundreds of cell types that make up a mammal. Using single-molecule cDNA sequencing, we mapped transcription start sites (TSSs) and their usage in human and mouse primary cells, cell lines and tissues to produce a comprehensive overview of mammalian gene expression across the human body. We find that few genes are truly ‘housekeeping’, whereas many mammalian promoters are composite entities composed of several closely separated TSSs, with independent cell-type-specific expression profiles. TSSs specific to different cell types evolve at different rates, whereas promoters of broadly expressed genes are the most conserved. Promoter-based expression analysis reveals key transcription factors defining cell states and links them to binding-site motifs. The functions of identified novel transcripts can be predicted by coexpression and sample ontology enrichment analyses. The functional annotation of the mammalian genome 5 (FANTOM5) project provides comprehensive expression profiles and functional annotation of mammalian cell-type-specific transcriptomes with wide applications in biomedical research. A study from the FANTOM consortium using single-molecule cDNA sequencing of transcription start sites and their usage in human and mouse primary cells, cell lines and tissues reveals insights into the specificity and diversity of transcription patterns across different mammalian cell types. Mapping the human transcription FANTOM5 (standing for functional annotation of the mammalian genome 5) is the fifth major stage of a major international collaboration that aims to dissect the transcriptional regulatory networks that define every human cell type. Two Articles in this issue of Nature present some of the project's latest results. The first paper uses the FANTOM5 panel of tissue and primary cell samples to define an atlas of active, in vivo bidirectionally transcribed enhancers across the human body. These authors show that bidirectional capped RNAs are a signature feature of active enhancers and identify more than 40,000 enhancer candidates from over 800 human cell and tissue samples. The enhancer atlas is used to compare regulatory programs between different cell types and identify disease-associated regulatory SNPs, and will be a resource for studies on cell-type-specific enhancers. In the second paper, single-molecule sequencing is used to map human and mouse transcription start sites and their usage in a panel of distinct human and mouse primary cells, cell lines and tissues to produce the most comprehensive mammalian gene expression atlas to date. The data provide a plethora of insights into open reading frames and promoters across different cell types in addition to valuable annotation of mammalian cell-type-specific transcriptomes.

This paper concerns the notions of closed and open maps in the setting of partial frames, which, in contrast to full frames, do not necessarily have all joins. Examples of these include bounded distributive lattices, σ - and κ -frames and full frames. We define closed and open maps using geometrically intuitively appealing conditions involving preservation of closed, respectively open, congruences under certain maps. We then characterize them in terms of algebraic identities involving adjoints. We note that partial frame maps need have neither right nor left adjoints whereas frame maps of course always have right adjoints. The embedding of a partial frame in either its free frame or its congruence frame has proved illuminating and useful. We consider the conditions under which these embeddings are closed, open or skeletal. We then look at preservation and reflection of closed or open maps under the functors providing the free frame or the congruence frame. Points arise naturally in the construction of the spectrum functor for partial frames to partial spaces. They may be viewed as maps from the given partial frame to the 2-chain or as certain kinds of filters; using the former description we consider closed and open points. Any point of a partial frame extends naturally to a point on its free frame and a point on its congruence frame; we consider the closedness or openness of these.

The eukaryotic 5' untranslated region (UTR) is critical for ribosome recruitment to the messenger RNA (mRNA) and start codon choice and plays a major role in the control of translation efficiency and shaping the cellular proteome. The ribosomal initiation complex is assembled on the mRNA via a cap-dependent or cap-independent mechanism. We describe various mechanisms controlling ribosome scanning and initiation codon selection by 5' upstream open reading frames, translation initiation factors, and primary and secondary structures of the 5'UTR, including particular sequence motifs. We also discuss translational control via phosphorylation of eukaryotic initiation factor 2, which is implicated in learning and memory, neurodegenerative diseases, and cancer.

In this paper we connect the well-established discrete frame theory of generalized shift invariant systems to a continuous frame theory. To do so, we let Γj\\Gamma _{\\!j}, j∈Jj \\in J, be a countable family of closed, co-compact subgroups of a second countable locally compact abelian group GG and study systems of the form ⋃j∈J{gj,p(⋅−γ)}γ∈Γj,p∈Pj\\bigcup _{j \\in J}\\{ g_{j,p}(\\cdot - \\gamma )\\}_{\\gamma \\in \\Gamma _{\\!j}, p \\in P_j} with generators gj,pg_{j,p} in L2(G)L^2(G) and with each PjP_j being a countable or an uncountable index set. We refer to systems of this form as generalized translation invariant (GTI) systems. Many of the familiar transforms, e.g., the wavelet, shearlet and Gabor transform, both their discrete and continuous variants, are GTI systems. Under a technical α\\alpha local integrability condition (α\\alpha-LIC) we characterize when GTI systems constitute tight and dual frames that yield reproducing formulas for L2(G)L^2(G). This generalizes results on generalized shift invariant systems, where each PjP_j is assumed to be countable and each Γj\\Gamma _{\\!j} is a uniform lattice in GG, to the case of uncountably many generators and (not necessarily discrete) closed, co-compact subgroups. Furthermore, even in the case of uniform lattices Γj\\Gamma _{\\! j}, our characterizations improve known results since the class of GTI systems satisfying the α\\alpha-LIC is strictly larger than the class of GTI systems satisfying the previously used local integrability condition. As an application of our characterization results, we obtain new characterizations of translation invariant continuous frames and Gabor frames for L2(G)L^2(G). In addition, we will see that the admissibility conditions for the continuous and discrete wavelet and Gabor transform in L2(Rn)L^2(\\mathbb {R}^n) are special cases of the same general characterizing equations.

The main purpose of this paper is to establish some new sufficient conditions under which shift-invariant systems become frames in L super(2)( super( )n. As applications, we obtain new results for Gabor frames.

In this work, we start by introducing a general methodology to generate new relay fusion frames from given ones, namely the Spatial Complement Method, and analyze the relationships between the parameters of the original and the new relay fusion frame. We then present another simple approach to obtain relay fusion frames by considering fusion frames for its components. An explicit characterization concerning the existence of Parseval relay fusion frame consisting of two initial subspaces is given. Moreover, we obtain a necessary and sufficient condition under which the spatial complements of alternate dual relay fusion frames remain to be alternate dual relay fusion frames. Some results about Bessel relay fusion sequences are included. Finally, several examples are also given.