An Explicit Framework for Interaction Nets

Interaction nets are a graphical formalism inspired by Linear Logic proof-nets often used for studying higher order rewriting e.g. \Beta-reduction. Traditional presentations of interaction nets are based on graph theory and rely on elementary properties of graph theory. We give here a more explicit presentation based on notions borrowed from Girard's Geometry of Interaction: interaction nets are presented as partial permutations and a composition of nets, the gluing, is derived from the execution formula. We then define contexts and reduction as the context closure of rules. We prove strong confluence of the reduction within our framework and show how interaction nets can be viewed as the quotient of some generalized proof-nets

Dagger Categories of Tame Relations

Within the context of an involutive monoidal category the notion of a comparison relation is identified. Instances are equality on sets, inequality on posets, orthogonality on orthomodular lattices, non-empty intersection on powersets, and inner product on vector or Hilbert spaces. Associated with a collection of such (symmetric) comparison relations a dagger category is defined with "tame" relations as morphisms. Examples include familiar categories in the foundations of quantum mechanics, such as sets with partial injections, or with locally bifinite relations, or with formal distributions between them, or Hilbert spaces with bounded (continuous) linear maps. Of one particular example of such a dagger category of tame relations, involving sets and bifinite multirelations between them, the categorical structure is investigated in some detail. It turns out to involve symmetric monoidal dagger structure, with biproducts, and dagger kernels. This category may form an appropriate universe for discrete quantum computations, just like Hilbert spaces form a universe for continuous computation

Deep generative modeling for single-cell transcriptomics.

Single-cell transcriptome measurements can reveal unexplored biological diversity, but they suffer from technical noise and bias that must be modeled to account for the resulting uncertainty in downstream analyses. Here we introduce single-cell variational inference (scVI), a ready-to-use scalable framework for the probabilistic representation and analysis of gene expression in single cells ( https://github.com/YosefLab/scVI ). scVI uses stochastic optimization and deep neural networks to aggregate information across similar cells and genes and to approximate the distributions that underlie observed expression values, while accounting for batch effects and limited sensitivity. We used scVI for a range of fundamental analysis tasks including batch correction, visualization, clustering, and differential expression, and achieved high accuracy for each task

On the reaction time of some synchronous systems

This paper presents an investigation of the notion of reaction time in some synchronous systems. A state-based description of such systems is given, and the reaction time of such systems under some classic composition primitives is studied. Reaction time is shown to be non-compositional in general. Possible solutions are proposed, and applications to verification are discussed. This framework is illustrated by some examples issued from studies on real-time embedded systems.Comment: In Proceedings ICE 2011, arXiv:1108.014

Normalizing single-cell RNA sequencing data: challenges and opportunities

Single-cell transcriptomics is becoming an important component of the molecular biologist's toolkit. A critical step when analyzing data generated using this technology is normalization. However, normalization is typically performed using methods developed for bulk RNA sequencing or even microarray data, and the suitability of these methods for single-cell transcriptomics has not been assessed. We here discuss commonly used normalization approaches and illustrate how these can produce misleading results. Finally, we present alternative approaches and provide recommendations for single-cell RNA sequencing users

Decoding the regulatory network of early blood development from single-cell gene expression measurements.

Reconstruction of the molecular pathways controlling organ development has been hampered by a lack of methods to resolve embryonic progenitor cells. Here we describe a strategy to address this problem that combines gene expression profiling of large numbers of single cells with data analysis based on diffusion maps for dimensionality reduction and network synthesis from state transition graphs. Applying the approach to hematopoietic development in the mouse embryo, we map the progression of mesoderm toward blood using single-cell gene expression analysis of 3,934 cells with blood-forming potential captured at four time points between E7.0 and E8.5. Transitions between individual cellular states are then used as input to develop a single-cell network synthesis toolkit to generate a computationally executable transcriptional regulatory network model of blood development. Several model predictions concerning the roles of Sox and Hox factors are validated experimentally. Our results demonstrate that single-cell analysis of a developing organ coupled with computational approaches can reveal the transcriptional programs that underpin organogenesis.We thank J. Downing (St. Jude Children's Research Hospital, Memphis, TN, USA) for the Runx1-ires-GFP mouse. Research in the authors' laboratory is supported by the Medical Research Council, Biotechnology and Biological Sciences Research Council, Leukaemia and Lymphoma Research, the Leukemia and Lymphoma Society, Microsoft Research and core support grants by the Wellcome Trust to the Cambridge Institute for Medical Research and Wellcome Trust - MRC Cambridge Stem Cell Institute. V.M. is supported by a Medical Research Council Studentship and Centenary Award and S.W. by a Microsoft Research PhD Scholarship.This is the accepted manuscript for a paper published in Nature Biotechnology 33, 269–276 (2015) doi:10.1038/nbt.315

T cell cytolytic capacity is independent of initial stimulation strength.

How cells respond to myriad stimuli with finite signaling machinery is central to immunology. In naive T cells, the inherent effect of ligand strength on activation pathways and endpoints has remained controversial, confounded by environmental fluctuations and intercellular variability within populations. Here we studied how ligand potency affected the activation of CD8+ T cells in vitro, through the use of genome-wide RNA, multi-dimensional protein and functional measurements in single cells. Our data revealed that strong ligands drove more efficient and uniform activation than did weak ligands, but all activated cells were fully cytolytic. Notably, activation followed the same transcriptional pathways regardless of ligand potency. Thus, stimulation strength did not intrinsically dictate the T cell-activation route or phenotype; instead, it controlled how rapidly and simultaneously the cells initiated activation, allowing limited machinery to elicit wide-ranging responses

Single-cell transcriptomics reveals common epithelial response patterns in human acute kidney injury

BACKGROUND: Acute kidney injury (AKI) occurs frequently in critically ill patients and is associated with adverse outcomes. Cellular mechanisms underlying AKI and kidney cell responses to injury remain incompletely understood. METHODS: We performed single-nuclei transcriptomics, bulk transcriptomics, molecular imaging studies, and conventional histology on kidney tissues from 8 individuals with severe AKI (stage 2 or 3 according to Kidney Disease: Improving Global Outcomes (KDIGO) criteria). Specimens were obtained within 1-2 h after individuals had succumbed to critical illness associated with respiratory infections, with 4 of 8 individuals diagnosed with COVID-19. Control kidney tissues were obtained post-mortem or after nephrectomy from individuals without AKI. RESULTS: High-depth single cell-resolved gene expression data of human kidneys affected by AKI revealed enrichment of novel injury-associated cell states within the major cell types of the tubular epithelium, in particular in proximal tubules, thick ascending limbs, and distal convoluted tubules. Four distinct, hierarchically interconnected injured cell states were distinguishable and characterized by transcriptome patterns associated with oxidative stress, hypoxia, interferon response, and epithelial-to-mesenchymal transition, respectively. Transcriptome differences between individuals with AKI were driven primarily by the cell type-specific abundance of these four injury subtypes rather than by private molecular responses. AKI-associated changes in gene expression between individuals with and without COVID-19 were similar. CONCLUSIONS: The study provides an extensive resource of the cell type-specific transcriptomic responses associated with critical illness-associated AKI in humans, highlighting recurrent disease-associated signatures and inter-individual heterogeneity. Personalized molecular disease assessment in human AKI may foster the development of tailored therapies

Resolving early mesoderm diversification through single-cell expression profiling.

In mammals, specification of the three major germ layers occurs during gastrulation, when cells ingressing through the primitive streak differentiate into the precursor cells of major organ systems. However, the molecular mechanisms underlying this process remain unclear, as numbers of gastrulating cells are very limited. In the mouse embryo at embryonic day 6.5, cells located at the junction between the extra-embryonic region and the epiblast on the posterior side of the embryo undergo an epithelial-to-mesenchymal transition and ingress through the primitive streak. Subsequently, cells migrate, either surrounding the prospective ectoderm contributing to the embryo proper, or into the extra-embryonic region to form the yolk sac, umbilical cord and placenta. Fate mapping has shown that mature tissues such as blood and heart originate from specific regions of the pre-gastrula epiblast, but the plasticity of cells within the embryo and the function of key cell-type-specific transcription factors remain unclear. Here we analyse 1,205 cells from the epiblast and nascent Flk1(+) mesoderm of gastrulating mouse embryos using single-cell RNA sequencing, representing the first transcriptome-wide in vivo view of early mesoderm formation during mammalian gastrulation. Additionally, using knockout mice, we study the function of Tal1, a key haematopoietic transcription factor, and demonstrate, contrary to previous studies performed using retrospective assays, that Tal1 knockout does not immediately bias precursor cells towards a cardiac fate.We thank M. de Bruijn, A. Martinez-Arias, J. Nichols and C. Mulas for discussion, the Cambridge Institute for Medical Research Flow Cytometry facility for their expertise in single-cell index sorting, and S. Lorenz from the Sanger Single Cell Genomics Core for supervising purification of Tal1−/− sequencing libraries. ChIP-seq reads were processed by R. Hannah. Research in the authors’ laboratories is supported by the Medical Research Council, Cancer Research UK, the Biotechnology and Biological Sciences Research Council, Bloodwise, the Leukemia and Lymphoma Society, and the Sanger-EBI Single Cell Centre, and by core support grants from the Wellcome Trust to the Cambridge Institute for Medical Research and Wellcome Trust - MRC Cambridge Stem Cell Institute and by core funding from Cancer Research UK and the European Molecular Biology Laboratory. Y.T. was supported by a fellowship from the Japan Society for the Promotion of Science. W.J. is a Wellcome Trust Clinical Research Fellow. A.S. is supported by the Sanger-EBI Single Cell Centre. This work was funded as part of Wellcome Trust Strategic Award 105031/D/14/Z ‘Tracing early mammalian lineage decisions by single-cell genomics’ awarded to W. Reik, S. Teichmann, J. Nichols, B. Simons, T. Voet, S. Srinivas, L. Vallier, B. Göttgens and J. Marioni.This is the author accepted manuscript. The final version is available from Nature Publishing Group via http://dx.doi.org/10.1038/nature1863