Cubical Type Theory: A Constructive Interpretation of the Univalence Axiom

This paper presents a type theory in which it is possible to directly manipulate $n$-dimensional cubes (points, lines, squares, cubes, etc.) based on an interpretation of dependent type theory in a cubical set model. This enables new ways to reason about identity types, for instance, function extensionality is directly provable in the system. Further, Voevodsky\u27s univalence axiom is provable in this system. We also explain an extension with some higher inductive types like the circle and propositional truncation. Finally we provide semantics for this cubical type theory in a constructive meta-theory

Cubical Type Theory: a constructive interpretation of the univalence axiom

International audienceThis paper presents a type theory in which it is possible to directly manipulate n-dimensional cubes (points, lines, squares, cubes, etc.) based on an interpretation of dependent type theory in a cubical set model. This enables new ways to reason about identity types, for instance, function extensionality is directly provable in the system. Further, Voevodsky's univalence axiom is provable in this system. We also explain an extension with some higher inductive types like the circle and propositional truncation. Finally we provide semantics for this cubical type theory in a constructive meta-theory

Association of YY1 with maternal mRNAs in oocyte mRNPs

Early embryonic development in vertebrates is directed in part by maternal mRNAs expressed in oocytes and stored in cytoplasmic messenger ribonucleoprotein particles (mRNPs). Abundant evidence demonstrates the importance of mRNPs in embryonic development and in post-embryonic cellular function; however their characterization has been hampered by lack of suitable methodologies. The Xenopus oocyte has been the primary model system for studies of mRNPs. YY1 is a well-studied transcriptional regulatory factor that is sequestered in the oocyte cytoplasm and present entirely in cytoplasmic oocyte mRNPs. The objective of this thesis was to examine the biochemistry of YY1 association with maternal mRNA molecules in order to shed light on the role of YY1 in development and the poorly understood biology of oocyte mRNPs. The initial working hypotheses were that association of YY1 with mRNPs is dependent on sequence-specific RNA-binding activity and, therefore, that YY1 associates with a definite subset of maternal mRNA. A number of unique methods were developed in this study to address these hypotheses. RNA immunoprecipitation-DNA microarray (RIP-CHIP) analysis establishes that YY1 associates with a subset of mRNAs in the oocyte pool. A novel sequence-specific RNA-binding activity of the YY1 protein is demonstrated, and the RNA-binding activity of YY1 is shown to be required for its association with oocyte mRNPs in vivo. The functional roles of YY1 mRNA substrates are discussed in the context of embryological development and the biological function of YY1 in oocyte mRNPs. Extension of the experimental approaches developed in this thesis to the entire set of mRNP proteins would significantly advance our understanding of mRNP composition and heterogeneity, as well as the biological function of maternal mRNAs and mRNPs in development

Sequence-dependent thermodynamics of a coarse-grained DNA model

We introduce a sequence-dependent parametrization for a coarse-grained DNA model [T. E. Ouldridge, A. A. Louis, and J. P. K. Doye, J. Chem. Phys. 134, 085101 (2011)] originally designed to reproduce the properties of DNA molecules with average sequences. The new parametrization introduces sequence-dependent stacking and base-pairing interaction strengths chosen to reproduce the melting temperatures of short duplexes. By developing a histogram reweighting technique, we are able to fit our parameters to the melting temperatures of thousands of sequences. To demonstrate the flexibility of the model, we study the effects of sequence on: (a) the heterogeneous stacking transition of single strands, (b) the tendency of a duplex to fray at its melting point, (c) the effects of stacking strength in the loop on the melting temperature of hairpins, (d) the force-extension properties of single strands and (e) the structure of a kissing-loop complex. Where possible we compare our results with experimental data and find a good agreement. A simulation code called oxDNA, implementing our model, is available as free software.Comment: 15 page

Pressure-dependent EPANET extension

In water distribution systems (WDSs), the available flow at a demand node is dependent on the pressure at that node. When a network is lacking in pressure, not all consumer demands will be met in full. In this context, the assumption that all demands are fully satisfied regardless of the pressure in the system becomes unreasonable and represents the main limitation of the conventional demand driven analysis (DDA) approach to WDS modelling. A realistic depiction of the network performance can only be attained by considering demands to be pressure dependent. This paper presents an extension of the renowned DDA based hydraulic simulator EPANET 2 to incorporate pressure-dependent demands. This extension is termed “EPANET-PDX” (pressure-dependent extension) herein. The utilization of a continuous nodal pressure-flow function coupled with a line search and backtracking procedure greatly enhance the algorithm’s convergence rate and robustness. Simulations of real life networks consisting of multiple sources, pipes, valves and pumps were successfully executed and results are presented herein. Excellent modelling performance was achieved for analysing both normal and pressure deficient conditions of the WDSs. Detailed computational efficiency results of EPANET-PDX with reference to EPANET 2 are included as well