Realms: A Structure for Consolidating Knowledge about Mathematical Theories

Since there are different ways of axiomatizing and developing a mathematical theory, knowledge about a such a theory may reside in many places and in many forms within a library of formalized mathematics. We introduce the notion of a realm as a structure for consolidating knowledge about a mathematical theory. A realm contains several axiomatizations of a theory that are separately developed. Views interconnect these developments and establish that the axiomatizations are equivalent in the sense of being mutually interpretable. A realm also contains an external interface that is convenient for users of the library who want to apply the concepts and facts of the theory without delving into the details of how the concepts and facts were developed. We illustrate the utility of realms through a series of examples. We also give an outline of the mechanisms that are needed to create and maintain realms.Comment: As accepted for CICM 201

The Multi-Configurational Hartree-Fock close-coupling ansatz: application to Argon photoionization cross section and delays

We present a robust, ab initio method for addressing atom-light interactions and apply it to photoionization of argon. We use a close-coupling ansatz constructed on a multi-configurational Hartree-Fock description of localized states and B-spline expansions of the electron radial wave functions. In this implementation, the general many-electron problem can be tackled thanks to the use of the ATSP2K libraries [CPC 176 (2007) 559]. In the present contribution, we combine this method with exterior complex scaling, thereby allowing for the computation of the complex partial amplitudes that encode the whole dynamics of the photoionization process. The method is validated on the 3s3p6np series of resonances converging to the 3s extraction. Then, it is used for computing the energy dependent differential atomic delay between 3p and 3s photoemission, and agreement is found with the measurements of Gu\'enot et al. [PRA 85 (2012) 053424]. The effect of the presence of resonances in the one-photon spectrum on photoionization delay measurements is studied.Comment: 15 pages, 8 figures, 4 table

Coalescence of the sites of cowpea mosaic virus RNA replication into a cytopathic structure

Cowpea mosaic virus (CPMV) replication induces an extensive proliferation of endoplasmic reticulum (ER) membranes, leading to the formation of small membranous vesicles where viral RNA replication takes place. Using fluorescent in situ hybridization, we found that early in the infection of cowpea protoplasts, CPMV plus-strand RNA accumulates at numerous distinct subcellular sites distributed randomly throughout the cytoplasm which rapidly coalesce into a large body located in the center of the cell, often near the nucleus. The combined use of immunostaining and a green fluorescent protein ER marker revealed that during the course of an infection, CPMV RNA colocalizes with the 110-kDa viral polymerase and other replication proteins and is always found in close association with proliferated ER membranes, indicating that these sites correspond to the membranous site of viral replication. Experiments with the cytoskeleton inhibitors oryzalin and latrunculin B point to a role of actin and not tubulin in establishing the large central structure. The induction of ER membrane proliferations in CPMV-infected protoplasts did not coincide with increased levels of BiP mRNA, indicating that the unfolded-protein response is not involved in this proces

Theory Morphisms in Church's Type Theory with Quotation and Evaluation

${\rm CTT}_{\rm qe}$ is a version of Church's type theory with global quotation and evaluation operators that is engineered to reason about the interplay of syntax and semantics and to formalize syntax-based mathematical algorithms. ${\rm CTT}_{\rm uqe}$ is a variant of ${\rm CTT}_{\rm qe}$ that admits undefined expressions, partial functions, and multiple base types of individuals. It is better suited than ${\rm CTT}_{\rm qe}$ as a logic for building networks of theories connected by theory morphisms. This paper presents the syntax and semantics of ${\rm CTT}_{\rm uqe}$, defines a notion of a theory morphism from one ${\rm CTT}_{\rm uqe}$ theory to another, and gives two simple examples that illustrate the use of theory morphisms in ${\rm CTT}_{\rm uqe}$.Comment: 17 page

Syntax for free: representing syntax with binding using parametricity

We show that, in a parametric model of polymorphism, the type ∀ α. ((α → α) → α) → (α → α → α) → α is isomorphic to closed de Bruijn terms. That is, the type of closed higher-order abstract syntax terms is isomorphic to a concrete representation. To demonstrate the proof we have constructed a model of parametric polymorphism inside the Coq proof assistant. The proof of the theorem requires parametricity over Kripke relations. We also investigate some variants of this representation

Formalizing Mathematical Knowledge as a Biform Theory Graph: A Case Study

A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for formalizing algorithms that manipulate mathematical expressions. A theory graph is a network of theories connected by meaning-preserving theory morphisms that map the formulas of one theory to the formulas of another theory. Theory graphs are in turn well suited for formalizing mathematical knowledge at the most convenient level of abstraction using the most convenient vocabulary. We are interested in the problem of whether a body of mathematical knowledge can be effectively formalized as a theory graph of biform theories. As a test case, we look at the graph of theories encoding natural number arithmetic. We used two different formalisms to do this, which we describe and compare. The first is realized in ${\rm CTT}_{\rm uqe}$, a version of Church's type theory with quotation and evaluation, and the second is realized in Agda, a dependently typed programming language.Comment: 43 pages; published without appendices in: H. Geuvers et al., eds, Intelligent Computer Mathematics (CICM 2017), Lecture Notes in Computer Science, Vol. 10383, pp. 9-24, Springer, 201

A theoretical study of the C- 4So_3/2 and 2Do_{3/2,5/2} bound states and C ground configuration: fine and hyperfine structures, isotope shifts and transition probabilities

This work is an ab initio study of the 2p3 4So_3/2, and 2Do_{3/2,5/2} states of C- and 2p2 3P_{0,1,2}, 1D_2, and 1S_0 states of neutral carbon. We use the multi-configuration Hartree-Fock approach, focusing on the accuracy of the wave function itself. We obtain all C- detachment thresholds, including correlation effects to about 0.5%. Isotope shifts and hyperfine structures are calculated. The achieved accuracy of the latter is of the order of 0.1 MHz. Intra-configuration transition probabilities are also estimated.Comment: 15 pages, 2 figures, 12 table

alpha-Sarcin catalytic activity is not required for cytotoxicity

<p>Abstract</p> <p>Background</p> <p>α-Sarcin is a protein toxin produced by <it>Aspergillus giganteus</it>. It belongs to a family of cytotoxic ribonucleases that inactivate the ribosome and inhibit protein synthesis. α-Sarcin cleaves a single phosphodiester bond within the RNA backbone of the large ribosomal subunit, which makes the ribosome unrecognizable to elongation factors and, in turn, blocks protein synthesis. Although it is widely held that the protein synthesis inhibition caused by the toxin leads to cell death, it has not been directly shown that catalytically inactive mutants of α-sarcin are non-toxic when expressed directly within the cytoplasm of cells. This is important since recent studies have cast doubt on whether protein synthesis inhibition is sufficient to initiate apoptosis.</p> <p>Results</p> <p>In this report, we assay α-sarcin cytotoxicity and ability to inhibit protein synthesis by direct cytoplasmic expression. We show that mutations in α-sarcin, which impair α-sarcin's ability to inhibit protein synthesis, do not affect its cytotoxicity. The mutants are unable to activate JNK, confirming that the sarcin-ricin loop remains intact and that the α-sarcin mutants are catalytically inactive. In addition, both mutant and wildtype variants of α-sarcin localize to the nucleus and cytoplasm, where they co-localize with ribosomal marker RPS6.</p> <p>Conclusion</p> <p>We conclude that although protein synthesis inhibition likely contributes to cell death, it is not required. Thus, our results suggest that α-sarcin can promote cell death through a previously unappreciated mechanism that is independent of rRNA cleavage and JNK activation.</p