Volumetric finite-element modelling of biological growth

Differential growth is the driver of tissue morphogenesis in plants, and also plays a fundamental role in animal development. Although the contributions of growth to shape change have been captured through modelling tissue sheets or isotropic volumes, a framework for modelling both isotropic and anisotropic volumetric growth in three dimensions over large changes in size and shape has been lacking. Here, we describe an approach based on finite-element modelling of continuous volumetric structures, and apply it to a range of forms and growth patterns, providing mathematical validation for examples that admit analytic solution. We show that a major difference between sheet and bulk tissues is that the growth of bulk tissue is more constrained, reducing the possibility of tissue conflict resolution through deformations such as buckling. Tissue sheets or cylinders may be generated from bulk shapes through anisotropic specified growth, oriented by a polarity field. A second polarity field, orthogonal to the first, allows sheets with varying lengths and widths to be generated, as illustrated by the wide range of leaf shapes observed in nature. The framework we describe thus provides a key tool for developing hypotheses for plant morphogenesis and is also applicable to other tissues that deform through differential growth or contraction

Evolution of flowers and inflorescences

Plant development depends on the activity of meristems which continually reiterate a common plan. Permutations around this plan can give rise to a wide range of morphologies. To understand the mechanisms underlying this variation, the effects of parallel mutations in key developmental genes are being studied in different species. In Antirrhinum, three of these key genes are: (l)floricaula ffio) a gene required for the production of flowers (2) centror&- dialis (cen), a gene controlling flower position (3) cycloidea (cyc), a gene controlling flower symmetry. Several plant species, exhibiting a range of inflorescence types and floral symmetries are being analysed in detail. Comparative genetic and molecular analysis shows that inflorescence architecture depends on two underlying parameters: a basic inflorescence branching pattern and the positioning of flowers. Theflo and cen genes play a key role in the positioning of flowers, and variation in the site and timing of expression of these genes, may account for many of the different inflorescence types. The evolution of inflorescence stiucture may also have influenced the evolution of floral asymmetry, as illustrated by the cen mutation which changes both inflorescence type and the symmetry of some flowers. Conflicting theories about the origins of irregular flowers and how they have coevolved with inflorescence architecture can be directly assessed by examining the role of cyc- and cen-like genes in species displaying various floral symmetries and inflorescence types

A Bi-Directional Refinement Algorithm for the Calculus of (Co)Inductive Constructions

The paper describes the refinement algorithm for the Calculus of (Co)Inductive Constructions (CIC) implemented in the interactive theorem prover Matita. The refinement algorithm is in charge of giving a meaning to the terms, types and proof terms directly written by the user or generated by using tactics, decision procedures or general automation. The terms are written in an "external syntax" meant to be user friendly that allows omission of information, untyped binders and a certain liberal use of user defined sub-typing. The refiner modifies the terms to obtain related well typed terms in the internal syntax understood by the kernel of the ITP. In particular, it acts as a type inference algorithm when all the binders are untyped. The proposed algorithm is bi-directional: given a term in external syntax and a type expected for the term, it propagates as much typing information as possible towards the leaves of the term. Traditional mono-directional algorithms, instead, proceed in a bottom-up way by inferring the type of a sub-term and comparing (unifying) it with the type expected by its context only at the end. We propose some novel bi-directional rules for CIC that are particularly effective. Among the benefits of bi-directionality we have better error message reporting and better inference of dependent types. Moreover, thanks to bi-directionality, the coercion system for sub-typing is more effective and type inference generates simpler unification problems that are more likely to be solved by the inherently incomplete higher order unification algorithms implemented. Finally we introduce in the external syntax the notion of vector of placeholders that enables to omit at once an arbitrary number of arguments. Vectors of placeholders allow a trivial implementation of implicit arguments and greatly simplify the implementation of primitive and simple tactics

Implementing Type Theory in Higher Order Constraint Logic Programming

International audienceIn this paper we are interested in high-level programming languages to implement the core components of an interactive theorem prover for a dependently typed language: the kernel — responsible for type-checking closed terms — and the elaborator — that manipulates terms with holes or, equivalently, partial proof terms. In the first part of the paper we confirm that λProlog, the language developed by Miller and Nadathur since the 80s, is extremely suitable for implementing the kernel, even when efficient techniques like reduction machines are employed. In the second part of the paper we turn our attention to the elaborator and we observe that the eager generative semantics inherited by Prolog makes it impossible to reason by induction over terms containing metavariables. We also conclude that the minimal extension to λProlog that allows to do so is the possibility to delay inductive predicates over flexible terms, turning them into (set of) constraints to be propagated according to user provided constraint propagation rules. Therefore we propose extensions to λProlog to declare and manipulate higher order constraints, and we implement the proposed extensions in the ELPI system. Our test case is the implementation of an elaborator for a type theory as a CLP extension to a kernel written in plain λProlog

Implementing HOL in an Higher Order Logic Programming Language

International audienceWe present a proof-of-concept prototype of a (constructive variant of an) HOL interactive theorem prover written in a Higher Order Logic Programming (HOLP) language, namely an extension of λProlog. The prototype is meant to support the claim, that we reinforce , that HOLP is the class of languages that provides the right abstraction level and programming primitives to obtain concise implementations of theorem provers. We identify and advocate for a programming technique, that we call semi-shallow embedding, while at the same time identifying the reasons why pure λProlog is not sufficient to support that technique, and it needs to be extended

Ectopic BASL Reveals Tissue Cell Polarity throughout Leaf Development in Arabidopsis thaliana

Tissue-wide polarity fields, in which cell polarity is coordinated across the tissue, have been described for planar organs such as the Drosophila wing and are considered important for coordinating growth and differentiation [1]. In planar plant organs, such as leaves, polarity fields have been identified for subgroups of cells, such as stomatal lineages [2], trichomes [3, 4], serrations [5], or early developmental stages [6]. Here, we show that ectopic induction of the stomatal protein BASL (BREAKING OF ASYMMETRY IN THE STOMATAL LINEAGE) reveals a tissue-wide epidermal polarity field in leaves throughout development. Ectopic GFP-BASL is typically localized toward the proximal end of cells and to one lobe of mature pavement cells, revealing a polarity field that aligns with the proximodistal axis of the leaf (base to tip). The polarity field is largely parallel to the midline of the leaf but diverges in more lateral positions, particularly at later stages in development, suggesting it may be deformed during growth. The polarity field is observed in the speechless mutant, showing that it is independent of stomatal lineages, and is observed in isotropic cells, showing that cell shape anisotropy is not required for orienting polarity. Ectopic BASL forms convergence and divergence points at serrations, mirroring epidermal PIN polarity patterns, suggesting a common underlying polarity mechanism. Thus, we show that similar to the situation in animals, planar plant organs have a tissue-wide cell polarity field, and this may provide a general cellular mechanism for guiding growth and differentiation

Homeotic genes controlling flower development in Antirrhinum

In order to study genes controlling flower development, we have carried out an extensive transposon-mutagenesis experiment in Antirrhinum majus. More than 15 independent homeotic mutations were obtained, allowing three categories of genes to be defined. The first includes floricaula (flo), a primary gene required for the initiation of the floral developmental pathway. In the absence of the wild-type flo product, proliferating inflorescence meristems arise in place of flowers. The flo gene has been isolated and shown to be expressed transiently in a subset of organ primordia in the floral meristem. The second category includes genes that affect the identity, and also sometimes the number, of whorls of organs in the flower. These genes act in overlapping domains so that each whorl has a distinct combination of gene functions, suggesting a model for the genetic control of whorl identity and number. Genes of the third category control differences between organs in the same whorl and hence the overall symmetry of the flower. We discuss how the basic plan of the flower and inflorescence may arise through the interactions between the three categories of genes

Assessment of bias in scoring of AI-based radiotherapy segmentation and planning studies using modified TRIPOD and PROBAST guidelines as an example

BACKGROUND AND PURPOSE Studies investigating the application of Artificial Intelligence (AI) in the field of radiotherapy exhibit substantial variations in terms of quality. The goal of this study was to assess the amount of transparency and bias in scoring articles with a specific focus on AI based segmentation and treatment planning, using modified PROBAST and TRIPOD checklists, in order to provide recommendations for future guideline developers and reviewers. MATERIALS AND METHODS The TRIPOD and PROBAST checklist items were discussed and modified using a Delphi process. After consensus was reached, 2 groups of 3 co-authors scored 2 articles to evaluate usability and further optimize the adapted checklists. Finally, 10 articles were scored by all co-authors. Fleiss' kappa was calculated to assess the reliability of agreement between observers. RESULTS Three of the 37 TRIPOD items and 5 of the 32 PROBAST items were deemed irrelevant. General terminology in the items (e.g., multivariable prediction model, predictors) was modified to align with AI-specific terms. After the first scoring round, further improvements of the items were formulated, e.g., by preventing the use of sub-questions or subjective words and adding clarifications on how to score an item. Using the final consensus list to score the 10 articles, only 2 out of the 61 items resulted in a statistically significant kappa of 0.4 or more demonstrating substantial agreement. For 41 items no statistically significant kappa was obtained indicating that the level of agreement among multiple observers is due to chance alone. CONCLUSION Our study showed low reliability scores with the adapted TRIPOD and PROBAST checklists. Although such checklists have shown great value during development and reporting, this raises concerns about the applicability of such checklists to objectively score scientific articles for AI applications. When developing or revising guidelines, it is essential to consider their applicability to score articles without introducing bias

ELPI: fast, Embeddable, λProlog Interpreter

International audienceWe present a new interpreter for λProlog that runs consistently faster than the byte code compiled by Teyjus, that is believed to be the best available implementation of λProlog. The key insight is the identification of a fragment of the language, which we call reduction-free fragment (L β λ), that occurs quite naturally in λProlog programs and that admits constant time reduction and unification rules