Extrapolation-Based Implicit-Explicit Peer Methods with Optimised Stability Regions

In this paper we investigate a new class of implicit-explicit (IMEX) two-step methods of Peer type for systems of ordinary differential equations with both non-stiff and stiff parts included in the source term. An extrapolation approach based on already computed stage values is applied to construct IMEX methods with favourable stability properties. Optimised IMEX-Peer methods of order p = 2, 3, 4, are given as result of a search algorithm carefully designed to balance the size of the stability regions and the extrapolation errors. Numerical experiments and a comparison to other implicit-explicit methods are included.Comment: 21 pages, 6 figure

Extrapolation-Based Implicit-Explicit Peer Methods with Optimised Stability Regions

In this paper we investigate an new class of implicit-explicit two-step methods of Peer type for systems of ordinary differential equations with both non-stiff and stiff parts included in the source term. An extrapolation approach based on already computed stage values with equally high consistency order is applied to construct such methods with strong stability properties. Optimised implicit-explicit Peer methods of order p=2,3,4, are given as result of a search algorithm carefully designed to balance the size of the stability regions and the extrapolation errors. Numerical experiments and a comparison to other implicit-explicit methods are included

Discrete variable methods for delay-differential equations with threshold-type delays

AbstractWe study numerical solution of systems of delay-differential equations in which the delay function, which depends on the unknown solution, is defined implicitly by the threshold condition. We study discrete variable numerical methods for these problems and present error analysis. The global error is composed of the error of solving the differential systems, the error from the threshold conditions and the errors in delay arguments. Our theoretical analysis is confirmed by numerical experiments on threshold problems from the theory of epidemics and from population dynamics

Achieving Heisenberg Scaling via interacting many-body dynamics

Màster Oficial de Ciència i Tecnologia Quàntiques / Quantum Science and Technology, Facultat de Física, Universitat de Barcelona. Curs: 2022-2023. Tutors: Martí Peranrnau-Llobet, John CalsamigliaTheoretical models describing quantum metrology schemes and the corresponding experimental demonstrations have so far mainly described step-bystep protocols that involve the preparation of the sensor into a carefully engineered quantum state; interaction of the sensor with an external (unknown) field and measurement of the sensor to retrieve information about the signal. However, the process of preparation can sometimes be lengthy and require fine tuning in time. The main goal of this project is to contribute to this challenge by using many-body interactions to entangle the state while field encodes its information into it. In this way the process of preparing the state is eliminated along with the different challenges that come with it

Dynamique des corps lipidiques dans la graine d'Arabidopsis thaliana

Chez les végétaux, les lipides de réserve sont stockés dans des structures subcellulaires, les corps lipidiques (CL). Ces organelles quasi-sphériques sont constituées d'un coeur de triacylglyceérols (TAGs), entourés d'une monocouche de phospholipides (PLs) et sont produites à partir du réticulum endoplasmique avant d'être libérés dans le cytoplasme cellulaire. Les oléosines, dont il existe 5 isoformes graine spécifiques (S1 à S5) chez Arabidopsis thaliana, sont des protéines majeures du CL, insérées à la surface de sa demi-membrane. La dynamique du CL (chargement/déchargement en huile) est complexe et reste largement mal comprise. L'objectif de ce travail est de modéliser la formation et la dynamique des corps lipidiques dans la graine en développement de l'espèce Arabidopsis thaliana, afin de mieux appréhender les mécanismes responsables de la biogenèse et la dynamique des CLs. L utilisation de colorants des lipides neutres constituant les CLs, couplée à la microscopie confocale, a permis l obtention de piles d images de CLs d embryons à différents jours du développement, en contexte sauvage et en contexte déplétif pour une, deux ou trois oléosines (S1, S3 et S4). - Un pipeline de segmentation d'images a tout d abord été développé pour extraire différents estimateurs caractérisant la taille et la dispersion spatiale des corps lipidiques. Les estimateurs ont permis d'analyser l'évolution de la taille et de la dispersion spatiale des corps lipidiques en fonction du temps du développement, et de mettre en évidence la variabilité entre génotypes.- Ces données ont ensuite été analysées et étudiées statistiquement par des approches utilisant des modèles linéaires et des modèle quantile qui ont permis de conclure sur l'effet de chacune des oléosines étudiées, ainsi que celui de leurs interactions, sur la distribution des corps lipidiques.- Enfin, un modèle décrivant la dynamique de coalescence de la population des corps lipidiques a été proposé, simulé numériquement, puis comparé aux données expérimentales. Ce modèle a permis de tester différentes hypothèses de la dynamique de biogenèse et de croissance par coalescence du corps lipidique formalisées dans le modèle mathématique. Différents effets de la composition du corps lipidique en oléosines sur la vitesse de coalescence des corps lipidiques ont été mis en évidence. Les résultats de ces trois axes ont permis de proposer et discuter des rôles associés à chacune oléosine dans une perspective de compréhension des mécanismes mis en œuvre dans la dynamique du corps lipidique.In plants, lipid reserves are stored in subcellular structures called lipid bodies (LB). These virtually spherical organelles consist of a core of triacylglycerols (TAG), surrounded by a monolayer of phospholipids (PLs), are produced from the endoplasmic reticulum and then released into the cell cytoplasm. Oleosins, composed of five seed-specific isoforms (S1 to S5) in Arabidopsis thaliana, are major proteins of the LB, inserted on the surface of the half-membrane. The dynamics of LB (charging / uncharging oil) is complex and remains largely misunderstood. The objective of this work is to model the formation and dynamics of lipid bodies in the developing seed of Arabidopsis thaliana, to better understand the mechanisms responsible for the biogenesis and dynamics of LBs. The use of dyes staining neutral lipids constituting the LD, coupled with confocal microscopy, allowed obtaining image stacks of LB from embryos at different days of development, in a wild-type or depleted (mutant) context for one, two or three oleosins (S1, S3 and S4).- An image segmentation pipeline has been first developed, enabling extraction of various estimators for characterizing the size and spatial dispersion of the lipid bodies. Estimators were used to analyse the evolution of the size and spatial dispersion of lipid bodies as a function of stage of development, and to highlight the variability between genotypes.- These data were then processed and statistically analysed by approaches using linear as well as quantile model that concluded on the effect of each of oleosins investigated as well as their interactions on the distribution of lipid bodies.- Last, a model describing the coalescence dynamics of LB populations has been proposed, digitally simulated and compared to experimental data sets. This model was used to test various hypotheses on the dynamics of biogenesis and coalescence-based growth of lipid bodies as formalized according to the mathematical model. Several effects of oleosin composition on LB coalescence rate have been highlighted. The results of these three axes allowed to propose and discuss the roles associated with each oleosin in the broader perspective of understanding the mechanisms involved in the lipid bodies dynamics.PARIS11-SCD-Bib. électronique (914719901) / SudocSudocFranceF

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions

Fully Composable and Adequate Verified Compilation with Direct Refinements between Open Modules (Technical Report)

Verified compilation of open modules (i.e., modules whose functionality depends on other modules) provides a foundation for end-to-end verification of modular programs ubiquitous in contemporary software. However, despite intensive investigation in this topic for decades, the proposed approaches are still difficult to use in practice as they rely on assumptions about the internal working of compilers which make it difficult for external users to apply the verification results. We propose an approach to verified compositional compilation without such assumptions in the setting of verifying compilation of heterogeneous modules written in first-order languages supporting global memory and pointers. Our approach is based on the memory model of CompCert and a new discovery that a Kripke relation with a notion of memory protection can serve as a uniform and composable semantic interface for the compiler passes. By absorbing the rely-guarantee conditions on memory evolution for all compiler passes into this Kripke Memory Relation and by piggybacking requirements on compiler optimizations onto it, we get compositional correctness theorems for realistic optimizing compilers as refinements that directly relate native semantics of open modules and that are ignorant of intermediate compilation processes. Such direct refinements support all the compositionality and adequacy properties essential for verified compilation of open modules. We have applied this approach to the full compilation chain of CompCert with its Clight source language and demonstrated that our compiler correctness theorem is open to composition and intuitive to use with reduced verification complexity through end-to-end verification of non-trivial heterogeneous modules that may freely invoke each other (e.g., mutually recursively)

Dimensional Analysis of Robot Software without Developer Annotations

Robot software risks the hazard of dimensional inconsistencies. These inconsistencies occur when a program incorrectly manipulates values representing real-world quantities. Incorrect manipulation has real-world consequences that range in severity from benign to catastrophic. Previous approaches detect dimensional inconsistencies in programs but require extra developer effort and technical complications. The extra effort involves developers creating type annotations for every variable representing a real-world quantity that has physical units, and the technical complications include toolchain burdens like specialized compilers or type libraries. To overcome the limitations of previous approaches, this thesis presents novel methods to detect dimensional inconsistencies without developer annotations. We start by empirically assessing the difficulty developers have in making type annotations. In a human study of 83 subjects, we find that developers are only 51% accurate and require more than 2 minutes per annotation. We further find that type suggestions have a significant impact on annotation accuracy. We find that when showing developers annotation suggestions, three suggestions are better than a single suggestion because they are as helpful when correct and less harmful when incorrect. Since developers struggle to make type annotations accurately, we present a novel method to infer physical unit types without developer annotations. This is novel because it is the first method to detect dimensional inconsistencies in ROS C++ without developer annotations, and this is important because robot software and ROS are increasingly used in real-world applications. Our method leverages a property of robotic middleware architecture that reuses standardized data structures, and we implement our method in an open-source tool, Phriky. We evaluate our method empirically on a corpus of 5.9 M lines of code and find that it detects real inconsistencies with an 87% TP rate. However, our method only assigns physical unit types to 25% of variables, leaving much of the annotation space unaddressed. To overcome these limitations, we extend our method to utilize uncertain evidence in identifiers using probabilistic reasoning. We implement our new probabilistic method in a tool Phys and find that it assigns units to 75% of variables while retaining a TP rate of 82%. We present the first open dataset of dimensional inconsistencies in open-source robotics code, to our knowledge. Lastly, we identify extensions to our work and next steps for software tool developers to build more powerful robot software development tools. Advisers: Sebastian Elbaum and Carrick Detweile

SciCADE 95: International conference on scientific computation and differential equations

This report consists of abstracts from the conference. Topics include algorithms, computer codes, and numerical solutions for differential equations. Linear and nonlinear as well as boundary-value and initial-value problems are covered. Various applications of these problems are also included