Incompleteness of States w.r.t. Traces in Model Checking

Cousot and Cousot introduced and studied a general past/future-time specification language, called mu*-calculus, featuring a natural time-symmetric trace-based semantics. The standard state-based semantics of the mu*-calculus is an abstract interpretation of its trace-based semantics, which turns out to be incomplete (i.e., trace-incomplete), even for finite systems. As a consequence, standard state-based model checking of the mu*-calculus is incomplete w.r.t. trace-based model checking. This paper shows that any refinement or abstraction of the domain of sets of states induces a corresponding semantics which is still trace-incomplete for any propositional fragment of the mu*-calculus. This derives from a number of results, one for each incomplete logical/temporal connective of the mu*-calculus, that characterize the structure of models, i.e. transition systems, whose corresponding state-based semantics of the mu*-calculus is trace-complete

The Invisible Thin Red Line

The aim of this paper is to argue that the adoption of an unrestricted principle of bivalence is compatible with a metaphysics that (i) denies that the future is real, (ii) adopts nomological indeterminism, and (iii) exploits a branching structure to provide a semantics for future contingent claims. To this end, we elaborate what we call Flow Fragmentalism, a view inspired by Kit Fine (2005)’s non-standard tense realism, according to which reality is divided up into maximally coherent collections of tensed facts. In this way, we show how to reconcile a genuinely A-theoretic branching-time model with the idea that there is a branch corresponding to the thin red line, that is, the branch that will turn out to be the actual future history of the world

Image-based Quantification of 3D Morphology for Bifurcations in the Left Coronary Artery: Application to Stent Design

Background Improved strategies for stent‐based treatment of coronary artery disease at bifurcations require a greater understanding of artery morphology. Objective We developed a workflow to quantify morphology in the left main coronary (LMCA), left anterior descending (LAD), and left circumflex (LCX) artery bifurcations. Methods Computational models of each bifurcation were created for 55 patients using computed tomography images in 3D segmentation software. Metrics including cross‐sectional area, length, eccentricity, taper, curvature, planarity, branching law parameters, and bifurcation angles were assessed using open‐sources software and custom applications. Geometric characterization was performed by comparison of means, correlation, and linear discriminant analysis (LDA). Results Differences between metrics suggest dedicated or multistent approaches should be tailored for each bifurcation. For example, the side branch of the LCX (i.e., obtuse marginal; OM) was longer than that of the LMCA (i.e., LCXprox) and LAD (i.e., first diagonal; D1). Bifurcation metrics for some locations (e.g., LMCA Finet ratio) provide results and confidence intervals agreeing with prior findings, while revised metric values are presented for others (e.g., LAD and LCX). LDA revealed several metrics that differentiate between artery locations (e.g., LMCA vs. D1, LMCA vs. OM, LADprox vs. D1, and LCXprox vs. D1). Conclusions These results provide a foundation for elucidating common parameters from healthy coronary arteries and could be leveraged in the future for treating diseased arteries. Collectively the current results may ultimately be used for design iterations that improve outcomes following implantation of future dedicated bifurcation stents

Transport on river networks: A dynamical approach

This study is motivated by problems related to environmental transport on river networks. We establish statistical properties of a flow along a directed branching network and suggest its compact parameterization. The downstream network transport is treated as a particular case of nearest-neighbor hierarchical aggregation with respect to the metric induced by the branching structure of the river network. We describe the static geometric structure of a drainage network by a tree, referred to as the static tree, and introduce an associated dynamic tree that describes the transport along the static tree. It is well known that the static branching structure of river networks can be described by self-similar trees (SSTs); we demonstrate that the corresponding dynamic trees are also self-similar. We report an unexpected phase transition in the dynamics of three river networks, one from California and two from Italy, demonstrate the universal features of this transition, and seek to interpret it in hydrological terms.Comment: 38 pages, 15 figure

Emergence of the mitochondrial reticulum from fission and fusion dynamics

Mitochondria form a dynamic tubular reticulum within eukaryotic cells. Currently, quantitative understanding of its morphological characteristics is largely absent, despite major progress in deciphering the molecular fission and fusion machineries shaping its structure. Here we address the principles of formation and the large-scale organization of the cell-wide network of mitochondria. On the basis of experimentally determined structural features we establish the tip-to-tip and tip-to-side fission and fusion events as dominant reactions in the motility of this organelle. Subsequently, we introduce a graph-based model of the chondriome able to encompass its inherent variability in a single framework. Using both mean-field deterministic and explicit stochastic mathematical methods we establish a relationship between the chondriome structural network characteristics and underlying kinetic rate parameters. The computational analysis indicates that mitochondrial networks exhibit a percolation threshold. Intrinsic morphological instability of the mitochondrial reticulum resulting from its vicinity to the percolation transition is proposed as a novel mechanism that can be utilized by cells for optimizing their functional competence via dynamic remodeling of the chondriome. The detailed size distribution of the network components predicted by the dynamic graph representation introduces a relationship between chondriome characteristics and cell function. It forms a basis for understanding the architecture of mitochondria as a cell-wide but inhomogeneous organelle. Analysis of the reticulum adaptive configuration offers a direct clarification for its impact on numerous physiological processes strongly dependent on mitochondrial dynamics and organization, such as efficiency of cellular metabolism, tissue differentiation and aging