What's Decidable About Sequences?

We present a first-order theory of sequences with integer elements, Presburger arithmetic, and regular constraints, which can model significant properties of data structures such as arrays and lists. We give a decision procedure for the quantifier-free fragment, based on an encoding into the first-order theory of concatenation; the procedure has PSPACE complexity. The quantifier-free fragment of the theory of sequences can express properties such as sortedness and injectivity, as well as Boolean combinations of periodic and arithmetic facts relating the elements of the sequence and their positions (e.g., "for all even i's, the element at position i has value i+3 or 2i"). The resulting expressive power is orthogonal to that of the most expressive decidable logics for arrays. Some examples demonstrate that the fragment is also suitable to reason about sequence-manipulating programs within the standard framework of axiomatic semantics.Comment: Fixed a few lapses in the Mergesort exampl

Potential role of coronary vasoconstriction in ischaemic heart disease: effect of exercise

Coronary vasomotion plays an important role in the regulation of coronary perfusion at rest and during exercise. Normal coronary arteries show coronary vasodilation of the proximal (+20%) and distal (+40%) vessel segments during supine bicycle exercise. However, patients with coronary artery disease show exercise-induced vasoconstriction of the stenotic vessel segments. The exact mechanism of exercise-induced stenosis narrowing is not clear but might be related to a passive collapse of the disease-free vessel wall (Venturi mechanism), elevated plasma levels of circulating catecholamines, an insufficient production of the endothelium-derived vesorelaxing factor or increased platelet aggregation due to turbulent blood flow with release of thromboxane A2 and serotonin. Various vasoactive drugs, such as nitroglycerin and calcium antagonists, prevent exercise-induced stenosis vasoconstriction. An additive effect on coronary vasodilation of the stenotic vessel segment was observed after combination of nitroglycerin with diltiazem. Thus, exercise-induced stenosis narrowing plays an important role in the pathophysiology of myocardial ischaemia during dynamic exercise. The antianginal effect of vasoactive substances can be explained—besides the effect on pre- and afterload—by a direct action on coronary stenosis vasomotio

Ecological strategies in stable and disturbed environments depend on species specialisation

Ecological strategies are integral to understanding species survival in different environments. However, how habitat specialisation is involved in such strategies is not fully understood, particularly in heterogeneous and disturbed environments. Here, we studied the trait associations between specialisation, dispersal ability, competitiveness, reproductive investment and survival rate in a spatially explicit metacommunity model under various disturbance rates. Though no unique trait values were associated with specialisation, relationships were uncovered depending on environmental factors. We found strong trait associations mainly for generalist species, while specialist species exhibited a larger range of trait combinations. Trait associations were driven first by the disturbance rate and second by species’ dispersal ability and generation overlap. With disturbance, low dispersal ability was strongly selected against, for specialists as well as for generalists. Our results demonstrate that habitat specialisation is critical for the emergence of trait strategies in metacommunities and that disturbance in interaction with dispersal ability limits not only the range of trait values but also the type of possible trait associations

Trees over Infinite Structures and Path Logics with Synchronization

We provide decidability and undecidability results on the model-checking problem for infinite tree structures. These tree structures are built from sequences of elements of infinite relational structures. More precisely, we deal with the tree iteration of a relational structure M in the sense of Shelah-Stupp. In contrast to classical results where model-checking is shown decidable for MSO-logic, we show decidability of the tree model-checking problem for logics that allow only path quantifiers and chain quantifiers (where chains are subsets of paths), as they appear in branching time logics; however, at the same time the tree is enriched by the equal-level relation (which holds between vertices u, v if they are on the same tree level). We separate cleanly the tree logic from the logic used for expressing properties of the underlying structure M. We illustrate the scope of the decidability results by showing that two slight extensions of the framework lead to undecidability. In particular, this applies to the (stronger) tree iteration in the sense of Muchnik-Walukiewicz.Comment: In Proceedings INFINITY 2011, arXiv:1111.267

On Second-Order Monadic Monoidal and Groupoidal Quantifiers

We study logics defined in terms of second-order monadic monoidal and groupoidal quantifiers. These are generalized quantifiers defined by monoid and groupoid word-problems, equivalently, by regular and context-free languages. We give a computational classification of the expressive power of these logics over strings with varying built-in predicates. In particular, we show that ATIME(n) can be logically characterized in terms of second-order monadic monoidal quantifiers

Logics for Unranked Trees: An Overview

Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for expressing navigational properties, and some make it easy to relate complex properties of trees to the existence of tree automata for those properties. Furthermore, logics differ significantly in their model-checking properties, their automata models, and their behavior on ordered and unordered trees. In this paper we present a survey of logics for unranked trees

Emergent dynamic chirality in a thermally driven artificial spin ratchet

Modern nanofabrication techniques have opened the possibility to create novel functional materials, whose properties transcend those of their constituent elements. In particular, tuning the magnetostatic interactions in geometrically frustrated arrangements of nanoelements called artificial spin ice1, 2 can lead to specific collective behaviour3, including emergent magnetic monopoles4, 5, charge screening6, 7 and transport8, 9, as well as magnonic response10, 11, 12. Here, we demonstrate a spin-ice-based active material in which energy is converted into unidirectional dynamics. Using X-ray photoemission electron microscopy we show that the collective rotation of the average magnetization proceeds in a unique sense during thermal relaxation. Our simulations demonstrate that this emergent chiral behaviour is driven by the topology of the magnetostatic field at the edges of the nanomagnet array, resulting in an asymmetric energy landscape. In addition, a bias field can be used to modify the sense of rotation of the average magnetization. This opens the possibility of implementing a magnetic Brownian ratchet13, 14, which may find applications in novel nanoscale devices, such as magnetic nanomotors, actuators, sensors or memory cells

Deep learning based classification of dynamic processes in time-resolved X-ray tomographic microscopy

Time-resolved X-ray tomographic microscopy is an invaluable technique to investigate dynamic processes in 3D for extended time periods. Because of the limited signal-to-noise ratio caused by the short exposure times and sparse angular sampling frequency, obtaining quantitative information through post-processing remains challenging and requires intensive manual labor. This severely limits the accessible experimental parameter space and so, prevents fully exploiting the capabilities of the dedicated time-resolved X-ray tomographic stations. Though automatic approaches, often exploiting iterative reconstruction methods, are currently being developed, the required computational costs typically remain high. Here, we propose a highly efficient reconstruction and classification pipeline (SIRT-FBP-MS-D-DIFF) that combines an algebraic filter approximation and machine learning to significantly reduce the computational time. The dynamic features are reconstructed by standard filtered back-projection with an algebraic filter to approximate iterative reconstruction quality in a computationally efficient manner. The raw reconstructions are post-processed with a trained convolutional neural network to extract the dynamic features from the low signal-to-noise ratio reconstructions in a fully automatic manner. The capabilities of the proposed pipeline are demonstrated on three different dynamic fuel cell datasets, one exploited for training and two for testing without network retraining. The proposed approach enables automatic processing of several hundreds of datasets in a single day on a single GPU node readily available at most institutions, so extending the possibilities in future dynamic X-ray tomographic investigations