Rings and spirals in barred galaxies. I Building blocks

In this paper we present building blocks which can explain the formation and properties both of spirals and of inner and outer rings in barred galaxies. We first briefly summarise the main results of the full theoretical description we have given elsewhere, presenting them in a more physical way, aimed to an understanding without the requirement of extended knowledge of dynamical systems or of orbital structure. We introduce in this manner the notion of manifolds, which can be thought of as tubes guiding the orbits. The dynamics of these manifolds can govern the properties of spirals and of inner and outer rings in barred galaxies. We find that the bar strength affects how unstable the L1 and L2 Lagrangian points are, the motion within the 5A5A5Amanifold tubes and the time necessary for particles in a manifold to make a complete turn around the galactic centre. We also show that the strength of the bar, or, to be more precise, of the non-axisymmetric forcing at and somewhat beyond the corotation region, determines the resulting morphology. Thus, less strong bars give rise to R1 rings or pseudorings, while stronger bars drive R2, R1R2 and spiral morphologies. We examine the morphology as a function of the main parameters of the bar and present descriptive two dimensional plots to that avail. We also derive how the manifold morphologies and properties are modified if the L1 and L2 Lagrangian points become stable. Finally, we discuss how dissipation affects the manifold properties and compare the manifolds in gas-like and in stellar cases. Comparison with observations, as well as clear predictions to be tested by observations will be given in an accompanying paper.Comment: Typos corrected to match the version in press in MNRA

Justifications in Constraint Handling Rules for Logical Retraction in Dynamic Algorithms

We present a straightforward source-to-source transformation that introduces justifications for user-defined constraints into the CHR programming language. Then a scheme of two rules suffices to allow for logical retraction (deletion, removal) of constraints during computation. Without the need to recompute from scratch, these rules remove not only the constraint but also undo all consequences of the rule applications that involved the constraint. We prove a confluence result concerning the rule scheme and show its correctness. When algorithms are written in CHR, constraints represent both data and operations. CHR is already incremental by nature, i.e. constraints can be added at runtime. Logical retraction adds decrementality. Hence any algorithm written in CHR with justifications will become fully dynamic. Operations can be undone and data can be removed at any point in the computation without compromising the correctness of the result. We present two classical examples of dynamic algorithms, written in our prototype implementation of CHR with justifications that is available online: maintaining the minimum of a changing set of numbers and shortest paths in a graph whose edges change.Comment: Pre-proceedings paper presented at the 27th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur, Belgium, 10-12 October 2017 (arXiv:1708.07854

Selection-free predictions in global games with endogenous information and multiple equilibria

Global games with endogenous information often exhibit multiple equilibria. In this paper, we show how one can nevertheless identify useful predictions that are robust across all equilibria and that cannot be delivered in the common-knowledge counterparts of these games. Our analysis is conducted within a flexible family of games of regime change, which have been used to model, inter alia, speculative currency attacks, debt crises, and political change. The endogeneity of information originates in the signaling role of policy choices. A novel procedure of iterated elimination of nonequilibrium strategies is used to deliver probabilistic predictions that an outside observer—an econometrician—can form under arbitrary equilibrium selections. The sharpness of these predictions improves as the noise gets smaller, but disappears in the complete-information version of the model

Confluence of CHR Revisited:Invariants and Modulo Equivalence

Abstract simulation of one transition system by another is introduced as a means to simulate a potentially infinite class of similar transition sequences within a single transition sequence. This is useful for proving confluence under invariants of a given system, as it may reduce the number of proof cases to consider from infinity to a finite number. The classical confluence results for Constraint Handling Rules (CHR) can be explained in this way, using CHR as a simulation of itself. Using an abstract simulation based on a ground representation, we extend these results to include confluence under invariant and modulo equivalence, which have not been done in a satisfactory way before.Comment: Pre-proceedings paper presented at the 28th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2018), Frankfurt am Main, Germany, 4-6 September 2018 (arXiv:1808.03326

A cardiac hydatid cyst underlying pulmonary embolism: a case report

Hydatid cysts located in the interatrial septum are especially rare but when they occur, they might cause intracavity rupture. We report on a patient with acute pulmonary embolism caused by an isolated, ruptured hydatid cyst on the right side of the interatrial septum. A 16-year-old-boy with an uneventful history was hospitalized for exercise-induced dyspnea and blood expectorations. Multiple and bilateral opacities were visualized on standard chest x-ray. Signs of right-sided hypertrophy were seen on ECG. Imaging findings led to the diagnosis of pulmonary embolism complicating cardiac hydatid cysts. An operation was performed through median sternotomy to remove the cardiac cyst. The pleural cavity was entered through the fifth intercostal space to withdraw lung hydatid cysts. Operative recovery was uneventful and the patient resumed his normal activities 19 months later. Prompt diagnosis and an appropriate surgical treatment prevented a potentially fatal outcome.Key words: Echinococcosis, Hydatidosis, Pulmonary embolism, cardiac, hydatid cys

Confluence Modulo Equivalence in Constraint Handling Rules

Previous results on proving confluence for Constraint Handling Rules are extended in two ways in order to allow a larger and more realistic class of CHR programs to be considered confluent. Firstly, we introduce the relaxed notion of confluence modulo equivalence into the context of CHR: while confluence for a terminating program means that all alternative derivations for a query lead to the exact same final state, confluence modulo equivalence only requires the final states to be equivalent with respect to an equivalence relation tailored for the given program. Secondly, we allow non-logical built-in predicates such as var/1 and incomplete ones such as is/2, that are ignored in previous work on confluence. To this end, a new operational semantics for CHR is developed which includes such predicates. In addition, this semantics differs from earlier approaches by its simplicity without loss of generality, and it may also be recommended for future studies of CHR. For the purely logical subset of CHR, proofs can be expressed in first-order logic, that we show is not sufficient in the present case. We have introduced a formal meta-language that allows reasoning about abstract states and derivations with meta-level restrictions that reflect the non-logical and incomplete predicates. This language represents subproofs as diagrams, which facilitates a systematic enumeration of proof cases, pointing forward to a mechanical support for such proofs

Confluence and Convergence in Probabilistically Terminating Reduction Systems

Convergence of an abstract reduction system (ARS) is the property that any derivation from an initial state will end in the same final state, a.k.a. normal form. We generalize this for probabilistic ARS as almost-sure convergence, meaning that the normal form is reached with probability one, even if diverging derivations may exist. We show and exemplify properties that can be used for proving almost-sure convergence of probabilistic ARS, generalizing known results from ARS.Comment: Pre-proceedings paper presented at the 27th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur, Belgium, 10-12 October 2017 (arXiv:1708.07854