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

Automatic structures of bounded degree revisited

The first-order theory of a string automatic structure is known to be decidable, but there are examples of string automatic structures with nonelementary first-order theories. We prove that the first-order theory of a string automatic structure of bounded degree is decidable in doubly exponential space (for injective automatic presentations, this holds even uniformly). This result is shown to be optimal since we also present a string automatic structure of bounded degree whose first-order theory is hard for 2EXPSPACE. We prove similar results also for tree automatic structures. These findings close the gaps left open in a previous paper of the second author by improving both, the lower and the upper bounds.Comment: 26 page

Languages ordered by the subword order

We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the language, the used predicates, and the fragment of the logic, we determine four new combinations that yield decidable theories. These results extend earlier ones where only the language of all words without the cover relation and fragments of first-order logic were considered

Dynamics of Simple Balancing Models with State Dependent Switching Control

Time-delayed control in a balancing problem may be a nonsmooth function for a variety of reasons. In this paper we study a simple model of the control of an inverted pendulum by either a connected movable cart or an applied torque for which the control is turned off when the pendulum is located within certain regions of phase space. Without applying a small angle approximation for deviations about the vertical position, we see structurally stable periodic orbits which may be attracting or repelling. Due to the nonsmooth nature of the control, these periodic orbits are born in various discontinuity-induced bifurcations. Also we show that a coincidence of switching events can produce complicated periodic and aperiodic solutions.Comment: 36 pages, 12 figure

A European Perspective on Auditory Processing Disorder-Current Knowledge and Future Research Focus

Current notions of “hearing impairment,” as reflected in clinical audiological practice, do not acknowledge the needs of individuals who have normal hearing pure tone sensitivity but who experience auditory processing difficulties in everyday life that are indexed by reduced performance in other more sophisticated audiometric tests such as speech audiometry in noise or complex non-speech sound perception. This disorder, defined as “Auditory Processing Disorder” (APD) or “Central Auditory Processing Disorder” is classified in the current tenth version of the International Classification of diseases as H93.25 and in the forthcoming beta eleventh version. APDs may have detrimental effects on the affected individual, with low esteem, anxiety, and depression, and symptoms may remain into adulthood. These disorders may interfere with learning per se and with communication, social, emotional, and academic-work aspects of life. The objective of the present paper is to define a baseline European APD consensus formulated by experienced clinicians and researchers in this specific field of human auditory science. A secondary aim is to identify issues that future research needs to address in order to further clarify the nature of APD and thus assist in optimum diagnosis and evidence-based management. This European consensus presents the main symptoms, conditions, and specific medical history elements that should lead to auditory processing evaluation. Consensus on definition of the disorder, optimum diagnostic pathway, and appropriate management are highlighted alongside a perspective on future research focus

Compositional Message Sequence Charts (CMSCs) Are Better to Implement Than MSCs

Abstract. Communicating Finite States Machines (CFMs) and Mes-sage Sequence Graphs (MSC-graphs for short) are two popular spec-ification formalisms for communicating systems. MSC-graphs capture requirements (scenarios), hence they are the starting point of the de-sign process. Implementing an MSC-graph means obtaining an equiva-lent deadlock-free CFM, since CFMs correspond to distributed message-passing algorithms. Several partial answers for the implementation have been proposed. E.g., local-choice MSC-graphs form a subclass of deadlock-free CFM: Testing equivalence with some local-choice MSC-graph is thus a partial answer to the implementation problem. Using Compositional MSCs, we propose a new algorithm which captures more implementable models than with MSCs. Furthermore, the size of the implementation is reduced by one exponential.

A mathematical framework for critical transitions: normal forms, variance and applications

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio