428 research outputs found
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
A comparison of taxon co-occurrence patterns for macro- and microorganisms
We examine co-occurrence patterns of microorganisms to evaluate community assembly ârules.â We use methods previously applied to macroorganisms, both to evaluate their applicability to microorganisms and to allow comparison of co-occurrence patterns observed in microorganisms to those found in macroorganisms. We use a null model analysis of 124 incidence matrices from microbial communities, including bacteria, archaea, fungi, and algae, and we compare these results to previously published findings from a meta-analysis of almost 100 macroorganism data sets. We show that assemblages of microorganisms demonstrate nonrandom patterns of co-occurrence that are broadly similar to those found in assemblages of macroorganisms. These results suggest that some taxon co-occurrence patterns may be general characteristics of communities of organisms from all domains of life. We also find that co-occurrence in microbial communities does not vary among taxonomic groups or habitat types. However, we find that the degree of co-occurrence does vary among studies that use different methods to survey microbial communities. Finally, we discuss the potential effects of the undersampling of microbial communities on our results, as well as processes that may contribute to nonrandom patterns of co-occurrence in both macrobial and microbial communities such as competition, habitat filtering, historical effects, and neutral processes
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
Blackbody-radiation shift in a 88Sr+ ion optical frequency standard
The blackbody radiation (BBR) shift of the 5s - 4d_{5/2} clock transition in
88Sr+ is calculated to be 0.250(9) Hz at room temperature, T=300K, using the
relativistic all-order method where all single and double excitations of the
Dirac-Fock wave function are included to all orders of perturbation theory. The
BBR shift is a major component in the uncertainty budget of the optical
frequency standard based on the 88Sr+ trapped ion. The scalar polarizabilities
of the 5s and 4d_{5/2} levels, as well as the tensor polarizability of the
4d_{5/2} level, are presented together with the evaluation of their
uncertainties. The lifetimes of the 4d_{3/2}, 4d_{5/2}, 5p_{1/2}, and 5p_{3/2}
states are calculated and compared with experimental values.Comment: 6 page
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
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