The dependency pair framework: Combining techniques for automated termination proofs

Abstract. The dependency pair approach is one of the most powerful techniques for automated termination proofs of term rewrite systems. Up to now, it was regarded as one of several possible methods to prove termination. In this paper, we show that dependency pairs can instead be used as a general concept to integrate arbitrary techniques for termination analysis. In this way, the benefits of different techniques can be combined and their modularity and power are increased significantly. We refer to this new concept as the “dependency pair framework ” to distinguish it from the old “dependency pair approach”. Moreover, this framework facilitates the development of new methods for termination analysis. To demonstrate this, we present several new techniques within the dependency pair framework which simplify termination problems considerably. We implemented the dependency pair framework in our termination prover AProVE and evaluated it on large collections of examples.

Effect of Haptic Assistance on Learning Vehicle Reverse Parking Skills

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Stochastic modeling of cargo transport by teams of molecular motors

Many different types of cellular cargos are transported bidirectionally along microtubules by teams of molecular motors. The motion of this cargo-motors system has been experimentally characterized in vivo as processive with rather persistent directionality. Different theoretical approaches have been suggested in order to explore the origin of this kind of motion. An effective theoretical approach, introduced by M\"uller et al., describes the cargo dynamics as a tug-of-war between different kinds of motors. An alternative approach has been suggested recently by Kunwar et al., who considered the coupling between motor and cargo in more detail. Based on this framework we introduce a model considering single motor positions which we propagate in continuous time. Furthermore, we analyze the possible influence of the discrete time update schemes used in previous publications on the system's dynamic.Comment: Cenference proceedings - Traffic and Granular Flow 1

First-order formative rules

This paper discusses the method of formative rules for first-order term rewriting, which was previously defined for a higher-order setting. Dual to the well-known usable rules, formative rules allow dropping some of the term constraints that need to be solved during a termination proof. Compared to the higher-order definition, the first-order setting allows for significant improvements of the technique

Generic flow profiles induced by a beating cilium

We describe a multipole expansion for the low Reynolds number fluid flows generated by a localized source embedded in a plane with a no-slip boundary condition. It contains 3 independent terms that fall quadratically with the distance and 6 terms that fall with the third power. Within this framework we discuss the flows induced by a beating cilium described in different ways: a small particle circling on an elliptical trajectory, a thin rod and a general ciliary beating pattern. We identify the flow modes present based on the symmetry properties of the ciliary beat.Comment: 12 pages, 6 figures, to appear in EPJ

Nonlinearity of Mechanochemical Motions in Motor Proteins

The assumption of linear response of protein molecules to thermal noise or structural perturbations, such as ligand binding or detachment, is broadly used in the studies of protein dynamics. Conformational motions in proteins are traditionally analyzed in terms of normal modes and experimental data on thermal fluctuations in such macromolecules is also usually interpreted in terms of the excitation of normal modes. We have chosen two important protein motors - myosin V and kinesin KIF1A - and performed numerical investigations of their conformational relaxation properties within the coarse-grained elastic network approximation. We have found that the linearity assumption is deficient for ligand-induced conformational motions and can even be violated for characteristic thermal fluctuations. The deficiency is particularly pronounced in KIF1A where the normal mode description fails completely in describing functional mechanochemical motions. These results indicate that important assumptions of the theory of protein dynamics may need to be reconsidered. Neither a single normal mode, nor a superposition of such modes yield an approximation of strongly nonlinear dynamics.Comment: 10 pages, 6 figure

Formation and Interaction of Membrane Tubes

We show that the formation of membrane tubes (or membrane tethers), which is a crucial step in many biological processes, is highly non-trivial and involves first order shape transitions. The force exerted by an emerging tube is a non-monotonic function of its length. We point out that tubes attract each other, which eventually leads to their coalescence. We also show that detached tubes behave like semiflexible filaments with a rather short persistence length. We suggest that these properties play an important role in the formation and structure of tubular organelles.Comment: 4 pages, 3 figure

Complexity Bounds for Ordinal-Based Termination

`What more than its truth do we know if we have a proof of a theorem in a given formal system?' We examine Kreisel's question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program running times. Our main tool for this are length function theorems, which provide complexity bounds on the use of well quasi orders. We illustrate how to prove such theorems in the simple yet until now untreated case of ordinals. We show how to apply this new theorem to derive complexity bounds on programs when they are proven to terminate thanks to a ranking function into some ordinal.Comment: Invited talk at the 8th International Workshop on Reachability Problems (RP 2014, 22-24 September 2014, Oxford

Multisensory information facilitates reaction speed by enlarging activity difference between superior colliculus hemispheres in rats

Animals can make faster behavioral responses to multisensory stimuli than to unisensory stimuli. The superior colliculus (SC), which receives multiple inputs from different sensory modalities, is considered to be involved in the initiation of motor responses. However, the mechanism by which multisensory information facilitates motor responses is not yet understood. Here, we demonstrate that multisensory information modulates competition among SC neurons to elicit faster responses. We conducted multiunit recordings from the SC of rats performing a two-alternative spatial discrimination task using auditory and/or visual stimuli. We found that a large population of SC neurons showed direction-selective activity before the onset of movement in response to the stimuli irrespective of stimulation modality. Trial-by-trial correlation analysis showed that the premovement activity of many SC neurons increased with faster reaction speed for the contraversive movement, whereas the premovement activity of another population of neurons decreased with faster reaction speed for the ipsiversive movement. When visual and auditory stimuli were presented simultaneously, the premovement activity of a population of neurons for the contraversive movement was enhanced, whereas the premovement activity of another population of neurons for the ipsiversive movement was depressed. Unilateral inactivation of SC using muscimol prolonged reaction times of contraversive movements, but it shortened those of ipsiversive movements. These findings suggest that the difference in activity between the SC hemispheres regulates the reaction speed of motor responses, and multisensory information enlarges the activity difference resulting in faster responses