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.

Microtubule length dependence of motor traffic in cells

In living cells, motor proteins, such as kinesin and dynein can move processively along microtubule (MT), and also detach from or attach to MT stochastically. Experiments have found that, the traffic of motor might be jammed, and various theoretical models have been designed to understand this traffic jam phenomenon. But previous studies mainly focus on motor attachment/detachment rate dependent properties. Recent experiment of Leduc {\it et al.} found that the traffic jam formation of motor protein kinesin depends also on the length of MT [Proc. Natl. Acad. Sci. U.S.A. {\bf 109}, 6100-6105 (2012)]. In this study, the MT length dependent properties of motor traffic will be analyzed. We found that MT length has one {\it critical value} $N_c$, traffic jam occurs only when MT length $N>N_c$. The jammed length of MT increases with total MT length, while the non-jammed MT length might not change monotonically with the total MT length. The critical value $N_c$ increases with motor detachment rate from MT, but decreases with motor attachment rate to MT

Reakcija β-amino-α,γ-dicianokrotononitrila s acetofenonom: sinteza derivata piridina, piridazina i tiofena s antimikrobnim djelovanjem

Condensation of β-amino-α,γ-dicyanocrotononitrile (1) with acetophenone gave the 2-amino-4-phenylpenta-1,3-diene-1,1,3-tricarbonitrile (2). The latter product was used in a series of heterocyclization reactions when react with different reagents like diazonium salts, hydrazines, hydroxylamine and elemental sulfur to give pyridazine, pyrazole, isoxazole and thiophene derivatives, respectively. On the other hand, it gave pyridine derivatives with aromatic aldehydes followed by reaction with cyanomethylene reagents. The MIC values for the newly synthesized product were measured against E. coli, B. cereus, B. subtilis and C. albicansKondenzacijom β-amino-α,γ-dicijanokrotononitrila 1 s acetofenonom dobiven je 2-amino-4-fenilpenta-1,3-dien-1,1,3-trikarbonitril (2) koji je upotrebljen u reakcijama heterociklizacije s različitim reagensima poput diazonijevih soli, hidrazina, hidroksilamina i elementarnog sumpora pri čemu su nastali derivati piridazina, pirazola, izoksazola, odnosno tiofena. Spoj 2 je u reakciji s aromatskim aldehidima te naknadno sa cijanometilenima dao derivate piridina. Određene su MIC vrijednosti za novosintetizirane spojeve protiv E. coli, B. cereus, B. subtilis i C. albicans

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

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

Possible origins of macroscopic left-right asymmetry in organisms

I consider the microscopic mechanisms by which a particular left-right (L/R) asymmetry is generated at the organism level from the microscopic handedness of cytoskeletal molecules. In light of a fundamental symmetry principle, the typical pattern-formation mechanisms of diffusion plus regulation cannot implement the "right-hand rule"; at the microscopic level, the cell's cytoskeleton of chiral filaments seems always to be involved, usually in collective states driven by polymerization forces or molecular motors. It seems particularly easy for handedness to emerge in a shear or rotation in the background of an effectively two-dimensional system, such as the cell membrane or a layer of cells, as this requires no pre-existing axis apart from the layer normal. I detail a scenario involving actin/myosin layers in snails and in C. elegans, and also one about the microtubule layer in plant cells. I also survey the other examples that I am aware of, such as the emergence of handedness such as the emergence of handedness in neurons, in eukaryote cell motility, and in non-flagellated bacteria.Comment: 42 pages, 6 figures, resubmitted to J. Stat. Phys. special issue. Major rewrite, rearranged sections/subsections, new Fig 3 + 6, new physics in Sec 2.4 and 3.4.1, added Sec 5 and subsections of Sec

Prime movers : mechanochemistry of mitotic kinesins

Mitotic spindles are self-organizing protein machines that harness teams of multiple force generators to drive chromosome segregation. Kinesins are key members of these force-generating teams. Different kinesins walk directionally along dynamic microtubules, anchor, crosslink, align and sort microtubules into polarized bundles, and influence microtubule dynamics by interacting with microtubule tips. The mechanochemical mechanisms of these kinesins are specialized to enable each type to make a specific contribution to spindle self-organization and chromosome segregation