Equations over free inverse monoids with idempotent variables

We introduce the notion of idempotent variables for studying equations in inverse monoids. It is proved that it is decidable in singly exponential time (DEXPTIME) whether a system of equations in idempotent variables over a free inverse monoid has a solution. The result is proved by a direct reduction to solve language equations with one-sided concatenation and a known complexity result by Baader and Narendran: Unification of concept terms in description logics, 2001. We also show that the problem becomes DEXPTIME hard , as soon as the quotient group of the free inverse monoid has rank at least two. Decidability for systems of typed equations over a free inverse monoid with one irreducible variable and at least one unbalanced equation is proved with the same complexity for the upper bound. Our results improve known complexity bounds by Deis, Meakin, and Senizergues: Equations in free inverse monoids, 2007. Our results also apply to larger families of equations where no decidability has been previously known.Comment: 28 pages. The conference version of this paper appeared in the proceedings of 10th International Computer Science Symposium in Russia, CSR 2015, Listvyanka, Russia, July 13-17, 2015. Springer LNCS 9139, pp. 173-188 (2015

Peptidases compartmentalized to the Ascaris suum intestinal lumen and apical intestinal membrane

The nematode intestine is a tissue of interest for developing new methods of therapy and control of parasitic nematodes. However, biological details of intestinal cell functions remain obscure, as do the proteins and molecular functions located on the apical intestinal membrane (AIM), and within the intestinal lumen (IL) of nematodes. Accordingly, methods were developed to gain a comprehensive identification of peptidases that function in the intestinal tract of adult female Ascaris suum. Peptidase activity was detected in multiple fractions of the A. suum intestine under pH conditions ranging from 5.0 to 8.0. Peptidase class inhibitors were used to characterize these activities. The fractions included whole lysates, membrane enriched fractions, and physiological- and 4 molar urea-perfusates of the intestinal lumen. Concanavalin A (ConA) was confirmed to bind to the AIM, and intestinal proteins affinity isolated on ConA-beads were compared to proteins from membrane and perfusate fractions by mass spectrometry. Twenty-nine predicted peptidases were identified including aspartic, cysteine, and serine peptidases, and an unexpectedly high number (16) of metallopeptidases. Many of these proteins co-localized to multiple fractions, providing independent support for localization to specific intestinal compartments, including the IL and AIM. This unique perfusion model produced the most comprehensive view of likely digestive peptidases that function in these intestinal compartments of A. suum, or any nematode. This model offers a means to directly determine functions of these proteins in the A. suum intestine and, more generally, deduce the wide array functions that exist in these cellular compartments of the nematode intestine

Green's relations and stability for subsemigroups

We prove new results on inheritance of Green's relations by subsemigroups in the presence of stability of elements. We provide counterexamples in other cases to show in particular that not all right-stable semigroups are embeddable in left-stable semigroups. This is carried out in the context of a survey of the various closely related notions of stability and minimality of Green's classes that have appeared in the literature over the last sixty years, and which have sometimes been presented in different forms

Vigilance of mustached tamarins in single-species and mixed-species groups—the influence of group composition

Species that participate in mixed-species groups (MSG) may have complementary roles in antipredator strategies. We studied vigilance in mustached tamarins (Saguinus mystax), small arboreal primates that form stable mixed-species groups with saddleback tamarins (Saguinus fuscicollis), in order to examine how the direction of vigilance changes with different species group compositions and whether the division of labor between the two species can be confirmed. We did so by comparing quantitative and qualitative differences in vigilance behavior between same individuals in and out of association (case A); MSG and single-species groups of the same total group size from two different populations (case B); and MSG of the same group size but with a different ratio of conspecifics to heterospecifics (case C). We predicted that individuals would increase downward scanning when heterospecifics are absent or their percentage is low, but total vigilance would increase only in case A due to the group size effect. However, mustached tamarins increased total vigilance due to horizontal scanning in cases A and C, and the predictions were confirmed only in small-sized groups in case B. Thus, we found indications that associating tamarin species in MSG might complement each other in the direction of vigilance, but the division of labor alone does not satisfactorily explain all the findings. There appear to be other mechanisms at work that define how direction of vigilance changes with group size and species composition. Complementarity of species probably occurs due to species vertical stratification rather than differences in the direction of vigilance

Vigilance in a Cooperatively Breeding Primate

Collective vigilance is considered a major advantage of group living in animals. We investigated vigilance behavior in wild mustached tamarins (Saguinus mystax), small, arboreal, cooperatively breeding New World primates that form stable mixed-species groups with saddleback tamarins (Saguinus fuscicollis). We aimed 1) to investigate whether vigilance patterns change according to individual activity and 2) to examine whether there is a social component of vigilance in their cooperative and nonaggressive society. We studied 11 factors that may influence vigilance and used this data to interpret the possible functions of vigilance. We observed 44 individuals in 3 mixed-species and 2 single-species groups of 2 populations that differed in population density and home range sizes. Vigilance changed greatly when individuals were engaged in different activities and individual vigilance was affected by different sets of factors depending on the activity. As vigilance decreased in proximity of conspecifics and heterospecifics when feeding, and in larger mixed-species groups when resting, we conclude that the predominant function of vigilance in mustached tamarins is predator related. However, the absence of the group size effect in very large single-species groups suggests that it may also function to maintain group cohesion. In the population with higher density and smaller home ranges individuals also increased their vigilance in home range overlap areas. We found no evidence that mustached tamarins monitor group mates to avoid food stealing or aggression. The effect of heterospecifics on individual vigilance suggests that collective vigilance might have been an important incentive in the evolution of tamarin mixed-species groups