Fast Monte Carlo Algorithms for Permutation Groups

AbstractWe introduce new, elementary Monte Carlo methods to speed up and greatly simplify the manipulation of permutation groups (given by a list of generators). The methods are of a combinatorial character, using only elementary group theory. The key idea is that under certain conditions, "random subproducts" of the generators successfully emulate truly random elements of a group. We achieve a nearly optimal O(n3 logcn) asymptotic running time for membership testing, where n is the size of the permutation domain. This is an improvement of two orders of magnitude compared to known elementary algorithms and one order of magnitude compared to algorithms which depend on heavy use of group theory. An even greater asymptotic speedup is achieved for normal closures, a key ingredient in group-theoretic computation, now constructible in Monte Carlo time O(n2 logcn), i.e., essentially linear time (as a function of the input length). Some of the new techniques are sufficiently general to allow polynomial-time implementations in the very general model of "black box groups" (group operations are performed by an oracle). In particular, the normal closure algorithm has a number of applications to matrix-group computation. It should be stressed that our randomized algorithms are not heuristic: the probability of error is guaranteed not to exceed a bound ϵ > 0, prescribed by the user. The cost of this requirement is a factor of |log ϵ| in the running time

Food availability limits avian reproduction in the city: An experimental study on great tits Parus major

1. The altered ecological and environmental conditions in towns and cities strongly affect demographic traits of urban animal populations, for example avian reproductive success is often reduced. Previous work suggests that this is partly driven by low insect availability during the breeding season, but robust experimental evidence that supports this food limitation hypothesis is not yet available. 2. We tested core predictions of the food limitation hypothesis using a controlled experiment that provided supplementary insect food (nutritionally enhanced mealworms supplied daily to meet 40%–50% of each supplemented brood's food requirements) to great tit nestlings in urban and forest habitats. 3. We measured parental provisioning rates and estimated the amount of supplementary food consumed by control and experimental nestlings, and assessed their body size and survival rates. 4. Provisioning rates were similar across habitats and control and supplemented broods, but supplemented (and not control) broods consumed large quantities of supplementary food. As predicted by the food limitation hypothesis we found that nestlings in (a) urban control broods had smaller body size and nestling survival rates than those in forest control broods; (b) forest supplemented and control broods had similar body size and survival rates; (c) urban supplemented nestlings had larger body size and survival rates than those in urban control broods; and crucially (d) urban supplemented broods had similar body size and survival rates to nestlings in forest control broods. 5. Our results provide rare experimental support for the strong negative effects of food limitation during the nestling rearing period on urban birds' breeding success. Furthermore, the fact that supplementary food almost completely eliminated habitat differences in survival rate and nestling body size suggest that urban stressors other than food shortage contributed relatively little to the reduced avian breeding success. Finally, given the impacts of the amount of supplementary food that we provided and taking clutch size differences into account, our results suggest that urban insect populations in our study system would need to be increased by a factor of at least 2.5 for urban and forest great tits to have similar reproductive success

An adaptive prefix-assignment technique for symmetry reduction

This paper presents a technique for symmetry reduction that adaptively assigns a prefix of variables in a system of constraints so that the generated prefix-assignments are pairwise nonisomorphic under the action of the symmetry group of the system. The technique is based on McKay's canonical extension framework [J.~Algorithms 26 (1998), no.~2, 306--324]. Among key features of the technique are (i) adaptability---the prefix sequence can be user-prescribed and truncated for compatibility with the group of symmetries; (ii) parallelizability---prefix-assignments can be processed in parallel independently of each other; (iii) versatility---the method is applicable whenever the group of symmetries can be concisely represented as the automorphism group of a vertex-colored graph; and (iv) implementability---the method can be implemented relying on a canonical labeling map for vertex-colored graphs as the only nontrivial subroutine. To demonstrate the practical applicability of our technique, we have prepared an experimental open-source implementation of the technique and carry out a set of experiments that demonstrate ability to reduce symmetry on hard instances. Furthermore, we demonstrate that the implementation effectively parallelizes to compute clusters with multiple nodes via a message-passing interface.Comment: Updated manuscript submitted for revie

System-Wide Immunohistochemical Analysis of Protein Co-Localization

Background: The analysis of co-localized protein expression in a tissue section is often conducted with immunofluorescence histochemical staining which is typically visualized in localized regions. On the other hand, chromogenic immunohistochemical staining, in general, is not suitable for the detection of protein co-localization. Here, we developed a new protocol, based on chromogenic immunohistochemical stain, for system-wide detection of protein co-localization and differential expression. Methodology/Principal Findings: In combination with a removable chromogenic stain, an efficient antibody stripping method was developed to enable sequential immunostaining with different primary antibodies regardless of antibody’s host species. Sections were scanned after each staining, and the images were superimposed together for the detection of protein co-localization and differential expression. As a proof of principle, differential expression and co-localization of glutamic acid decarboxylase67 (GAD67) and parvalbumin proteins was examined in mouse cortex. Conclusions/Significance: All parvalbumin-containing neurons express GAD67 protein, and GAD67-positive neurons that do not express parvalbumin were readily visualized from thousands of other neurons across mouse cortex. The method provided a global view of protein co-localization as well as differential expression across an entire tissue section. Repeate

Hippocampal pyramidal cells: the reemergence of cortical lamination

The increasing resolution of tract-tracing studies has led to the definition of segments along the transverse axis of the hippocampal pyramidal cell layer, which may represent functionally defined elements. This review will summarize evidence for a morphological and functional differentiation of pyramidal cells along the radial (deep to superficial) axis of the cell layer. In many species, deep and superficial sublayers can be identified histologically throughout large parts of the septotemporal extent of the hippocampus. Neurons in these sublayers are generated during different periods of development. During development, deep and superficial cells express genes (Sox5, SatB2) that also specify the phenotypes of superficial and deep cells in the neocortex. Deep and superficial cells differ neurochemically (e.g. calbindin and zinc) and in their adult gene expression patterns. These markers also distinguish sublayers in the septal hippocampus, where they are not readily apparent histologically in rat or mouse. Deep and superficial pyramidal cells differ in septal, striatal, and neocortical efferent connections. Distributions of deep and superficial pyramidal cell dendrites and studies in reeler or sparsely GFP-expressing mice indicate that this also applies to afferent pathways. Histological, neurochemical, and connective differences between deep and superficial neurons may correlate with (patho-) physiological phenomena specific to pyramidal cells at different radial locations. We feel that an appreciation of radial subdivisions in the pyramidal cell layer reminiscent of lamination in other cortical areas may be critical in the interpretation of studies of hippocampal anatomy and function

Personality Traits and Behavioral Syndromes in Differently Urbanized Populations of House Sparrows (Passer domesticus)

Urbanization creates novel environments for wild animals where selection pressures may differ drastically from those in natural habitats. Adaptation to urban life involves changes in various traits, including behavior. Behavioral traits often vary consistently among individuals, and these so-called personality traits can be correlated with each other, forming behavioral syndromes. Despite their adaptive significance and potential to act as constraints, little is known about the role of animal personality and behavioral syndromes in animals' adaptation to urban habitats. In this study we tested whether differently urbanized habitats select for different personalities and behavioral syndromes by altering the population mean, inter-individual variability, and correlations of personality traits. We captured house sparrows (Passer domesticus) from four different populations along the gradient of urbanization and assessed their behavior in standardized test situations. We found individual consistency in neophobia, risk taking, and activity, constituting three personality axes. On the one hand, urbanization did not consistently affect the mean and variance of these traits, although there were significant differences between some of the populations in food neophobia and risk taking (both in means and variances). On the other hand, both urban and rural birds exhibited a behavioral syndrome including object neophobia, risk taking and activity, whereas food neophobia was part of the syndrome only in rural birds. These results indicate that there are population differences in certain aspects of personality in house sparrows, some of which may be related to habitat urbanization. Our findings suggest that urbanization and/or other population-level habitat differences may not only influence the expression of personality traits but also alter their inter-individual variability and the relationships among them, changing the structure of behavioral syndromes

Axonal Dynamics of Excitatory and Inhibitory Neurons in Somatosensory Cortex

Electrophysiology-delivery of fluorescent viral vectors-and two-photon microscopy were used to demonstrate the rapidity of axonal restructuring of both excitatory and inhibitory neurons in rodent cortical layer II/III following alterations in sensory experience