Leavitt RR-algebras over countable graphs embed into L2,RL_{2,R}

For a commutative ring $R$ with unit we show that the Leavitt path algebra $L_R(E)$ of a graph $E$ embeds into $L_{2,R}$ precisely when $E$ is countable. Before proving this result we prove a generalised Cuntz-Krieger Uniqueness Theorem for Leavitt path algebras over $R$.Comment: 17 pages. At the request of a referee the previous version of this paper has been split into two papers. This version is the first of these papers. The second will also be uploaded to the arXi

L2,Z⊗L2,ZL_{2,\mathbb{Z}} \otimes L_{2,\mathbb{Z}} does not embed in L2,ZL_{2,\mathbb{Z}}

For a commutative ring $R$ with unit we investigate the embedding of tensor product algebras into the Leavitt algebra $L_{2,R}$. We show that the tensor product $L_{2,\mathbb{Z}}\otimes L_{2,\mathbb{Z}}$ does not embed in $L_{2,\mathbb{Z}}$ (as a unital $*$-algebra). We also prove a partial non-embedding result for the more general $L_{2,R} \otimes L_{2,R}$. Our techniques rely on realising Thompson's group $V$ as a subgroup of the unitary group of $L_{2,R}$.Comment: 16 pages. At the request of a referee the paper arXiv:1503.08705v2 was split into two papers. This is the second of those paper

Image scoring in ad-hoc networks : an investigation on realistic settings

Encouraging cooperation in distributed Multi-Agent Systems (MAS) remains an open problem. Emergent application domains such as Mobile Ad-hoc Networks (MANETs) are characterised by constraints including sparse connectivity and a lack of direct interaction history. Image scoring, a simple model of reputation proposed by Nowak and Sigmund, exhibits low space and time complexity and promotes cooperation through indirect reciprocity, in which an agent can expect cooperation in the future without repeat interactions with the same partners. The low overheads of image scoring make it a promising technique for ad-hoc networking domains. However, the original investigation of Nowak and Sigmund is limited in that it (i) used a simple idealised setting, (ii) did not consider the effects of incomplete information on the mechanism’s efficacy, and (iii) did not consider the impact of the network topology connecting agents. We address these limitations by investigating more realistic values for the number of interactions agents engage in, and show that incomplete information can cause significant errors in decision making. As the proportion of incorrect decisions rises, the efficacy of image scoring falls and selfishness becomes more dominant. We evaluate image scoring on three different connection topologies: (i) completely connected, which closely approximates Nowak and Sigmund’s original setup, (ii) random, with each pair of nodes connected with a constant probability, and (iii) scale-free, which is known to model a number of real world environments including MANETs

Segregation of cortical head direction cell assemblies on alternating theta cycles

High-level cortical systems for spatial navigation, including entorhinal grid cells, critically depend on input from the head direction system. We examined spiking rhythms and modes of synchrony between neurons participating in head direction networks for evidence of internal processing, independent of direct sensory drive, which may be important for grid cell function. We found that head direction networks of rats were segregated into at least two populations of neurons firing on alternate theta cycles (theta cycle skipping) with fixed synchronous or anti-synchronous relationships. Pairs of anti-synchronous theta cycle skipping neurons exhibited larger differences in head direction tuning, with a minimum difference of 40 degrees of head direction. Septal inactivation preserved the head direction signal, but eliminated theta cycle skipping of head direction cells and grid cell spatial periodicity. We propose that internal mechanisms underlying cycle skipping in head direction networks may be critical for downstream spatial computation by grid cells.We kindly thank S. Gillet, J. Hinman, E. Newman and L. Ewell for their invaluable consultations and comments on previous versions of this manuscript, as well as M. Connerney, S. Eriksson, C. Libby and T. Ware for technical assistance and behavioral training. This work was supported by grants from the National Institute of Mental Health (R01 MH60013 and MH61492) and the Office of Naval Research Multidisciplinary University Research Initiative (N00014-10-1-0936). (R01 MH60013 - National Institute of Mental Health; MH61492 - National Institute of Mental Health; N00014-10-1-0936 - Office of Naval Research Multidisciplinary University Research Initiative)Accepted manuscrip

Exceptional Sequences on Rational C*-Surfaces

Inspired by Bondal's conjecture, we study the behavior of exceptional sequences of line bundles on rational C*-surfaces under homogeneous degenerations. In particular, we provide a sufficient criterion for such a sequence to remain exceptional under a given degeneration. We apply our results to show that, for toric surfaces of Picard rank 3 or 4, all full exceptional sequences of line bundles may be constructed via augmentation. We also discuss how our techniques may be used to construct noncommutative deformations of derived categories.Comment: 30 pages, 11 figures. Some parts of this preprint originally appeared in arXiv:0906.4292v2 but have been revised and expanded upon. Minor changes, to appear in Manuscripta Mathematic

A field evaluation of a trap for invasive American bullfrogs

Native to the eastern United States, American bullfrogs (Rana catesbeiana [Lithobates catesbeianus]) have been introduced in many countries throughout the world. There have been relatively few effective and efficient control methods developed to manage bullfrogs. Particularly in the Hawaiian Islands, Pacific coast of North America, and Japan, finding effective methods for controlling invasive bullfrogs is needed with special emphasis on low impacts for sensitive native species. We conducted a field study to examine the efficacy of a newly designed live trap for capturing invasive bullfrogs. We found that our trap was successful at capturing bullfrogs because we captured up to seven in a single trap overnight. Fishing lures, live crickets, and lights were used as attractants and all capture bullfrogs, however more research is needed for finding effective attractants. We captured one known non-target frog that was released. Our findings suggest that the multiple capture traps could effectively be used as part of an integrated pest management strategy for controlling invasive bullfrog populations

A field evaluation of a trap for invasive American bullfrogs

Native to the eastern United States, American bullfrogs (Rana catesbeiana [Lithobates catesbeianus]) have been introduced in many countries throughout the world. There have been relatively few effective and efficient control methods developed to manage bullfrogs. Particularly in the Hawaiian Islands, Pacific coast of North America, and Japan, finding effective methods for controlling invasive bullfrogs is needed with special emphasis on low impacts for sensitive native species. We conducted a field study to examine the efficacy of a newly designed live trap for capturing invasive bullfrogs. We found that our trap was successful at capturing bullfrogs because we captured up to seven in a single trap overnight. Fishing lures, live crickets, and lights were used as attractants and all capture bullfrogs, however more research is needed for finding effective attractants. We captured one known non-target frog that was released. Our findings suggest that the multiple capture traps could effectively be used as part of an integrated pest management strategy for controlling invasive bullfrog populations

A field evaluation of a trap for invasive American bullfrogs

Native to the eastern United States, American bullfrogs (Rana catesbeiana [Lithobates catesbeianus]) have been introduced in many countries throughout the world. There have been relatively few effective and efficient control methods developed to manage bullfrogs. Particularly in the Hawaiian Islands, Pacific coast of North America, and Japan, finding effective methods for controlling invasive bullfrogs is needed with special emphasis on low impacts for sensitive native species. We conducted a field study to examine the efficacy of a newly designed live trap for capturing invasive bullfrogs. We found that our trap was successful at capturing bullfrogs because we captured up to seven in a single trap overnight. Fishing lures, live crickets, and lights were used as attractants and all capture bullfrogs, however more research is needed for finding effective attractants. We captured one known non-target frog that was released. Our findings suggest that the multiple capture traps could effectively be used as part of an integrated pest management strategy for controlling invasive bullfrog populations