Genus Bounds for Harmonic Group Actions on Finite Graphs

This paper develops graph analogues of the genus bounds for the maximal size of an automorphism group of a compact Riemann surface of genus $g\ge 2$. Inspired by the work of M. Baker and S. Norine on harmonic morphisms between finite graphs, we motivate and define the notion of a harmonic group action. Denoting by M(g) the maximal size of such a harmonic group action on a graph of genus $g\ge 2$, we prove that $4(g-1)\le M(g)\le 6(g-1)$, and these bounds are sharp in the sense that both are attained for infinitely many values of g. Moreover, we show that the values $4(g-1)$ and $6(g-1)$ are the only values taken by the function $M(g)$.Comment: 14 pages with 6 figures; section 8 rewritten to correct an error in lemma 8.2; published versio

Agricultural Leadership Development: Insights and Experiences from Canada

In Canada, agriculture and its related industries are undergoing rapid and significant changes. Among the many issues facing farmers and other agri-business people are the development of biotechnologies, the decline of on-farm and rural populations, the emergence of new public policies, concerns over food safety, globalisation of markets, sensitivity to environmental issues, and the influence of regional and global trade agreements. Given the complexity of these issues, and the distinctiveness of various regions, sectors and commodities produced in Canada, there is a need for national agricultural leaders who understand the issues, and have the skills and networks to construct effective responses to those issues. The Canadian Farm Business Management Council has supported the development and pilot testing of a national leadership development program known as Canadian Agriculture Lifetime Leadership (CALL). CALL is a two-year program that selects men and women with demonstrated leadership potential and commitment to the agricultural industry, and provides those men and women with an opportunity to become more effective leaders. In addition to CALL, Ontario and New Brunswick have provincial leadership development programs targeted to agriculture. This paper introduces the context of agricultural leadership development programs in Canada. It then provides a short review of the CALL program and its provincial counterpart in Ontario. Based on this review, and on the perspectives provided by program graduates, a vision for the future of agricultural leadership programs in Canada is presented.Agribusiness, Agricultural and Food Policy,

Galois covers of the open p-adic disc

This paper investigates Galois branched covers of the open $p$-adic disc and their reductions to characteristic $p$. Using the field of norms functor of Fontaine and Wintenberger, we show that the special fiber of a Galois cover is determined by arithmetic and geometric properties of the generic fiber and its characteristic zero specializations. As applications, we derive a criterion for good reduction in the abelian case, and give an arithmetic reformulation of the local Oort Conjecture concerning the liftability of cyclic covers of germs of curves.Comment: 19 pages; substantial organizational and expository changes; this is the final version corresponding to the official publication in Manuscripta Mathematica; abstract update

Counting Arithmetical Structures on Paths and Cycles

Let G be a finite, connected graph. An arithmetical structure on G is a pair of positive integer vectors d, r such that (diag (d) - A) r=0 , where A is the adjacency matrix of G. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices (diag (d) - A)). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients ((2n-1)/(n-1)) , and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles

Botulinum toxin treatment of spasticity in diplegic cerebral palsy : a randomised, double-blind, placebo-controlled, dose-ranging study

This study evaluated the efficacy and safety of three doses of botulinum toxin A (BTX-A; Dysport®) in 125 patients (mean age 5.2 years, SD 2; 54% male)with dynamic equinus spasticity during walking. Participants were randomized to receive Dysport (10, 20, or 30 units/kg) or placebo to the gastrocnemius muscle of both legs. Muscle length was calculated from electrogoniometric measurements and the change in the dynamic component of gastrocnemius shortening at four weeks was prospectively identified as the primary outcome measure. All treatment groups showed statistically significant decreases in dynamic component compared with placebo at 4 weeks. Mean improvement in dynamic component was most pronounced in the 20 units/kg group, being equivalent to an increase in dorsiflexion with the knee extended at 19°, and was still present at 16 weeks. The safety profile of the toxin appears satisfactory

Counting Arithmetical Structures on Paths and Cycles

Let G be a finite, connected graph. An arithmetical structure on G is a pair of positive integer vectors d, r such that (diag (d) - A) r=0 , where A is the adjacency matrix of G. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices (diag (d) - A)). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients ((2n-1)/(n-1)) , and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles

Counting arithmetical structures on paths and cycles

Let G be a finite, connected graph. An arithmetical structure on G is a pair of positive integer vectors d, r such that (diag(d)-A)r = 0, where A is the adjacency matrix of G. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices (diag(d)-A)). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients C(2n-1,n-1), and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles

GABA transporter function, oligomerization state, and anchoring: correlates with subcellularly resolved FRET

The mouse γ-aminobutyric acid (GABA) transporter mGAT1 was expressed in neuroblastoma 2a cells. 19 mGAT1 designs incorporating fluorescent proteins were functionally characterized by [^3H]GABA uptake in assays that responded to several experimental variables, including the mutations and pharmacological manipulation of the cytoskeleton. Oligomerization and subsequent trafficking of mGAT1 were studied in several subcellular regions of live cells using localized fluorescence, acceptor photobleach Förster resonance energy transfer (FRET), and pixel-by-pixel analysis of normalized FRET (NFRET) images. Nine constructs were functionally indistinguishable from wild-type mGAT1 and provided information about normal mGAT1 assembly and trafficking. The remainder had compromised [^3H]GABA uptake due to observable oligomerization and/or trafficking deficits; the data help to determine regions of mGAT1 sequence involved in these processes. Acceptor photobleach FRET detected mGAT1 oligomerization, but richer information was obtained from analyzing the distribution of all-pixel NFRET amplitudes. We also analyzed such distributions restricted to cellular subregions. Distributions were fit to either two or three Gaussian components. Two of the components, present for all mGAT1 constructs that oligomerized, may represent dimers and high-order oligomers (probably tetramers), respectively. Only wild-type functioning constructs displayed three components; the additional component apparently had the highest mean NFRET amplitude. Near the cell periphery, wild-type functioning constructs displayed the highest NFRET. In this subregion, the highest NFRET component represented ~30% of all pixels, similar to the percentage of mGAT1 from the acutely recycling pool resident in the plasma membrane in the basal state. Blocking the mGAT1 C terminus postsynaptic density 95/discs large/zona occludens 1 (PDZ)-interacting domain abolished the highest amplitude component from the NFRET distributions. Disrupting the actin cytoskeleton in cells expressing wild-type functioning transporters moved the highest amplitude component from the cell periphery to perinuclear regions. Thus, pixel-by-pixel NFRET analysis resolved three distinct forms of GAT1: dimers, high-order oligomers, and transporters associated via PDZ-mediated interactions with the actin cytoskeleton and/or with the exocyst