Abstract:
We present an empirical comparison of invertebrate community structure between areas of undisturbed native eucalypt woodland and areas that have been cleared and replaced with plantations of exotic radiata pine (Pinus radiata). Implementation of a novel conceptual framework revealed that both insect (in autumn) and arachnid (in winter) assemblages demonstrated inhibition in response to the pine plantations. Species richness declines occurred in several taxonomic Orders (e.g., Hymenoptera, Blattodea, Acari) without compensated increases in other Orders in plantations. This was, however, a seasonal response, with shifts between inhibition and equivalency observed in both insects and arachnids across autumn and winter sampling periods. Equivalency responses were characterized by relatively similar levels of species richness in plantation and native habitats for several Orders (e.g., Coleoptera, Collembola, Psocoptera, Araneae). We propose testable hypotheses for the observed seasonal shifts between inhibition and equivalency that focus on diminished resource availability and the damp, moist conditions found in the plantations. Given the compelling evidence for seasonal shifts between categories, we recommend that seasonal patterns should be considered a critical component of further assemblage-level investigations of this novel framework for invasion ecology.

Abstract:
Severe acute respiratory syndrome coronavirus (SARS-CoV) encodes a papain-like protease (PLpro) with both deubiquitinating (DUB) and deISGylating activities that are proposed to counteract the post-translational modification of signaling molecules that activate the innate immune response. Here we examine the structural basis for PLpro's ubiquitin chain and interferon stimulated gene 15 (ISG15) specificity. We present the X-ray crystal structure of PLpro in complex with ubiquitin-aldehyde and model the interaction of PLpro with other ubiquitin-chain and ISG15 substrates. We show that PLpro greatly prefers K48- to K63-linked ubiquitin chains, and ISG15-based substrates to those that are mono-ubiquitinated. We propose that PLpro's higher affinity for K48-linked ubiquitin chains and ISG15 stems from a bivalent mechanism of binding, where two ubiquitin-like domains prefer to bind in the palm domain of PLpro with the most distal ubiquitin domain interacting with a “ridge” region of the thumb domain. Mutagenesis of residues within this ridge region revealed that these mutants retain viral protease activity and the ability to catalyze hydrolysis of mono-ubiquitin. However, a select number of these mutants have a significantly reduced ability to hydrolyze the substrate ISG15-AMC, or be inhibited by K48-linked diubuiquitin. For these latter residues, we found that PLpro antagonism of the nuclear factor kappa-light-chain-enhancer of activated B-cells (NFκB) signaling pathway is abrogated. This identification of key and unique sites in PLpro required for recognition and processing of diubiquitin and ISG15 versus mono-ubiquitin and protease activity provides new insight into ubiquitin-chain and ISG15 recognition and highlights a role for PLpro DUB and deISGylase activity in antagonism of the innate immune response.

Abstract:
We investigate stable operations in supersingular elliptic cohomology using isogenies of supersingular elliptic curves over finite fields. Our main results provide a framework in which we give a conceptually simple proof of an elliptic cohomology version of the Morava change of rings theorem and also gives models for explicit stable operations in terms of isogenies and morphisms in certain enlarged isogeny categories. We relate our work to that of G. Robert on the Hecke algebra structure of the ring of supersingular modular forms.

Abstract:
We investigate Hopf algebroids in the category of $L$-complete modules over a commutative Noetherian regular complete local ring. The main examples are provided by the Hopf algebroids associated to Lubin-Tate spectra in the K(n)-local stable homotopy category and we show that these have Landweber filtrations for all finitely generated discrete modules. Along the way we investigate the canonical Hopf algebras associated to Hopf algebroids over fields and introduce a notion of unipotent Hopf algebroid generalising that for Hopf algebras. In two appendices we continue the discussion of the connections with twisted group rings, and expand on a result of Hovey on the non-exactness of coproducts of L-complete modules.

Abstract:
These notes provide an informal introduction to a type of Mackey functor that arises naturally in algebraic topology in connection with Morava $K$-theory of classifying spaces of finite groups. The main aim is to identify key algebraic aspects of the Green functor structure obtained by applying a Morava $K$-theory to such classifying spaces.

Abstract:
We adopt the viewpoint that topological And\'e-Quillen theory for commutative $S$-algebras should provide usable (co)homology theories for doing calculations in the sense traditional within Algebraic Topology. Our main emphasis is on homotopical properties of universal derivations, especially their behaviour in multiplicative homology theories. There are algebraic derivation properties, but also deeper properties arising from the homotopical structure of the free algebra functor $\mathbb{P}_R$ and its relationship with extended powers of spectra. In the connective case in ordinary $\bmod{\,p}$ homology, this leads to useful formulae involving Dyer-Lashof operations in the homology of commutative $S$-algebras. Although many of our results could no doubt be obtained using stabilisation, our approach seems more direct. We also discuss a reduced free algebra functor $\tilde{\mathbb{P}}_R$.

Abstract:
Power operations in the homology of infinite loop spaces, and $H_\infty$ or $E_\infty$ ring spectra have a long history in Algebraic Topology. In the case of ordinary mod p homology for a prime p, the power operations of Kudo, Araki, Dyer and Lashof interact with Steenrod operations via the Nishida relations, but for many purposes this leads to complicated calculations once iterated applications of these functions are required.On the other hand, the homology coaction turns out to provide tractable formulae better suited to exploiting multiplicative structure. We show how to derive suitable formulae for the interaction between power operations and homology coactions in a wide class of examples; our approach makes crucial use of modern frameworks for spectra with well behaved smash products. In the case of mod $p$ homology, our formulae extend those of Bisson and Joyal to odd primes. We also show how to exploit our results in sample calculations, and produce some apparently new formulae for the Dyer-Lashof action on the dual Steenrod algebra.

Abstract:
We construct a free resolution of $R/I^s$ over $R$ where $I\ideal R$ is generated by a (finite or infinite) regular sequence. This generalizes the Koszul complex for the case $s=1$. For $s>1$, we easily deduce that the algebra structure of $\Tor^R_*(R/I,R/I^s)$ is trivial and the reduction map $R/I^s\lra R/I^{s-1}$ induces the trivial map of algebras.

Abstract:
Inspired by Stewart Priddy's cellular model for the $p$-local Brown-Peterson spectrum $BP$, we give a construction of a $p$-local $E_\infty$ ring spectrum $R$ which is a close approximation to $BP$. Indeed we can show that if $BP$ admits an $E_\infty$ structure then these are weakly equivalent as $E_\infty$ ring spectra. Our inductive cellular construction makes use of power operations on homotopy groups to define homotopy classes which are then killed by attaching $E_\infty$ cells.

Abstract:
We describe the action of power operations on the $p$-completed cooperation algebra $K^\vee_0 K = K_0(K)^{\displaystyle\hat{}}_p$ for $K$-theory at a prime~$p$.