Cannabis shenanigans: advocating for the restoration of an effective treatment of pain following spinal cord injury.

Cannabis is an effective treatment for pain following spinal cord injury that should be available to patients and researchers. The major argument against the rescheduling of cannabis is that the published research is not convincing. This argument is disingenuous at best, given that the evidence has been presented and rejected at many points during the political dialog. Moreover, the original decision to criminalize cannabis did not utilize scientific or medical data. There is tension between the needs of a society to protect the vulnerable by restricting the rights of others to live well and with less pain. It is clear that this 70-year war on cannabis has had little effect in controlling the supply of cannabis. Prohibition can never succeed; it is a tyranny from which every independent mind revolts. People living with chronic pain should not have to risk addiction, social stigma, restrictions on employment and even criminal prosecution in order to deal with their pain. It is time to end the shenanigans and have an open, transparent discussion of the true benefits of this much-beleaguered medicine

Generalized rook-Brauer algebras and their homology

Rook-Brauer algebras are a family of diagram algebras. They contain many interesting subalgebras: rook algebras, Brauer algebras, Motzkin algebras, Temperley-Lieb algebras and symmetric group algebras. In this paper, we generalize the rook-Brauer algebras and their subalgebras by allowing more structured diagrams. We introduce equivariance by labelling edges of a diagram with elements of a group $G$. We introduce braiding by insisting that when two strands cross, they do so as either an under-crossing or an over-crossing. We also introduce equivariant, braided diagrams by combining these structures. We then study the homology of our diagram algebras, as pioneered by Boyd and Hepworth, using methods introduced by Boyde. We show that, given certain invertible parameters, we can identify the homology of our generalized diagram algebras with the group homology of the braid groups $B_n$ and the semi-direct products $G^n\rtimes \Sigma_n$ and $G^n\rtimes B_n$. This allows us to deduce homological stability results for our generalized diagram algebras. We also prove that for diagrams with an odd number of edges, the homology of equivariant Brauer algebras and equivariant Temperley-Lieb algebras can be identified with the group homology of $G^n\rtimes \Sigma_n$ and $G^n$ respectively, without any conditions on parameters.Comment: 28 pages. Comments welcom

Categorifying equivariant monoids

Equivariant monoids are very important objects in many branches of mathematics: they combine the notion of multiplication and the concept of a group action. In this paper we will construct categories which encode the structure borne by monoids with a group action by combining the theory of PROPs and PROBs with the theory of crossed simplicial groups. PROPs and PROBs are categories used to encode structures borne by objects in symmetric and braided monoidal categories respectively, whilst crossed simplicial groups are categories which encode a unital, associative multiplication and a compatible group action. We will produce PROPs and PROBs whose categories of algebras are equivalent to the categories of monoids, comonoids and bimonoids with group action using extensions of the symmetric and braid crossed simplicial groups. We will extend this theory to balanced braided monoidal categories using the ribbon braid crossed simplicial group. Finally, we will use the hyperoctahedral crossed simplicial group to encode the structure of an involutive monoid with a compatible group action.Comment: 15 page

All Limbs Lead to the Trunk

This poster describes the development of and the psychometric properties of the trunk scale that measures the voluntary motor ability in the thoracic and upper lumbar regions. The function of the trunk musculature has far reaching implications, particularly in persons with SCI, where postural control and voluntary movement are compromised to varying degrees. Precisely coordinated muscle actions must occur in the appropriate sequence, duration, and combination for the optimal movement function and maintenance of balance and posture during dynamic activities. Trunk mobility is required for nearly all mobility tasks, particularly transitional movements such as rolling, supine to sit, and sit to stand, as well as activities of daily living which involve upper extremity movements such as reaching. The muscles innervated by the thoracic and lumbar spine play key roles in body positioning and posture which are very important in conducting functional activities such as ambulation, reaching and activities of daily living (ADL)1. Poster presented at: ISCOS Annual Meeting in Dublin Ireland.https://jdc.jefferson.edu/rmposters/1004/thumbnail.jp

Reflexive homology

Reflexive homology is the homology theory associated to the reflexive crossed simplicial group. It is defined in terms of functor homology and is the most general way one can build an involution into Hochschild homology. In this paper we give a bicomplex for computing reflexive homology together with some calculations. We show that reflexive homology satisfies Morita invariance. We give a decomposition of the reflexive homology of a group algebra indexed by conjugacy classes of group elements, where the summands are defined in terms of a reflexive analogue of group homology. We prove that under nice conditions the involutive Hochschild homology studied by Braun and by Fern\`andez-Val\`encia and Giansiracusa coincides with reflexive homology.Comment: 11 page