Alternating quaternary algebra structures on irreducible representations of sl(2,C)

We determine the multiplicity of the irreducible representation V(n) of the simple Lie algebra sl(2,C) as a direct summand of its fourth exterior power $\Lambda^4 V(n)$. The multiplicity is 1 (resp. 2) if and only if n = 4, 6 (resp. n = 8, 10). For these n we determine the multilinear polynomial identities of degree $\le 7$ satisfied by the sl(2,C)-invariant alternating quaternary algebra structures obtained from the projections $\Lambda^4 V(n) \to V(n)$. We represent the polynomial identities as the nullspace of a large integer matrix and use computational linear algebra to find the canonical basis of the nullspace.Comment: 26 pages, 13 table

Engaged queer scholarship: Probing a new paradigm of knowledge creation

This article features a reflexive iteration of engaged scholarship regarding the Queer Liberation Theory Project, a community-based research study with the social justice group Queer Ontario, which involves academics, activists, and artists, a number of whom are cross affiliated. We explore the tensions and challenges involved in developing and creating knowledge via an engaged scholarship process that must respect the historical philosophical perspectives of a social movement as well as today’s academic theories. This article addresses the challenges of developing new knowledge (a theory) that counters a powerful, neoliberal, mainstream segment of today’s lesbian, gay, bisexual, and transgender (LGBT) movements, with implications for society at large. The layered issues associated with engaged scholarship are disentangled, including vulnerability to neoliberalism, navigating competing perspectives, and how academics/activists/artists both understand and engage in knowledge creation

Successful intralesional bleomycin injections for the management of a huge life-threatening cervical lymphangioma in a 3-day-old neonate

Intralesional bleomycin injections (IBI) for the management of a huge life-threatening cervical cystic hygroma is superior to surgery. Surgery has a high rate of morbidity and even mortality. Recurrence and injury to major vessels, nerves, and lymphatics may be unavoidable. The authors report on a 3-day-old male infant who was diagnosed antenatally as a case of a huge cervical cystic hygroma. Postnatally, the patient required mechanical ventilation. The patient was treated successfully with IBI without complications. To our knowledge, this is the youngest case presenting acutely to be treated successfully with IBI without complications.Keywords: bleomycin, neonatal cystic hygroma, respiratory distres

Accelerating Self-Assembly of Crisscross Slat Systems

We present an abstract model of self-assembly of systems composed of "crisscross slats", which have been experimentally implemented as a single-stranded piece of DNA [Minev et al., 2021] or as a complete DNA origami structure [Wintersinger et al., 2022]. We then introduce a more physically realistic "kinetic" model and show how important constants in the model were derived and tuned, and compare simulation-based results to experimental results [Minev et al., 2021; Wintersinger et al., 2022]. Using these models, we show how we can apply optimizations to designs of slat systems in order to lower the numbers of unique slat types required to build target structures. In general, we apply two types of techniques to achieve greatly reduced numbers of slat types. Similar to the experimental work implementing DNA origami-based slats, in our designs the slats oriented in horizontal and vertical directions are each restricted to their own plane and sets of them overlap each other in square regions which we refer to as macrotiles. Our first technique extends their previous work of reusing slat types within macrotiles and requires analyses of binding domain patterns to determine the potential for errors consisting of incorrect slat types attaching at undesired translations and reflections. The second technique leverages the power of algorithmic self-assembly to efficiently reuse entire macrotiles which self-assemble in patterns following designed algorithms that dictate the dimensions and patterns of growth. Using these designs, we demonstrate that in kinetic simulations the systems with reduced numbers of slat types self-assemble more quickly than those with greater numbers. This provides evidence that such optimizations will also result in greater assembly speeds in experimental systems. Furthermore, the reduced numbers of slat types required have the potential to vastly reduce the cost and number of lab steps for crisscross assembly experiments