Efforts of controlling viral transmission began soon after the first cases of coronavirus disease 2019 (COVID-19) infections were identified. Initial efforts were related to contact precautions, hand hygiene, and maskwearing; however, it was soon evident that a robust global immunization drive was the most effective way to curb disease transmission. In the United States, the first doses of COVID-19 vaccines were rolled out soon after the FDA granted emergency use authorization for the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccine. What this also meant was that many of the routine phases that any new drug or vaccine goes through before being released publicly were bypassed. Over the past two years, various side effects and reactions have been seen after COVID-19 vaccine administration, the most common being local injection site events (e.g., pain, redness, swelling) and systemic effects (e.g., fatigue, headaches, myalgias). We report the case of a 64-year-old female who developed bilateral lower extremity numbness and tingling within weeks of receiving the third dose of Moderna SARS-CoV-2 vaccine. The patient underwent extensive testing to ascertain the diagnosis. She had negative autonomic testing and normal nerve conduction study/electromyography (EMG), which did not reveal large fiber neuropathy. Eventually, the patient underwent a skin biopsy, which revealed small fiber neuropathy. This case report highlights the importance of keeping a broad differential for rare side effects, such as small fiber neuropathy, that are currently being seen and reported in the literature.

Message broadcasting in networks could be carried over spanning trees. A set of spanning trees in the same network is node independent if two conditions are satisfied. First, all trees are rooted at node r. Second, for every node u in the network, all trees' paths from r to u are node-disjoint, excluding the end nodes r and u. Independent spanning trees have applications in fault-tolerant communications and secure message distributions.Gaussian networks and two-dimensional toroidal networks share similar topological characteristics. They are regular of degree four, symmetric, and node-transitive. Gaussian networks, however, have relatively lesser network diameter that could result in a better performance. This promotes Gaussian networks to be a potential alternative for twodimensional toroidal networks.In this paper, we present constructions for node independent spanning trees in dense Gaussian networks. Based on these constructions, we design routing algorithms that can be used in fault-tolerant routing and secure message distribution. We also design fault-tolerant algorithms to construct these trees in parallel.

Independent trees are used in building secure and/or fault-tolerant network communication protocols. They have been investigated for different network topologies including tori. Dense Gaussian networks are potential alternatives for 2-dimensional tori. They have similar topological properties; however, they are superiors in carrying communications due to their node-distance distributions and smaller diameters. In this paper, we present constructions of edge-disjoint node-independent spanning trees in dense Gaussian networks. Based on the constructed trees, we design algorithms that could be used in fault-tolerant routing or secure message distribution.

h i g h l i g h t s• Applications of Hamiltonian cycles are given in the introduction. • Rectangular representation is constructed to help finding the solution since it gives a clear visualization of the network. • The first 2 edge disjoint Hamiltonian cycles are constructed based on the rectangular representation.• The third Hamiltonian cycle is first divided into two cases, when norm is odd or even, and then it is constructed. a b s t r a c tMany communication algorithms in parallel systems can be efficiently solved by obtaining edge disjoint Hamiltonian cycles in the interconnection topology of the network. The Eisenstein-Jacobi (EJ) network generated by α = a+bρ, where ρ = (1+i √ 3)/2, is a degree six symmetric interconnection network. The hexagonal network is a special case of the EJ network that can be obtained by α = a+(a+1)ρ. Generating three edge disjoint Hamiltonian cycles in the EJ network with generator α = a + bρ for gcd(a, b) = 1 has been shown before. However, this problem has not been solved when gcd(a, b) = d > 1. In this paper, some results to this problem are given.

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