Simple groups, product actions, and generalized quadrangles

The classification of flag-transitive generalized quadrangles is a long-standing open problem at the interface of finite geometry and permutation group theory. Given that all known flag-transitive generalized quadrangles are also point-primitive (up to point–line duality), it is likewise natural to seek a classification of the point-primitive examples. Working toward this aim, we are led to investigate generalized quadrangles that admit a collineation group$G$preserving a Cartesian product decomposition of the set of points. It is shown that, under a generic assumption on$G$, the number of factors of such a Cartesian product can be at most four. This result is then used to treat various types of primitive and quasiprimitive point actions. In particular, it is shown that$G$cannot haveholomorph compoundO’Nan–Scott type. Our arguments also pose purely group-theoretic questions about conjugacy classes in nonabelian finite simple groups and fixities of primitive permutation groups.</jats:p

Structure and magnetic order in Fe2+xV1-xAl

We present a detailed structural investigation via neutron diffraction of differently heat treated samples Fe2VAl and Fe2+xV1-xAl. Moreover, the magnetic behaviour of these materials is studied by means of mSR and Mossbauer-experiments. Our structural investigation indicates that quenched Fe2VAl, exhibiting the previously reported "Kondo insulating like" behaviour, is off-stoichiometric (6%) in its Al content. Slowly cooled Fe2VAl is structurally better ordered and stoichiometric, and the microscopic magnetic probes establish long range ferromagnetic order below TC = 13K, consistent with results from bulk experiments. The magnetic state can be modelled as being generated by diluted magnetic ions in a non-magnetic matrix. Quantitatively, the required number of magnetic ions is too large as to be explained by a model of Fe/V site exchange. We discuss the implications of our findings for the ground state properties of Fe2VAl, in particular with respect to the role of crystallographic disorder.Comment: accepted for publication in J. Phys.: Condens. Matte

Electronic Structure, Local Moments and Transport in Fe_2VAl

Local spin density approximation calculations are used to elucidate electronic and magnetic properties of Heusler structure Fe_2VAl. The compound is found to be a low carrier density semimetal. The Fermi surface has small hole pockets derived from a triply degenerate Fe derived state at Gamma compensated by an V derived electron pocket at the X point. The ideal compound is found to be stable against ferromagnetism. Fe impurities on V sites, however, behave as local moments. Because of the separation of the hole and electron pockets the RKKY interaction between such local moments should be rapidly oscillating on the scale of its decay, leading to the likelihood of spin-glass behavior for moderate concentrations of Fe on V sites. These features are discussed in relation to experimental observations of an unusual insulating state in this compound.Comment: 16 pages, RevTeX, 5 figure

Implications of COVID-19 on Public Policy, Supply Chain Disruptions, and Monitoring Methods

Transmission of the severe acute respiratory syndrome coronavirus 2, referred to as COVID-19, has persisted beyond 2020 and led to a global pandemic with far reaching consequences. Many changes in public policy and health measures were developed and implemented with the intention of slowing the spread of the novel virus. Disruptions from the global pandemic created major supply chain consequences due to stockpiling of essential goods (alcohol-based hand sanitizers and surface disinfectants), impacts on trade routes, and limitations on modes of transportation due to border closures. Rapid increase in the use of hand sanitizers and surface disinfectants significantly affected the production capacity of high-quality ethanol (e.g., USP and FCC grade) resulting in regulatory changes in countries facing shortages. Prompt enactment of government policies allowed for use of alcohol with higher impurities to offset heightened demand and increase commercial availability. Changes in monitoring methods were also observed, where many agencies began to track viral shedding through municipal wastewater. In this chapter, we will discuss the impacts of COVID-19 on public policies and health measures, economics as it relates to supply chain disruptions, and the implementation of novel monitoring methods to survey the spread of COVID-19

The Aggregation Inhibitor Peptide QBP1 as a Therapeutic Molecule for the Polyglutamine Neurodegenerative Diseases

Misfolding and abnormal aggregation of proteins in the brain are implicated in the pathogenesis of various neurodegenerative diseases including Alzheimer's, Parkinson's, and the polyglutamine (polyQ) diseases. In the polyQ diseases, an abnormally expanded polyQ stretch triggers misfolding and aggregation of the disease-causing proteins, eventually resulting in neurodegeneration. In this paper, we introduce our therapeutic strategy against the polyQ diseases using polyQ binding peptide 1 (QBP1), a peptide that we identified by phage display screening. We showed that QBP1 specifically binds to the expanded polyQ stretch and inhibits its misfolding and aggregation, resulting in suppression of neurodegeneration in cell culture and animal models of the polyQ diseases. We further demonstrated the potential of protein transduction domains (PTDs) for in vivo delivery of QBP1. We hope that in the near future, chemical analogues of aggregation inhibitor peptides including QBP1 will be developed against protein misfolding-associated neurodegenerative diseases

Integrated modeling and validation for phase change with natural convection

Water-ice systems undergoing melting develop complex spatio-temporal interface dynamics and a non-trivial temperature field. In this contribution, we present computational aspects of a recently conducted validation study that aims at investigating the role of natural convection for cryo-interface dynamics of water-ice. We will present a fixed grid model known as the enthalpy porosity method. It is based on introducing a phase field and employs mixture theory. The resulting PDEs are solved using a finite volume discretization. The second part is devoted to experiments that have been conducted for model validation. The evolving water-ice interface is tracked based on optical images that shows both the water and the ice phase. To segment the phases, we use a binary Mumford Shah method, which yields a piece-wise constant approximation of the imaging data. Its jump set is the reconstruction of the measured phase interface. Our combined simulation and segmentation effort finally enables us to compare the modeled and measured phase interfaces continuously. We conclude with a discussion of our findings

Invariant higher-order variational problems II

Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as Riemannian cubics on object manifolds that are endowed with normal metrics. The prime examples of such object manifolds are the symmetric spaces. We characterize the class of cubics on object manifolds that can be lifted horizontally to cubics on the group of transformations. Conversely, we show that certain types of non-horizontal geodesics on the group of transformations project to cubics. Finally, we apply second-order Lagrange--Poincar\'e reduction to the problem of Riemannian cubics on the group of transformations. This leads to a reduced form of the equations that reveals the obstruction for the projection of a cubic on a transformation group to again be a cubic on its object manifold.Comment: 40 pages, 1 figure. First version -- comments welcome