On hyperovals of polar spaces

We derive lower and upper bounds for the size of a hyperoval of a finite polar space of rank 3. We give a computer-free proof for the uniqueness, up to isomorphism, of the hyperoval of size 126 of H(5, 4) and prove that the near hexagon E-3 has up to isomorphism a unique full embedding into the dual polar space DH(5, 4)

Strengthening Public Health in Wisconsin Through the Wisconsin Clinical Laboratory Network

The Wisconsin Clinical Laboratory Network (WCLN) at the University of Wisconsin–Madison is a partnership of 138 clinical and public health laboratories (as of February 2019) coordinated by the Wisconsin State Laboratory of Hygiene. This article describes the WCLN, its current activities, and lessons learned through this partnership. A laboratory technical advisory group, which consists of representatives from clinical laboratories, provides clinical laboratory perspective to the WCLN and fosters communication among laboratories. Activities and resources available through the WCLN include annual regional meetings, annual technical workshops, webinars, an email listserv, laboratory informational messages, in-person visits by a WCLN coordinator to clinical laboratories, and laboratory-based surveillance data and summaries distributed by the Wisconsin State Laboratory of Hygiene. One challenge to maintaining the WCLN is securing continual funding for network activities. Key lessons learned from this partnership of more than 20 years include the importance of in-person meetings, the clinical perspective of the laboratory technical advisory group, and providing activities and resources to clinical laboratories to foster sharing of data and clinical specimens for public health surveillance and outbreak response

An outline of polar spaces: basics and advances

This paper is an extended version of a series of lectures on polar spaces given during the workshop and conference 'Groups and Geometries', held at the Indian Statistical Institute in Bangalore in December 2012. The aim of this paper is to give an overview of the theory of polar spaces focusing on some research topics related to polar spaces. We survey the fundamental results about polar spaces starting from classical polar spaces. Then we introduce and report on the state of the art on the following research topics: polar spaces of infinite rank, embedding polar spaces in groups and projective embeddings of dual polar spaces

Near polygons and Fischer spaces

In this paper we exploit the relations between near polygons with lines of size 3 and Fischer spaces to classify near hexagons with quads and with lines of size three. We also construct some infinite families of near polygons

The Veldkamp space of multiple qubits

We introduce a point-line incidence geometry in which the commutation relations of the real Pauli group of multiple qubits are fully encoded. Its points are pairs of Pauli operators differing in sign and each line contains three pairwise commuting operators any of which is the product of the other two (up to sign). We study the properties of its Veldkamp space enabling us to identify subsets of operators which are distinguished from the geometric point of view. These are geometric hyperplanes and pairwise intersections thereof. Among the geometric hyperplanes one can find the set of self-dual operators with respect to the Wootters spin-flip operation well-known from studies concerning multiqubit entanglement measures. In the two- and three-qubit cases a class of hyperplanes gives rise to Mermin squares and other generalized quadrangles. In the three-qubit case the hyperplane with points corresponding to the 27 Wootters self-dual operators is just the underlying geometry of the E6(6) symmetric entropy formula describing black holes and strings in five dimensions.Comment: 15 pages, 1 figure; added references, corrected typos; minor change

Properties of field functionals and characterization of local functionals

Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the proper space of test functions (smooth functions) and of the relevant concept of differential (Bastiani differential) are discussed. The relation between the multiple derivatives of a functional and the corresponding distributions is described in detail. It is proved that, in a neighborhood of every test function, the support of a smooth functional is uniformly compactly supported and the order of the corresponding distribution is uniformly bounded. Relying on a recent work by Yoann Dabrowski, several spaces of functionals are furnished with a complete and nuclear topology. In view of physical applications, it is shown that most formal manipulations can be given a rigorous meaning. A new concept of local functionals is proposed and two characterizations of them are given: the first one uses the additivity (or Hammerstein) property, the second one is a variant of Peetre's theorem. Finally, the first step of a cohomological approach to quantum field theory is carried out by proving a global Poincar\'e lemma and defining multi-vector fields and graded functionals within our framework.Comment: 32 pages, no figur

Comparison of proton channel, phagocyte oxidase, and respiratory burst levels between human eosinophil and neutrophil granulocytes.

Robust production of reactive oxygen species (ROS) by phagocyte NADPH oxidase (phox) during the respiratory burst (RB) is a characteristic feature of eosinophil and neutrophil granulocytes. In these cells the voltage-gated proton channel (Hv1) is now considered as an ancillary subunit of the phox needed for intense ROS production. Multiple sources reported that the expression of phox subunits and RB is more intensive in eosinophils than in neutrophils. In most of these studies the eosinophils were not isolated from healthy individuals, and a comparative analysis of Hv1 expression had never been carried out. We performed a systematic comparison of the levels of essential phox subunits, Hv1 expression and ROS producing capacity between eosinophils and neutrophils of healthy individuals. The expression of phox components was similar, whereas the amount of Hv1 was approximately 10-fold greater in eosinophils. Furthermore, Hv1 expression correlated with Nox2 expression only in eosinophils. Additionally, in confocal microscopy experiments co-accumulation of Hv1 and Nox2 at the cell periphery was observed in resting eosinophils but not in neutrophils. While phorbol-12-myristate-13-acetate-induced peak extracellular ROS release was approximately 1.7-fold greater in eosinophils, oxygen consumption studies indicated that the maximal intensity of the RB is only approximately 1.4-fold greater in eosinophils. Our data reinforce that eosinophils, unlike neutrophils, generate ROS predominantly extracellularly. In contrast to previous works we have found that the two granulocyte types display very similar phox subunit expression and RB capacity. The large difference in Hv1 expression suggests that its support to intense ROS production is more important at the cell surface