Enumeration of Nonsingular Buekenhout Unitals

The only known enumeration of Buekenhout unitals occurs in the Desarguesian plane $PG(2,q^2)$.  In this paper we develop general techniques for enumerating the nonsingular Buekenhoutunitals embedded in any two-dimensional translation plane, and apply these techniques to obtain such an enumeration in the regular nearfield planes, the odd-order Hall planes, and the flag-transitive affine planes.  We also provide some computer data for small-order André planes of index two and give partial results toward an enumeration in this case

Patient-derived organoids and orthotopic xenografts of primary and recurrent gliomas represent relevant patient avatars for precision oncology

Patient-based cancer models are essential tools for studying tumor biology and for the assessment of drug responses in a translational context. We report the establishment a large cohort of unique organoids and patient-derived orthotopic xenografts (PDOX) of various glioma subtypes, including gliomas with mutations in IDH1, and paired longitudinal PDOX from primary and recurrent tumors of the same patient. We show that glioma PDOXs enable long-term propagation of patient tumors and represent clinically relevant patient avatars that retain histopathological, genetic, epigenetic, and transcriptomic features of parental tumors. We find no evidence of mouse-specific clonal evolution in glioma PDOXs. Our cohort captures individual molecular genotypes for precision medicine including mutations in IDH1, ATRX, TP53, MDM2/4, amplification of EGFR, PDGFRA, MET, CDK4/6, MDM2/4, and deletion of CDKN2A/B, PTCH, and PTEN. Matched longitudinal PDOX recapitulate the limited genetic evolution of gliomas observed in patients following treatment. At the histological level, we observe increased vascularization in the rat host as compared to mice. PDOX-derived standardized glioma organoids are amenable to high-throughput drug screens that can be validated in mice. We show clinically relevant responses to temozolomide (TMZ) and to targeted treatments, such as EGFR and CDK4/6 inhibitors in (epi)genetically defined subgroups, according to MGMT promoter and EGFR/CDK status, respectively. Dianhydrogalactitol (VAL-083), a promising bifunctional alkylating agent in the current clinical trial, displayed high therapeutic efficacy, and was able to overcome TMZ resistance in glioblastoma. Our work underscores the clinical relevance of glioma organoids and PDOX models for translational research and personalized treatment studies and represents a unique publicly available resource for precision oncology

Regular Hyperbolic Fibrations

A hyperbolic bration is a set of q 1 hyperbolic quadrics and two lines which together partition the points of PG(3; q). The classical example of a hyperbolic bration comes from a pencil of quadrics; however, several other families are now known. In this paper we begin the development of a general framework to study hyperbolic brations for odd prime powers q

Hyperbolic Fibrations of PG(3,q)

A hyperbolic fibration is set of q \Gamma 1 hyperbolic quadrics and two lines which together partition the points of PG(3; q). The classical example of a hyperbolic fibration comes from a pencil of quadrics; however, several other families are known. In this paper we construct a new family of hyperbolic fibrations for odd prime powers q. As an application of hyperbolic fibrations, we note that they can be used to construct 2 q\Gamma1 (not necessarily inequivalent) spreads of PG(3; q) by choosing one ruling family from each of the hyperbolic quadrics in the fibration. For our new fibration we discuss some properties of the spreads obtained in the above manner. 1 Introduction Let GF(q) denote the finite field of order q, and let GF(q) denote the nonzero elements of this field. Throughout the paper, PG(n; q) will denote n--dimensional projective space over GF(q). In recent years, many authors have studied different ways of partitioning PG(n; q) into various surfaces. For instance..