The subdivision of large simplicial cones in Normaliz

Normaliz is an open-source software for the computation of lattice points in rational polyhedra, or, in a different language, the solutions of linear diophantine systems. The two main computational goals are (i) finding a system of generators of the set of lattice points and (ii) counting elements degree-wise in a generating function, the Hilbert Series. In the homogeneous case, in which the polyhedron is a cone, the set of generators is the Hilbert basis of the intersection of the cone and the lattice, an affine monoid. We will present some improvements to the Normaliz algorithm by subdividing simplicial cones with huge volumes. In the first approach the subdivision points are found by integer programming techniques. For this purpose we interface to the integer programming solver SCIP to our software. In the second approach we try to find good subdivision points in an approximating overcone that is faster to compute.Comment: To appear in the proceedings of the ICMS 2016, published by Springer as Volume 9725 of Lecture Notes in Computer Science (LNCS

Four generated, squarefree, monomial ideals

Let $I\supsetneq J$ be two squarefree monomial ideals of a polynomial algebra over a field generated in degree $\geq d$, resp. $\geq d+1$ . Suppose that $I$ is either generated by three monomials of degrees $d$ and a set of monomials of degrees $\geq d+1$, or by four special monomials of degrees $d$. If the Stanley depth of $I/J$ is $\leq d+1$ then the usual depth of $I/J$ is $\leq d+1$ too.Comment: to appear in "Bridging Algebra, Geometry, and Topology", Editors Denis Ibadula, Willem Veys, Springer Proceed. in Math. and Statistics, 96, 201

The Good Doctor: Exploring and Designing a Journey through Simon and Chekhov’s Russia

This thesis is an exploratory look at the process for designing the costumes for Neil Simon’s The Good Doctor. This production was produced at the University of New Orleans as part of its 2012-2013 season. Within this thesis we explore the multifaceted journey of the costume design process. As a designer, it is one’s job to use both historical and textual analysis in order to create a design that supports the thematic structure of the play. The following journey begins with initial research on the complex relationship between Neil Simon and his subject Anton Chekhov. It continues to include individual character concepts, as well as a re-telling of the production process. Finally, it concludes with an analysis of the validity of the design as a whole. Costume Design, Neil Simon, Anton Chekhov, The Good Docto

Dispersal in microbes: fungi in indoor air are dominated by outdoor air and show dispersal limitation at short distances.

The indoor microbiome is a complex system that is thought to depend on dispersal from the outdoor biome and the occupants' microbiome combined with selective pressures imposed by the occupants' behaviors and the building itself. We set out to determine the pattern of fungal diversity and composition in indoor air on a local scale and to identify processes behind that pattern. We surveyed airborne fungal assemblages within 1-month time periods at two seasons, with high replication, indoors and outdoors, within and across standardized residences at a university housing facility. Fungal assemblages indoors were diverse and strongly determined by dispersal from outdoors, and no fungal taxa were found as indicators of indoor air. There was a seasonal effect on the fungi found in both indoor and outdoor air, and quantitatively more fungal biomass was detected outdoors than indoors. A strong signal of isolation by distance existed in both outdoor and indoor airborne fungal assemblages, despite the small geographic scale in which this study was undertaken (<500 m). Moreover, room and occupant behavior had no detectable effect on the fungi found in indoor air. These results show that at the local level, outdoor air fungi dominate the patterning of indoor air. More broadly, they provide additional support for the growing evidence that dispersal limitation, even on small geographic scales, is a key process in structuring the often-observed distance-decay biogeographic pattern in microbial communities

Linear resolutions of powers and products

The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see, this condition is strongly correlated to good primary decompositions of the products and good homological and arithmetical properties of the associated multi-Rees algebras. The following families will be discussed in detail: polymatroidal ideals, ideals generated by linear forms and Borel fixed ideals of maximal minors. The main tools are Gr\"obner bases and Sagbi deformation

(Bi-)Cohen-Macaulay simplicial complexes and their associated coherent sheaves

Via the BGG correspondence a simplicial complex Delta on [n] is transformed into a complex of coherent sheaves on P^n-1. We show that this complex reduces to a coherent sheaf F exactly when the Alexander dual Delta^* is Cohen-Macaulay. We then determine when both Delta and Delta^* are Cohen-Macaulay. This corresponds to F being a locally Cohen-Macaulay sheaf. Lastly we conjecture for which range of invariants of such Delta it must be a cone.Comment: 16 pages, some minor change

Time Domain Simulations of the CLIC PETS (Power Extraction and Transfer Structure) with GdfidL

The Compact Linear Collider (CLIC) PETS is required to produce about 0.5 GW RF power per metre in the 30 GHz CLIC decelerator when driven by the high current beam (~ 270 A). To avoid beam break-up in the decelerator it is necessary to provide strong damping of the transverse deflecting modes. A PETS geometry with a level of damping consistent with stable drive beam operation has been designed, using the frequency domain code HFSS. A verification of the overall performance of this structure has been made recently using the code GdfidL, which permits a very fine mesh analysis of a full-length structure in the time domain. This paper gives the results of this analysis