Topological noetherianity for cubic polynomials

Let $P_3(\mathbf{C}^{\infty})$ be the space of complex cubic polynomials in infinitely many variables. We show that this space is $\mathbf{GL}_{\infty}$-noetherian, meaning that any $\mathbf{GL}_{\infty}$-stable Zariski closed subset is cut out by finitely many orbits of equations. Our method relies on a careful analysis of an invariant of cubics introduced here called q-rank. This result is motivated by recent work in representation stability, especially the theory of twisted commutative algebras. It is also connected to certain stability problems in commutative algebra, such as Stillman's conjecture.Comment: 13 page

Portable beveling tool

Portable tool was designed to semiautomatically bevel end surfaces of tubular or cylindrical components. Tool may be used for fabrication of elbow assembly which requires mating flange and elbow by fusion butt welding

Radiation effects on silicon second quarterly progress report, sep. 1 - nov. 30, 1964

Electron spin resonance measurements on P-doped silicon - vacancy phosphorus defec

Probing the structure of the cold dark matter halo with ancient mica

Mica can store (for >1 Gy) etchable tracks caused by atoms recoiling from WIMPs. Ancient mica is a directional detector despite the complex motions it makes with respect to the WIMP "wind". We can exploit the properties of directionality and long integration time to probe for structure in the dark matter halo of our galaxy. We compute a sample of possible signals in mica for a plausible model of halo structure.Comment: 7 pages, 2 figure

Model reduction in mathematical pharmacology: integration, reduction and linking of PBPK and systems biology models

In this paper we present a framework for the reduction and linking of physiologically based pharmacokinetic (PBPK) models with models of systems biology to describe the effects of drug administration across multiple scales. To address the issue of model complexity, we propose the reduction of each type of model separately prior to being linked. We highlight the use of balanced truncation in reducing the linear components of PBPK models, whilst proper lumping is shown to be efficient in reducing typically nonlinear systems biology type models. The overall methodology is demonstrated via two example systems; a model of bacterial chemotactic signalling in Escherichia coli and a model of extracellular regulatory kinase activation mediated via the extracellular growth factor and nerve growth factor receptor pathways. Each system is tested under the simulated administration of three hypothetical compounds; a strong base, a weak base, and an acid, mirroring the parameterisation of pindolol, midazolam, and thiopental, respectively. Our method can produce up to an 80% decrease in simulation time, allowing substantial speed-up for computationally intensive applications including parameter fitting or agent based modelling. The approach provides a straightforward means to construct simplified Quantitative Systems Pharmacology models that still provide significant insight into the mechanisms of drug action. Such a framework can potentially bridge pre-clinical and clinical modelling - providing an intermediate level of model granularity between classical, empirical approaches and mechanistic systems describing the molecular scale

A Suborbital Payload for Soft X-ray Spectroscopy of Extended Sources

We present a suborbital rocket payload capable of performing soft X-ray spectroscopy on extended sources. The payload can reach resolutions of ~100(lambda/dlambda) over sources as large as 3.25 degrees in diameter in the 17-107 angstrom bandpass. This permits analysis of the overall energy balance of nearby supernova remnants and the detailed nature of the diffuse soft X-ray background. The main components of the instrument are: wire grid collimators, off-plane grating arrays and gaseous electron multiplier detectors. This payload is adaptable to longer duration orbital rockets given its comparatively simple pointing and telemetry requirements and an abundance of potential science targets.Comment: Accepted to Experimental Astronomy, 12 pages plus 1 table and 17 figure

The Supergiant Shell LMC2: II. Physical Properties of the 10^6 K Gas

LMC2 has the highest X-ray surface brightness of all know supergiant shells in the Large Magellanic Cloud (LMC). The X-ray emission peaks within the ionized filaments that define the shell boundary, but also extends beyond the southern border of LMC2 as an X-ray bright spur. ROSAT HRI images reveal the X-ray emission from LMC2 and the spur to be truly diffuse, indicating a hot plasma origin. We have obtained ROSAT PSPC and ASCA SIS spectra to study the physical conditions of the hot gas interior to LMC2 and the spur. Raymond-Smith thermal plasma model fits to the X-ray spectra, constrained by HI 21-cm emission-line measurements of the column density, show the plasma temperature of the hot gas interior of LMC2 to be kT = 0.1 - 0.7 keV and of the spur to be kT = 0.1 - 0.5 keV. We have compared the physical conditions of the hot gas interior to LMC2 with those of other supergiant shells, superbubbles, and supernova remnants (SNRs) in the LMC. We find that our derived electron densities for the hot gas inside LMC2 is higher than the value determined for the supergiant shell LMC4, comparable to the value determined for the superbubble N11, and lower than the values determined for the superbubble N44 and a number of SNRs.Comment: 29 pages, 5 figures, to be published in Ap