Examples of mathematical modeling tales from the crypt

Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems. The heavily regulated cell renewal cycle in the colonic crypt provides a good example of how modeling can be used to find out key features of the system kinetics, and help to explain both the breakdown of homeostasis and the initiation of tumorigenesis. We use the cell population model by Johnston et al. (2007) Proc. Natl. Acad. Sci. USA 104, 4008-4013, to illustrate the power of mathematical modeling by considering two key questions about the cell population dynamics in the colonic crypt. We ask: how can a model describe both homeostasis and unregulated growth in tumorigenesis; and to which parameters in the system is the model most sensitive? In order to address these questions, we discuss what type of modeling approach is most appropriate in the crypt. We use the model to argue why tumorigenesis is observed to occur in stages with long lag phases between periods of rapid growth, and we identify the key parameters

On the proportion of cancer stem cells in a tumour

It is now generally accepted that cancers contain a sub-population, the cancer stem cells (CSCs), which initiate and drive a tumour’s growth. At least until recently it has been widely assumed that only a small proportion of the cells in a tumour are CSCs. Here we use a mathematical model, supported by experimental evidence, to show that such an assumption is unwarranted. We show that CSCs may comprise any possible proportion of the tumour, and that the higher the proportion the more aggressive the tumour is likely to be

Submillimetre observations of a sample of broad absorption line quasars

The broad absorption line (BAL) features seen in a small fraction of quasar optical/UV spectra are attributed to bulk outflows away from the quasar core. Observational evidence suggests that dust plays a key role in these systems, although whether the inferred dust properties are a signature of orientation effects or whether they are indicative of an evolutionary sequence remains an outstanding issue. Submillimetre (submm) detections of BAL quasars (BALQSOs), which would clearly help to resolve this issue, have so far been sparse. This paper reports on new submm observations of seven BALQSOs. The strongest influence on the observed flux is found to be the redshift, with the two highest redshift sources appearing intrinsically more submm-luminous than the lower redshift ones. Since this trend is also seen in other high redshift AGN, including non-BAL quasars it implies that the dust emission properties of these systems are no different from those of the general AGN population, which is difficult to reconcile with the evolutionary interpretation of the BAL phenomenon.Comment: 5 Pages, to appear in ApJ Letter

Photoionization and Photoelectric Loading of Barium Ion Traps

Simple and effective techniques for loading barium ions into linear Paul traps are demonstrated. Two-step photoionization of neutral barium is achieved using a weak intercombination line (6s2 1S0 6s6p 3P1, 791 nm) followed by excitation above the ionization threshold using a nitrogen gas laser (337 nm). Isotopic selectivity is achieved by using a near Doppler-free geometry for excitation of the triplet 6s6p 3P1 state. Additionally, we report a particularly simple and efficient trap loading technique that employs an in-expensive UV epoxy curing lamp to generate photoelectrons.Comment: 5 pages, Accepted to PRA 3/20/2007 -fixed typo -clarified figure 3 caption -added reference [15

Seasonal abundance of small cladocerans in Lake Mangakaware, Waikato, New Zealand

The seasonal changes in the dynamics and life histories of the Cladocera in Lake Mangakaware, North Island, New Zealand, were studied over 19 months by sampling at weekly or 2-weekly intervals. Lake Mangakaware is a 13.3 ha polymictic lake with high nutrient status, low Secchi disc transparencies, and an unstable thermal regime. The four planktonic cladoceran species (Bosmina longirostris, B. meridionalis, Ceriodaphnia pulchella, and C. dubia) exhibited disjunct population maxima. Only B. longirostris was perennially present. All species exhibited low fecundities and low lipid content, indicating that food resources were limited and that competitive interactions and resistance to starvation were probably important in determining species success. Increases in body size in cooler seasons were unrelated to clutch size, giving further support for the view that available food was limited. These results are consistent with previous experimental findings that subtle differences in life history can determine seasonal success and the outcome of competition between similar species

An investigation for the development of an integrated optical data preprocessor

The successful fabrication and demonstration of an integrated optical circuit designed to perform a parallel processing operation by utilizing holographic subtraction to simultaneously compare N analog signal voltages with N predetermined reference voltages is summarized. The device alleviates transmission, storage and processing loads of satellite data systems by performing, at the sensor site, some preprocessing of data taken by remote sensors. Major accomplishments in the fabrication of integrated optics components include: (1) fabrication of the first LiNbO3 waveguide geodesic lens; (2) development of techniques for polishing TIR mirrors on LiNbO3 waveguides; (3) fabrication of high efficiency metal-over-photoresist gratings for waveguide beam splitters; (4) demonstration of high S/N holographic subtraction using waveguide holograms; and (5) development of alignment techniques for fabrication of integrated optics circuits. Important developments made in integrated optics are the discovery and suggested use of holographic self-subtraction in LiNbO3, development of a mathematical description of the operating modes of the preprocessor, and the development of theories for diffraction efficiency and beam quality of two dimensional beam defined gratings

A note on the lattice Boltzmann method beyond the Chapman Enskog limits

A non-perturbative analysis of the Bhatnagar-Gross-Krook (BGK) model kinetic equation for finite values of the Knudsen number is presented. This analysis indicates why discrete kinetic versions of the BGK equation, and notably the Lattice Boltzmann method, can provide semi-quantitative results also in the non-hydrodynamic, finite-Knudsen regime, up to $Kn\sim {\cal O}(1)$. This may help the interpretation of recent Lattice Boltzmann simulations of microflows, which show satisfactory agreement with continuum kinetic theory in the moderate-Knudsen regime.Comment: 7 PAGES, 1 FIGUR

Fact: Many SCUBA galaxies harbour AGNs

Deep SCUBA surveys have uncovered a large population of ultra-luminous galaxies at z>1. These sources are often assumed to be starburst galaxies, but there is growing evidence that a substantial fraction host an AGN (i.e., an accreting super-massive black hole). We present here possibly the strongest evidence for this viewpoint to date: the combination of ultra-deep X-ray observations (the 2 Ms Chandra Deep Field-North) and deep optical spectroscopic data. We argue that upward of 38% of bright (f850um>=5mJy) SCUBA galaxies host an AGN, a fraction of which are obscured QSOs (i.e., L_X>3x10^{44} erg/s). However, using evidence from a variety of analyses, we argue that in almost all cases the AGNs are not bolometrically important (i.e., <20%). Thus, star formation appears to dominate their bolometric output. A substantial fraction of bright SCUBA galaxies show evidence for binary AGN activity. Since these systems appear to be interacting and merging at optical/near-IR wavelengths, their super-massive black holes will eventually coalesce.Comment: Invited contribution - 10 pages, 4 figures, to appear in the Proceedings of the ESO/USM/MPE Workshop on "Multiwavelength Mapping of Galaxy Formation and Evolution", eds. R. Bender and A. Renzin

Plate-impact loading of cellular structures formed by selective laser melting

Porous materials are of great interest because of improved energy absorption over their solid counterparts. Their properties, however, have been difficult to optimize. Additive manufacturing has emerged as a potential technique to closely define the structure and properties of porous components, i.e. density, strut width and pore size; however, the behaviour of these materials at very high impact energies remains largely unexplored. We describe an initial study of the dynamic compression response of lattice materials fabricated through additive manufacturing. Lattices consisting of an array of intersecting stainless steel rods were fabricated into discs using selective laser melting. The resulting discs were impacted against solid stainless steel targets at velocities ranging from 300 to 700 m s-1 using a gas gun. Continuum CTH simulations were performed to identify key features in the measured wave profiles, while 3D simulations, in which the individual cells were modelled, revealed details of microscale deformation during collapse of the lattice structure. The validated computer models have been used to provide an understanding of the deformation processes in the cellular samples. The study supports the optimization of cellular structures for application as energy absorbers. © 2014 IOP Publishing Ltd