Stability Analysis of a Hybrid Cellular Automaton Model of Cell Colony Growth

Cell colonies of bacteria, tumour cells and fungi, under nutrient limited growth conditions, exhibit complex branched growth patterns. In order to investigate this phenomenon we present a simple hybrid cellular automaton model of cell colony growth. In the model the growth of the colony is limited by a nutrient that is consumed by the cells and which inhibits cell division if it falls below a certain threshold. Using this model we have investigated how the nutrient consumption rate of the cells affects the growth dynamics of the colony. We found that for low consumption rates the colony takes on a Eden-like morphology, while for higher consumption rates the morphology of the colony is branched with a fractal geometry. These findings are in agreement with previous results, but the simplicity of the model presented here allows for a linear stability analysis of the system. By observing that the local growth of the colony is proportional to the flux of the nutrient we derive an approximate dispersion relation for the growth of the colony interface. This dispersion relation shows that the stability of the growth depends on how far the nutrient penetrates into the colony. For low nutrient consumption rates the penetration distance is large, which stabilises the growth, while for high consumption rates the penetration distance is small, which leads to unstable branched growth. When the penetration distance vanishes the dispersion relation is reduced to the one describing Laplacian growth without ultra-violet regularisation. The dispersion relation was verified by measuring how the average branch width depends on the consumption rate of the cells and shows good agreement between theory and simulations.Comment: 8 pages, 6 figure

Stratification of the orbit space in gauge theories. The role of nongeneric strata

Gauge theory is a theory with constraints and, for that reason, the space of physical states is not a manifold but a stratified space (orbifold) with singularities. The classification of strata for smooth (and generalized) connections is reviewed as well as the formulation of the physical space as the zero set of a momentum map. Several important features of nongeneric strata are discussed and new results are presented suggesting an important role for these strata as concentrators of the measure in ground state functionals and as a source of multiple structures in low-lying excitations.Comment: 22 pages Latex, 1 figur

Dynamics in Times of Ionizing Radiation and Rainfalls in Tropical Region of Brazil

Low energy gamma rays and rainfalls were monitored each minute in the region around São José dos Campos, (230:10`S, 450:53`W) in Brazil, from March 7th to June 28th in 2017. In this period, it was possible to see the dynamic process that occurs between the presence of ionizing radiation (gamma rays) of low energy and the variation of rain intensity in (mm) / min in the same region. During this period, 12 major peaks of radiation intensity corresponding to 12 rains of high and low intensities were observed. This positive rainfall / radiation correlation is very noticeable in the tropical region of Brazil, which is certainly due to the presence of the decay of 238U uranium into radium 226Ra and arriving at the 222Rn radon with α emission particles and low energy gamma radiation. Therefore, the rain interferes in the presence of the local exhalation of the radon gas, causing the washing of this gas in the low atmosphere, increasing the intensity of radiation measured momentarily in that location. This work shows this dynamic measured in this interval in the year 2017, where there was rainy and dry weather in the place

Geometry, stochastic calculus and quantum fields in a non-commutative space-time

The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic quantum mechanics algebra is also unstable. Its stabilization requires the non-commutativity of the space-time coordinates and the existence of a fundamental length constant. The new relativistic quantum mechanics algebra has important consequences on the geometry of space-time, on quantum stochastic calculus and on the construction of quantum fields. Some of these effects are studied in this paper.Comment: 36 pages Latex, 1 eps figur

A comparative study of different integrate-and-fire neurons: spontaneous activity, dynamical response, and stimulus-induced correlation

Stochastic integrate-and-fire (IF) neuron models have found widespread applications in computational neuroscience. Here we present results on the white-noise-driven perfect, leaky, and quadratic IF models, focusing on the spectral statistics (power spectra, cross spectra, and coherence functions) in different dynamical regimes (noise-induced and tonic firing regimes with low or moderate noise). We make the models comparable by tuning parameters such that the mean value and the coefficient of variation of the interspike interval match for all of them. We find that, under these conditions, the power spectrum under white-noise stimulation is often very similar while the response characteristics, described by the cross spectrum between a fraction of the input noise and the output spike train, can differ drastically. We also investigate how the spike trains of two neurons of the same kind (e.g. two leaky IF neurons) correlate if they share a common noise input. We show that, depending on the dynamical regime, either two quadratic IF models or two leaky IFs are more strongly correlated. Our results suggest that, when choosing among simple IF models for network simulations, the details of the model have a strong effect on correlation and regularity of the output.Comment: 12 page

KLP+ ("hat") trap with semiochemical lures suitable for trapping two diabrotica spp. exotic to Europe.

The KLP+ (“hat”) trap baited with pheromone or floral lures is a highly efficient non-sticky trap for the western corn rootworm, Diabrotica v. virgifera. We tested the suitability of this trap design for the related species, D. speciosa and D. barberi, baited with their respective lures. Both species are exotic to Europe: the former inhabits South America, and the latter occurs in some parts of North America. In screening tests performed in Brazil, several synthetic floral compounds and their combinations were found to be attractive to D. speciosa. However, the greatest effect was recorded for the previously described attractant 1,4-dimethoxybenzene. When the most active compounds in the preliminary test, 2-phenylethanol, methyl anthranilate, eugenol or benzaldehyde were added to 1,4-dimethoxybenzene, no synergistic effects were observed. When1,4-dimethoxybenzene was formulated in three types of polyethylene (PE) dispensers in KLP+traps, PE bag dispensers were superior to two types of PE vial dispenser, and caught hundreds of D. speciosa. Unbaited traps caught only negligible numbers. There was an interesting non-target effect. KLP+ traps with 1,4-dimethoxybenzene caught large numbers of the cornsilk fly, Euxesta eluta, which is known as a maize pest. For D. barberi, both a pheromone and a potent floral lure are already known. In tests with KLP+ traps, we found that the pheromone and floral lures can be applied together in the same trap to maximize both male and female catches. In conclusion, for early detection programs in Europe, the application of KLP+ traps baited with 1,4-dimethoxybenzene in PE bag dispensers could be recommended for D. speciosa, and KLP+ traps with dual (pheromone and floral) lures for D. barberi. In the case of D. barberi, one should note that the lures also show some attraction for D. v. virgifera, and the ratio of D. barberi vs. D. v. virgifera in the catch will be pre- dominantly determined by the relative population densities at the given site