Nested recursions with ceiling function solutions

Consider a nested, non-homogeneous recursion R(n) defined by R(n) = \sum_{i=1}^k R(n-s_i-\sum_{j=1}^{p_i} R(n-a_ij)) + nu, with c initial conditions R(1) = xi_1 > 0,R(2)=xi_2 > 0, ..., R(c)=xi_c > 0, where the parameters are integers satisfying k > 0, p_i > 0 and a_ij > 0. We develop an algorithm to answer the following question: for an arbitrary rational number r/q, is there any set of values for k, p_i, s_i, a_ij and nu such that the ceiling function ceiling{rn/q} is the unique solution generated by R(n) with appropriate initial conditions? We apply this algorithm to explore those ceiling functions that appear as solutions to R(n). The pattern that emerges from this empirical investigation leads us to the following general result: every ceiling function of the form ceiling{n/q}$ is the solution of infinitely many such recursions. Further, the empirical evidence suggests that the converse conjecture is true: if ceiling{rn/q} is the solution generated by any recursion R(n) of the form above, then r=1. We also use our ceiling function methodology to derive the first known connection between the recursion R(n) and a natural generalization of Conway's recursion.Comment: Published in Journal of Difference Equations and Applications, 2010. 11 pages, 1 tabl

Echo in Optical Lattices: Stimulated Revival of Breathing Oscillations

We analyze a stimulated revival (echo) effect for the breathing modes of the atomic oscillations in optical lattices. The effect arises from the dephasing due to the weak anharmonicity being partly reversed in time by means of additional parametric excitation of the optical lattice. The shape of the echo response is obtained by numerically simulating the equation of motion for the atoms with subsequent averaging over the thermal initial conditions. A qualitative analysis of the phenomenon shows that the suggested echo mechanism combines the features of both spin and phonon echoes.Comment: 13 pages, 3 figure

Political airs : from monitoring to attuned sensing air pollution

In Madrid, as in many European cities, air pollution is known about and made accountable through techno-scientific monitoring processes based on data, and the toxicity of the air is defined through epidemiological studies and made political through policy. In 2009, Madrid’s City Council changed the location of its air quality monitoring stations without notice, reducing the average pollution of the city and therefore provoking a public scandal. This scandal challenged the monitoring process, as the data that used to be the evidence of pollution could not be relied on anymore. To identify the characteristics of some of the diverse forms of public’s participation that emerged, I route theories of environmental sensing from STS and feminist theory through the notion of attuned sensing. Reading environmental sensing through the processual and orientational processes of attunement expands the ways in which toxicity can be sensed outside of quantitative data. This mode of sensing recognizes how the different spontaneous attunements to and with air pollution and the scandal acknowledged Madrid’s chemical infrastructure, rendering visible qualitative conditions of toxicity. This mode of sensing politicized the toxicity of the air not through management or policy making, nor only through established forms environmental activism, but through contagion and accumulation of the different forms of public participation. All together, they made air pollution a matter of public concern. They also redistributed the actors, practices and objects that make the toxicity not only knowable, but also accountable, and most importantly, they opened up spaces for citizen intervention

Binary gene induction and protein expression in individual cells

BACKGROUND: Eukaryotic gene transcription is believed to occur in either a binary or a graded fashion. With binary induction, a transcription activator (TA) regulates the probability with which a gene template is switched from the inactive to the active state without affecting the rate at which RNA molecules are produced from the template. With graded, also called rheostat-like, induction the gene template has continuously varying levels of transcriptional activity, and the TA regulates the rate of RNA production. Support for each of these two mechanisms arises primarily from experimental studies measuring reporter proteins in individual cells, rather than from direct measurement of induction events at the gene template. METHODS AND RESULTS: In this paper, using a computational model of stochastic gene expression, we have studied the biological and experimental conditions under which a binary induction mode operating at the gene template can give rise to differentially expressed "phenotypes" (i.e., binary, hybrid or graded) at the protein level. We have also investigated whether the choice of reporter genes plays a significant role in determining the observed protein expression patterns in individual cells, given the diverse properties of commonly-used reporter genes. Our simulation confirmed early findings that the lifetimes of active/inactive promoters and half-lives of downstream mRNA/protein products are important determinants of various protein expression patterns, but showed that the induction time and the sensitivity with which the expressed genes are detected are also important experimental variables. Using parameter conditions representative of reporter genes including green fluorescence protein (GFP) and β-galactosidase, we also demonstrated that graded gene expression is more likely to be observed with GFP, a longer-lived protein with low detection sensitivity. CONCLUSION: The choice of reporter genes may determine whether protein expression is binary, graded or hybrid, even though gene induction itself operates in an all-or-none fashion

Comparison of blood toluene levels after inhalation and oral administration

The purpose of this investigation was to compare blood toluene levels in Sprague-Dawley rats after oral and inhalation administration. Groups of 30 rats were dosed by gavage with 86.7, 217, 433, or 867 mg toluene/kg body wt or exposed for up to 6 hr, 5 rats per exposure, to an atmosphere of either 200 or 1000 ppm toluene. Blood was sampled by cardiac puncture from 5 rats in each of the six dose groups at 0.5, 1.0, 2.0, 4.0, 6.0, and 24.0 hr after gavage dosing or the beginning of the inhalation exposure. Blood toluene levels were analyzed. A four-parameter model was fitted to the blood toluene levels of the orally dosed rats. The area under the curve generated by this model, representing total blood toluene concentration over 6 hr, was calculated and compared to the area under the blood toluene curve for the 6-hr inhalation exposure. Integrated areas from the two routes of exposure were used for direct comparison of oral and inhalation exposures. The data demonstrate that gavage dosing can be used to approximate inhalation exposure to toluene.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27406/1/0000439.pd