Deposit Central School District and Deposit Teachers Association

In the Matter of Impasse Between The Deposit Central School District and The Deposit Teacher Association. PERB Case M2006-053. Sally C. Gillespie, Fact Finder

Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation

We present computer-assisted methods for analyzing stochastic models of gene regulatory networks. The main idea that underlies this equation-free analysis is the design and execution of appropriately-initialized short bursts of stochastic simulations; the results of these are processed to estimate coarse-grained quantities of interest, such as mesoscopic transport coefficients. In particular, using a simple model of a genetic toggle switch, we illustrate the computation of an effective free energy and of a state-dependent effective diffusion coefficient that characterize an unavailable effective Fokker-Planck equation. Additionally we illustrate the linking of equation-free techniques with continuation methods for performing a form of stochastic "bifurcation analysis"; estimation of mean switching times in the case of a bistable switch is also implemented in this equation-free context. The accuracy of our methods is tested by direct comparison with long-time stochastic simulations. This type of equation-free analysis appears to be a promising approach to computing features of the long-time, coarse-grained behavior of certain classes of complex stochastic models of gene regulatory networks, circumventing the need for long Monte Carlo simulations.Comment: 33 pages, submitted to The Journal of Chemical Physic

Associated strangeness production in the pp to pK^+K^-p and pp to pK^+ pi^0 Sigma^0 reactions

The total and differential cross sections for associated strangeness production in the $pp \to pK^+K^-p$ and $pp \to pK^+\pi^0\Sigma^0$ reactions have been studied in a unified approach using an effective Lagrangian model. It is assumed that both the $K^-p$ and $\pi^0\Sigma^0$ final states originate from the decay of the $\Lambda(1405)$ resonance which was formed in the production chain $pp\to p(N^*(1535)\to K^+\Lambda(1405))$. The available experimental data are well reproduced, especially the ratio of the two total cross sections, which is much less sensitive to the particular model of the entrance channel. The significant coupling of the $N^*(1535)$ resonance to $\Lambda(1405) K$ is further evidence for large $s \bar{s}$ components in the quark wave function of the $N^*(1535)$ resonance.Comment: Published in Phys. Rev.

Internal thermal noise in the LIGO test masses : a direct approach

The internal thermal noise in LIGO's test masses is analyzed by a new technique, a direct application of the Fluctuation-Dissipation Theorem to LIGO's readout observable, $x(t)=$(longitudinal position of test-mass face, weighted by laser beam's Gaussian profile). Previous analyses, which relied on a normal-mode decomposition of the test-mass motion, were valid only if the dissipation is uniformally distributed over the test-mass interior, and they converged reliably to a final answer only when the beam size was a non-negligible fraction of the test-mass cross section. This paper's direct analysis, by contrast, can handle inhomogeneous dissipation and arbitrary beam sizes. In the domain of validity of the previous analysis, the two methods give the same answer for $S_x(f)$, the spectral density of thermal noise, to within expected accuracy. The new analysis predicts that thermal noise due to dissipation concentrated in the test mass's front face (e.g. due to mirror coating) scales as $1/r_0^2$, by contrast with homogeneous dissipation, which scales as $1/r_0$ ($r_0$ is the beam radius); so surface dissipation could become significant for small beam sizes.Comment: 6 pages, RevTex, 1 figur

Stronger computational modelling of signalling pathways using both continuous and discrete-state methods

Starting from a biochemical signalling pathway model expresses in a process algebra enriched with quantitative information, we automatically derive both continuous-space and discrete-space representations suitable for numerical evaluation. We compare results obtained using approximate stochastic simulation thereby exposing a flaw in the use of the differentiation procedure producing misleading results

Akaitcho (ca. 1786-1838)

The Yellowknife Indian leader Akaitcho stepped upon the stage of Canadian history in the afternoon of 30 July 1820 when he met Captain John Franklin and affirmed his willingness to guide and provision Franklin's expedition of exploration "to the shores of the polar sea". ... Known in Franklin's time as Copper Indians, the Yellowknives were the northwesternmost division of the widespread Chipewyan peoples. ... Ranging broadly in the caribou lands from the East Arm of Great Slave Lake to the Coppermine River, Akaitcho and the Yellowknives traded as meat provisioners into the North West Company post of Fort Providence on the North Arm of Great Slave Lake. For at least a decade the Yellowknives had pillaged furs, stolen women, and occasionally killed Dogrib and Hare Indians, their neighbours to the west and northwest. Dogribs were forced to avoid parts of their traditional hunting range during Akaitcho's years of aggressive leadership. ... When, after the terrible overland return from the arctic coast, the starving remnants of the Franklin expedition were rescued by Yellowknives, Akaitcho revealed another facet of his character. Treated with the "utmost tenderness" by their rescuers, Franklin and his party from Fort Enterprise were conveyed to the camp of "our chief and companion Akaitcho." ... In consequence of the merger of the North West Company and the Hudson's Bay Company in 1821, the post of Fort Providence had closed in 1823. Akaitcho and the Yellowknives now perforce had to direct their trade into Fort Resolution in company with Chipewyans already attached to that post. (Their intermarriage and absorption into that population brought the eventual disappearance of the Yellowknives as a distinct people.) Driven by vengeance or desperation over killings perpetrated by Yellowknives earlier in the year, in October of 1823 Dogribs attacked the Yellowknife Long Legs and his band, who were encamped in the area between Hottah Lake and Great Bear Lake. Thirty-four Yellowknives perished - four men, thirteen women, and seventeen children. This was a bitter reversal. Akaitcho refused to join Franklin's expedition to Great Bear Lake, sending word that he and his hunters would not go into the lands where their kinsmen had died, "lest we should attempt to renew the war." "Peace" took the form of mutual avoidance between Dogribs and Akaitcho's band. In 1829 a tense encounter, apparently the first since the destruction of Long Legs's band, was resolved without bloodshed. ..