Model Construction Sample Clauses

Model Construction. 2.1 MODEL HYPOTHESIS It is assumed that the financial industry chain composed of a risk neutral financial provider M and a risk aversion firm

Model Construction. We consider a two-period revenue-sharing model. We adopt the Stackelberg game in game theory as a basic model and use the backward induction to solve the problem. Following Xxxxxxx-Xxxxx (2013), we consider promotional efforts to our model setting. Table 1 lists all the parameters and decision variables in the model. First, the distributor considers the expected revenue for the following two periods. The distributor’s revenue function in the first period is 𝜋𝑀 = 𝜌{[(1 − 𝜃)(1 − 𝑏𝑞1) + 𝑤]𝑞1 + 𝜋ℎ } 2𝑀 +(1 − 𝜌){[(1 − 𝜃)(Xx − 𝑏𝑞1) + 𝑤]𝑞1 + 𝜋 𝑙 }. 2𝑀 (1) However, the theater also considers the expected revenue for the following two periods. The theater’s revenue function in the first period is 𝜋𝑅 = 𝜌{[𝜃(1 − 𝑏𝑞1) − 𝑤]𝑞1 + 𝜋ℎ } 2𝑅 +(1 − 𝜌){[𝜃(Xx − 𝑏𝑞1) − 𝑤]��1 + 𝜋 𝑙 }.2𝑅 (2) At the end of the first period, the demand will be realized and thus creating the following two cases at this moment:

Model Construction. Xxxxx provides a structured editor for constructing and modifying models stored in the database. As mentioned above, this facilitates easy extension as well as incre- mental development and analysis of models. Rodin needs further improvement to make it easier to perform standard editing tasks such as text search, copy/paste and undo/redo. Rodin will be extended to provide refactoring facilities, such as identifier renaming, that can be applied not just to models but to proof obligations, proofs and other forms of elements. Better support for browsing refinement links between models will be provided, for example, allowing the refinements and abstractions of events to be followed down or up a refinement chain.

Model Construction services consisting of preparation of: .01 Small scale block model(s) showing relationship of structure(s) to site .02 Moderate scale block model(s) of structure(s) designed for the Project

Model Construction. ‌ Table 1 lists all the parameters relevant for our simple probabilistic model for T cell dynamics in the thymus and the periphery. Table 1: Model 1 Parameters Abbreviation Description Values p-MHC peptide presented on MHC sp-MHC self-peptide presented on MHC DC-self self-peptides presented on *all* DC p Probability of signaling (TCR binding) per encounter (Signal 1) range [0,1] p1 = p Probability of T cell clonal deletion per signal 1 encounter in the thymus range [0,1] p2 = p/k k n1 Probability of T cell activation per signal 1 encounter in the periphery Difference factorDifference in probability of apoptosis in thymus vs. actiation in the periphery number of DC encounters in thymus k ≥ 1 k ≥ 1 4000 n2 number of DC encounters in periphery n2 varies Let p be the probability of signal 1 and measured by the avidity and affinity of a TRC against an sp-MHC complex. In our simple models, signal 1 leads to either clonal deletion in the thymus (p1) or T cell activation in the periphery(p2) following an encounter with a DC for a DC-self reactive T cell. p takes into account factors such as both the 1. level of expression of the relevant DC-self peptide, and 2. the affinity of the TCR for the peptide, and it can range from 0 to 1. If this T-cells has n1 encounters with DC in the thymus then the probability that the cell escapes depletion in the thymus is: probability of escape in thymus = PE = (1 − p1)n1 If the T cell has n2 encounters with activated DC in the periphery then the prob- ability of activation in the periphery is: S − − 2 prob. of stimulation in periphery = P = 1 (1 p )n2 prob. of n`o st˛i¸m. ixn n2 trials and for autoimmunity to occur the T cell must escape deletion in the thymus and be stim- ulated in the periphery17. ` ˛¸ x prob. autoimmunity = PA = PE×PS = (1 − p1)n1 prob. of no stim in thymus 1 (1 p )n2 prob. `of stim˛¸in pexriphery Based on previous quantitative estimates of the amount of T-DC contacts during negative selection, we chose n1 = 4000 similarly to Mu¨ller and Xxxxxxxxxx 9. The amount of T-DC encounters in the periphery, denoted by n2, is hard to quantify depending on the context of the T cell condition we are assessing. Moreover, the factor k equals the difference in probability of thymic selection in the periphery and the probability of peripheral stimulation (p2 = p/k). In our simple consideration, we set the requirements for clonal deletion the same as the requirements for peripheral stimulation, thus k=1. And we proposed that it...

Model Construction. ‌ We hypothesize that the multiple encounters of DCs necessary for priming pro- duce multiplicative signals that restrict the probability of stimulation upon encounter. We hypothesize that every successful encounter will increase the signal by an additive signal manipulator constant of α, and once the signal exceeds a threshold τ , then the T cell will proliferate (stimulated). Meanwhile, Xxxxxx et al., has shown that a T cell is constantly migratory. If it is not stimulated after the priming phase of one lymph node, then the T cell migrates to another lymph node and starts the priming process all over again. We used a probabilistic model, modeling the probability of proliferation using fac- tors such as the number of serial encounters, the increasing signal factor per every successful encounter, and the probability of stimulation per encounter at the periphery. In our model, time is a discrete variable and we assume that one time interval is one T-Dendritic cell interaction. Computationally, if the encounter is successful (determined by a randomly gen- erated probability compared to p), then the integrated signal (Si) increases by a ( +a) (Algorithm 1). When the integrated signal (Si) reaches the threshold τ , then a T cell is activated. This turns out to be a binomial model in which we can calculate the combined probability density of a binomial distribution function given a certain probability of success- ful encounters (p) (Algorithm 1 execution, p.nd function). We chose n2 = 60 for the number of encounters in the periphery. Biologically, this is the approximate number of T-Dendritic cell encounters during one lymph node priming phase (Table 2). This is similar to a biologi- cal local acute infection, and we assume that all DCs that the T cells encounter are activated (DCs express costimulatory molecules such as CD80), thus signal 2 is present during all DC encounters. By using this small n2, we are assuming that the memory of integrated signals is cleared if the T cell is not stimulated in one lymph node– the signal accumulation restarts once the T cell enters another lymph node. This assumption is in place to allow us to un- derstand what happens during one T cell priming series of one lymph node, and obtain an upper bound to the level of self-reactivity and potential probability of autoimmunity of the system. Moreover, T cell’s serial encounter of dendritic cells and integrated signals have shown to not only happen in the periphery, but also in the ...

Model Construction