A complexity dichotomy for poset constraint satisfaction

In this paper we determine the complexity of a broad class of problems that extends the temporal constraint satisfaction problems. To be more precise we study the problems Poset-SAT($\Phi$), where $\Phi$ is a given set of quantifier-free $\leq$-formulas. An instance of Poset-SAT($\Phi$) consists of finitely many variables $x_1,\ldots,x_n$ and formulas $\phi_i(x_{i_1},\ldots,x_{i_k})$ with $\phi_i \in \Phi$; the question is whether this input is satisfied by any partial order on $x_1,\ldots,x_n$ or not. We show that every such problem is NP-complete or can be solved in polynomial time, depending on $\Phi$. All Poset-SAT problems can be formalized as constraint satisfaction problems on reducts of the random partial order. We use model-theoretic concepts and techniques from universal algebra to study these reducts. In the course of this analysis we establish a dichotomy that we believe is of independent interest in universal algebra and model theory.Comment: 29 page

Hydrocarbon molar water solubility predicts NMDA vs. GABAA receptor modulation.

BackgroundMany anesthetics modulate 3-transmembrane (such as NMDA) and 4-transmembrane (such as GABAA) receptors. Clinical and experimental anesthetics exhibiting receptor family specificity often have low water solubility. We hypothesized that the molar water solubility of a hydrocarbon could be used to predict receptor modulation in vitro.MethodsGABAA (α1β2γ2s) or NMDA (NR1/NR2A) receptors were expressed in oocytes and studied using standard two-electrode voltage clamp techniques. Hydrocarbons from 14 different organic functional groups were studied at saturated concentrations, and compounds within each group differed only by the carbon number at the ω-position or within a saturated ring. An effect on GABAA or NMDA receptors was defined as a 10% or greater reversible current change from baseline that was statistically different from zero.ResultsHydrocarbon moieties potentiated GABAA and inhibited NMDA receptor currents with at least some members from each functional group modulating both receptor types. A water solubility cut-off for NMDA receptors occurred at 1.1 mM with a 95% CI = 0.45 to 2.8 mM. NMDA receptor cut-off effects were not well correlated with hydrocarbon chain length or molecular volume. No cut-off was observed for GABAA receptors within the solubility range of hydrocarbons studied.ConclusionsHydrocarbon modulation of NMDA receptor function exhibits a molar water solubility cut-off. Differences between unrelated receptor cut-off values suggest that the number, affinity, or efficacy of protein-hydrocarbon interactions at these sites likely differ

The Reducts of the Homogeneous Binary Branching C-relation

Let (L;C) be the (up to isomorphism unique) countable homogeneous structure carrying a binary branching C-relation. We study the reducts of (L;C), i.e., the structures with domain L that are first-order definable in (L;C). We show that up to existential interdefinability, there are finitely many such reducts. This implies that there are finitely many reducts up to first-order interdefinability, thus confirming a conjecture of Simon Thomas for the special case of (L;C). We also study the endomorphism monoids of such reducts and show that they fall into four categories.Comment: 39 pages, 4 figure

Synthesis Of -Tcp Powder Via Wet Precipitation And Hydrothermal Methods

Matlamat kajian ini adalah untuk mensintesis β-TCP [β-Ca3(PO4)2] menggunakan Ca(OH)2 dan H3PO4 sebagai bahan mula. The purpose of this study is to synthesize β-TCP [β-Ca3(PO4)2] using Ca(OH)2 and H3PO4 as the starting material