Two New Proofs of Afriat's Theorem

We provide two, new simple proofs of Afriat's celebrated theorem..Afriat's theorem, SARP, GARP

Two New Proofs of Afriat's Theorem

Two New Proofs of Afriat's Theore

Revealed cardinal preference

I prove that as long as we allow the marginal utility for money (lambda) to vary between purchases (similarly to the budget) then the quasi-linear and the ordinal budget-constrained models rationalize the same data. However, we know that lambda is approximately constant. I provide a simple constructive proof for the necessary and sufficient condition for the constant lambda rationalization, which I argue should replace the Generalized Axiom of Revealed Preference in empirical studies of consumer behavior. 'Go Cardinals!' It is the minimal requirement of any scientifi c theory that it is consistent with the data it is trying to explain. In the case of (Hicksian) consumer theory it was revealed preference -introduced by Samuelson (1938,1948) - that provided an empirical test to satisfy this need. At that time most of economic reasoning was done in terms of a competitive general equilibrium, a concept abstract enough so that it can be built on the ordinal preferences over baskets of goods - even if the extremely specialized ones of Arrow and Debreu. However, starting in the sixties, economics has moved beyond the 'invisible hand' explanation of how -even competitive- markets operate. A seemingly unavoidable step of this 'revolution' was that ever since, most economic research has been carried out in a partial equilibrium context. Now, the partial equilibrium approach does not mean that the rest of the markets are ignored, rather that they are held constant. In other words, there is a special commodity -call it money - that reflects the trade-offs of moving purchasing power across markets. As a result, the basic building block of consumer behavior in partial equilibrium is no longer the consumer's preferences over goods, rather her valuation of them, in terms of money. This new paradigm necessitates a new theory of revealed preference

The Combinatorial World (of Auctions) According to GARP

Revealed preference techniques are used to test whether a data set is compatible with rational behaviour. They are also incorporated as constraints in mechanism design to encourage truthful behaviour in applications such as combinatorial auctions. In the auction setting, we present an efficient combinatorial algorithm to find a virtual valuation function with the optimal (additive) rationality guarantee. Moreover, we show that there exists such a valuation function that both is individually rational and is minimum (that is, it is component-wise dominated by any other individually rational, virtual valuation function that approximately fits the data). Similarly, given upper bound constraints on the valuation function, we show how to fit the maximum virtual valuation function with the optimal additive rationality guarantee. In practice, revealed preference bidding constraints are very demanding. We explain how approximate rationality can be used to create relaxed revealed preference constraints in an auction. We then show how combinatorial methods can be used to implement these relaxed constraints. Worst/best-case welfare guarantees that result from the use of such mechanisms can be quantified via the minimum/maximum virtual valuation function

Transcriptomic analysis of pathways regulated by toll-like receptor 4 in a murine model of chronic pulmonary inflammation and carcinogenesis

<p>Abstract</p> <p>Background</p> <p>Therapeutic strategies exist for human pulmonary neoplasia, however due to the heterogeneity of the disease, most are not very effective. The innate immunity gene, toll-like receptor 4 (TLR4), protects against chronic pulmonary inflammation and tumorigenesis in mice, but the mechanism is unclear. This study was designed to identify TLR4-mediated gene expression pathways that may be used as prognostic indicators of susceptibility to lung tumorigenesis in mice and provide insight into the mechanism.</p> <p>Methods</p> <p>Whole lung mRNA was isolated from C.C3H-<it>Tlr4</it>^{<it>Lps</it>-<it>d </it>}(BALB^{<it>Lps</it>-<it>d</it>}; <it>Tlr4 </it>mutant) and BALB/c (<it>Tlr4 </it>normal) mice following butylated hydroxytoluene (BHT)-treatment (four weekly ip. injections; 150-200 mg/kg/each; "promotion"). mRNA from micro-dissected tumors (adenomas) and adjacent uninvolved tissue from both strains were also compared 27 wks after a single carcinogen injection (3-methylcholanthrene (MCA), 10 μg/g; "control") or followed by BHT (6 weekly ip. injections; 125-200 mg/kg/each; "progression"). Bronchoalveolar lavage fluid was analyzed for inflammatory cell content and total protein determination, a marker of lung hyperpermeability; inflammation was also assessed using immunohistochemical staining for macrophages (F4/80) and lymphocytes (CD3) in mice bearing tumors (progression).</p> <p>Results</p> <p>During promotion, the majority of genes identified in the BALB^{<it>Lps</it>-<it>d </it>}compared to BALB/c mice (P < 0.05) were involved in epithelial growth factor receptor (EGFR) signaling (e.g. epiregulin (<it>Ereg</it>)), secreted phosphoprotein 1(<it>Spp1</it>)), which can lead to cell growth and eventual tumor development. Inflammation was significantly higher in BALB^{<it>Lps</it>-<it>d </it>}compared to BALB/c mice during progression, similar to the observed response during tumor promotion in these strains. Increases in genes involved in signaling through the EGFR pathway (e.g. <it>Ereg</it>, <it>Spp1</it>) were also observed during progression in addition to continued inflammation, chemotactic, and immune response gene expression in the BALB^{<it>Lps</it>-<it>d </it>}versus BALB/c mice (<it>P </it>< 0.05), which appears to provide more favorable conditions for cell growth and tumor development. In support of these findings, the BALB/c mice also had significantly reduced expression of many immune response and inflammatory genes in both the tumors and uninvolved tissue.</p> <p>Conclusion</p> <p>This transcriptomic study determined the protective effect of TLR4 in lung carcinogenesis inhibition of multiple pathways including EGFR (e.g. <it>Ereg</it>), inflammatory response genes (e.g. <it>Cxcl5)</it>, chemotaxis (e.g. <it>Ccr1</it>) and other cell proliferation genes (e.g. <it>Arg1</it>, <it>Pthlh</it>). Future studies will determine the utility of these pathways as indicators of immune system deficiencies and tumorigenesis.</p

Modeling biomedical experimental processes with OBI

BACKGROUND: Experimental descriptions are typically stored as free text without using standardized terminology, creating challenges in comparison, reproduction and analysis. These difficulties impose limitations on data exchange and information retrieval. RESULTS: The Ontology for Biomedical Investigations (OBI), developed as a global, cross-community effort, provides a resource that represents biomedical investigations in an explicit and integrative framework. Here we detail three real-world applications of OBI, provide detailed modeling information and explain how to use OBI. CONCLUSION: We demonstrate how OBI can be applied to different biomedical investigations to both facilitate interpretation of the experimental process and increase the computational processing and integration within the Semantic Web. The logical definitions of the entities involved allow computers to unambiguously understand and integrate different biological experimental processes and their relevant components. AVAILABILITY: OBI is available at http://purl.obolibrary.org/obo/obi/2009-11-02/obi.ow