Mechanics, cosmology and Mach's principle

It is pointed out that recent cosmological findings seem to support the view that the mass/energy distribution of the universe defines the Newtonian inertial frames as originally suggested by Mach. The background concepts of inertial frame, Newton's second law, and fictitious forces are clarified. A precise definition of Mach's principle is suggested. Then an approximation to general relativity discovered by Einstein, Infeld, and Hoffmann is used and it is found that this precise formulation of Mach's principle is realized provided the mass/energy density of the universe has a specific value. This value turns out to be twice the critical density. The implications of this approximate result is put into context.Comment: 9 pages, 34 references, 0 figure

Analytic results and weighted Monte Carlo simulations for CDO pricing

We explore the possibilities of importance sampling in the Monte Carlo pricing of a structured credit derivative referred to as Collateralized Debt Obligation (CDO). Modeling a CDO contract is challenging, since it depends on a pool of (typically about 100) assets, Monte Carlo simulations are often the only feasible approach to pricing. Variance reduction techniques are therefore of great importance. This paper presents an exact analytic solution using Laplace-transform and MC importance sampling results for an easily tractable intensity-based model of the CDO, namely the compound Poissonian. Furthermore analytic formulae are derived for the reweighting efficiency. The computational gain is appealing, nevertheless, even in this basic scheme, a phase transition can be found, rendering some parameter regimes out of reach. A model-independent transform approach is also presented for CDO pricing.Comment: 12 pages, 9 figure

The transcriptional activity of hepatocyte nuclear factor 4 alpha is inhibited via phosphorylation by ERK1/2

Hepatocyte nuclear factor 4 alpha (HNF4alpha) nuclear receptor is a master regulator of hepatocyte development, nutrient transport and metabolism. HNF4alpha is regulated both at the transcriptional and post-transcriptional levels by different mechanisms. Several kinases (PKA, PKC, AMPK) were shown to phosphorylate and decrease the activity of HNF4alpha. Activation of the ERK1/2 signalling pathway, inducing proliferation and survival, inhibits the expression of HNF4alpha. However, based on our previous results we hypothesized that HNF4alpha is also regulated at the post-transcriptional level by ERK1/2. Here we show that ERK1/2 is capable of directly phosphorylating HNF4alpha in vitro at several phosphorylation sites including residues previously shown to be targeted by other kinases, as well. Furthermore, we also demonstrate that phosphorylation of HNF4alpha leads to a reduced trans-activational capacity of the nuclear receptor in luciferase reporter gene assay. We confirm the functional relevance of these findings by demonstrating with ChIP-qPCR experiments that 30-minute activation of ERK1/2 leads to reduced chromatin binding of HNF4alpha. Accordingly, we have observed decreasing but not disappearing binding of HNF4alpha to the target genes. In addition, 24-hour activation of the pathway further decreased HNF4alpha chromatin binding to specific loci in ChIP-qPCR experiments, which confirms the previous reports on the decreased expression of the HNF4a gene due to ERK1/2 activation. Our data suggest that the ERK1/2 pathway plays an important role in the regulation of HNF4alpha-dependent hepatic gene expression

Heat sensitivity of different mustard ( Sinapis alba L.) genotype myrosinase enzyme

Mustard seed ( Sinapis alba L.) has valuable chemical composition and its cultivation in moderate climate, especially in Hungary is economically feasible. In spite of the advantageous chemical composition and colloid-chemical properties, the use of mustard seed flour is limited in food industry or in animal feeding because of its pungent taste. The pungent taste develops through the action of myrosinase; but it could be eliminated by heat inactivation of the enzyme. In the course of our preliminary experiments, it was observed that heat inactivation of the myrosinase enzyme depended on mustard variety. The heat stability of myrosinase enzyme prepared from different mustard varieties was examined and compared in our research work. Crude myrosinase was prepared from three mustard genotypes (Budakalászi, Tilney, and LM-1 (a low erucic acid content cultivar) and the heat stability was determined at 60, 70 or 80 °C for 5, 10, 15, 20 and 30 min. The semi-logarithmic plots of myrosinase activity as a function of time at different temperatures indicated that heat inactivation of crude myrosinase enzyme follows first-order kinetics. Characterising the rate of inactivation by the slope of the curve, significant differences were established in heat stability between genotypes at 60 °C. There were no significant differences between varieties at higher temperatures (70 and 80 °C). Longer than 10 min heat treatment causes more than 90% inactivation of the enzyme