Logics for belief functions on MV-algebras

In this paper we present a generalization of belief functions over fuzzy events. In particular we focus on belief functions defined in the algebraic framework of finite MV-algebras of fuzzy sets. We introduce a fuzzy modal logic to formalize reasoning with belief functions on many-valued events. We prove, among other results, that several different notions of belief functions can be characterized in a quite uniform way, just by slightly modifying the complete axiomatization of one of the modal logics involved in the definition of our formalism.     

Calibration of a multifactor model for the forward markets of several commodities

We propose a model for the evolution of forward prices of several commodities, which is an extension of the factor forward model in [1, 2], to a market where multiple commodities are traded. We calibrate this model in a market where forward contracts on multiple commodities are present, using historical forward prices. First, we calibrate separately the four coefficients of each individual commodity, using an approach based on quadratic variation/covariation of forward prices. Then, with the same technique, we pass to the estimation of the mutual correlation among the Brownian motions driving the different commodities. This calibration is compared to a calibration method used by practitioners, which uses rolling time series and requires a modification of the model, but turns out to be more accurate in practice, especially with a low frequency of observed transaction. We present efficient methods to perform the calibration with both methods, as well as the calibration of the intercommodity correlation matrix. Then we calibrate our model to WTI, ICE Brent and ICE Gasoil forward prices. Finally we present a method for estimating spot volatility from forward parameters, with an application to the WTI spot volatility.     

Footnote to a paper by hartshorne

We prove that every curve in the biliaison class of an extremal curve in P³ can be connected to an extremal curve.     

Curves in the double plane

We study in detail locally Cohen-Macaulay curves in P⁴ which are contained in a double plane 2H, thus completing the classification of curves lying on surfaces of degree two. We describe the irreducible components of the Hilbert schemes H _d,g(2H) of lo-cally Cohen-Macaulay curves in 2H of degree d and arithmetic genus g, and we show that H _d,g(2H) is connected. We also discuss the Rao module of these curves and liaison and biliaison equiva-lence classes.     

Measurement of Very Fast Exchange Rates of Individual Amide Protons in Proteins by NMR Spectroscopy

NMR spectroscopy is a pivotal technique to measure hydrogen exchange rates in proteins. However, currently available NMR methods to measure backbone exchange are limited to rates of up to a few per second. To raise this limit, we have developed an approach that is capable of measuring proton exchange rates up to approximately 10⁴ s⁻¹. Our method relies on the detection of signal loss due to the decorrelation of antiphase operators 2N_xH_z by exchange events that occur during a series of pi pulses on the ¹⁵N channel. In practice, signal attenuation was monitored in a series of 2D H(CACO)N spectra, recorded with varying pi-pulse spacing, and the exchange rate was obtained by numerical fitting to the evolution of the density matrix. The method was applied to the small calcium-binding protein Calbindin D_9k, where exchange rates up to 600 s⁻¹ were measured for amides, where no signal was detectable in ¹⁵N−¹H HSQC spectra. A temperature variation study allowed us to determine apparent activation energies in the range 47–69 kJ mol⁻¹ for these fast exchanging amide protons, consistent with hydroxide-catalyzed exchange.     

Quantifying turbulence-induced segregation of inertial particles

Particles with different density from the advecting turbulent fluids cluster due to the different response of light and heavy particles to turbulent fluctuations. This study focuses on the quantitative characterization of the segregation of dilute polydisperse inertial particles evolving in turbulent flow, as obtained from direct numerical simulation of homogeneous isotropic turbulence. We introduce an indicator of segregation amongst particles of different inertia and/or size, from which a length scale r_{seg}, quantifying the segregation degree between two particle types, is deduced.     

Ground state of graphene in the presence of random charged impurities

We calculate the carrier-density-dependent ground-state properties of graphene in the presence of random charged impurities in the substrate taking into account disorder and interaction effects nonperturbatively on an equal footing in a self-consistent theoretical formalism. We provide detailed quantitative results on the dependence of the disorder-induced spatially inhomogeneous two-dimensional carrier density distribution on the external gate bias, the impurity density, and the impurity location. We find that the interplay between disorder and interaction is strong, particularly at lower impurity densities. We show that, for the currently available typical graphene samples, inhomogeneity dominates graphene physics at low (< or approximately 10(12) cm(-2)) carrier density with the density fluctuations becoming larger than the average density.