A non-Gaussian Ornstein–Uhlenbeck model for pricing wind power futures

The recent introduction of wind power futures written on the German wind power production index has brought with it new interesting challenges in terms of modelling and pricing. Some particularities of this product are the strong seasonal component embedded in the underlying, the fact that the wind index is bounded from both above and below and also that the futures are settled against a synthetically generated spot index. Here, we consider the non-Gaussian Ornstein–Uhlenbeck type processes proposed by Barndorff-Nielsen and Shephard in the context of modelling the wind power production index. We discuss the properties of the model and estimation of the model parameters. Further, the model allows for an analytical formula for pricing wind power futures. We provide an empirical study, where the model is calibrated to 37 years of German wind power production index that is synthetically generated assuming a constant level of installed capacity. Also, based on 1 year of observed prices for wind power futures with different delivery periods, we study the market price of risk. Generally, we find a negative risk premium whose magnitude decreases as the length of the delivery period increases. To further demonstrate the benefits of our proposed model, we address the pricing of European options written on wind power futures, which can be achieved through Fourier techniques.     

Hlder Norm Estimate for a Hilbert Transform in Hermitean Clifford Analysis

A Hilbert transform for Hlder continuous circulant (2 × 2) matrix functions, on the d-summable (or fractal) boundary Γ of a Jordan domain Ω in R2n , has recently been introduced within the framework of Hermitean Clifford analysis. The main goal of the present paper is to estimate the Hlder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the Hlder exponents, the diameter of Γ and a specific d-sum (d d) of the Whitney decomposition of Ω. The result is shown to include the case of a more standard Hilbert transform for domains with left Ahlfors-David regular boundary.     

Charge Site Mass Spectra: Conformation-Sensitive Components of the Electron Capture Dissociation Spectrum of a Protein

A conventional electron capture dissociation (ECD) spectrum of a protein is uniquely characteristic of the first dimension of its linear structure. This sequence information is indicated by summing the primary c ^m+ and z ^m+? products of cleavage at each of its molecular ion’s inter-residue bonds. For example, the ECD spectra of ubiquitin (M?+?nH)ⁿ⁺ ions, n?=?7–13, provide sequence characterization of 72 of its 75 cleavage sites from 1843 ions in seven c ^(1–7)+ and eight z ^(1–8)+? spectra and their respective complements. Now we find that each of these c/z spectra is itself composed of “charge site (CS)” spectra, the c ^m+ or z ^m+? products of electron capture at a specific protonated basic residue. This charge site has been H-bonded to multiple other residues, producing multiple precursor ion forms; ECD at these residues yields the multiple products of that CS spectrum. Closely similar CS spectra are often formed from a range of charge states of ubiquitin and KIX ions; this indicates a common secondary conformation, but not the conventional α-helicity postulated previously. CS spectra should provide new capabilities for comparing regional conformations of gaseous protein ions and delineating ECD fragmentation pathways.

Nucleophilic Addition of Nitrogen to Aryl Cations: Mimicking Titan Chemistry

The reactivity of aryl cations toward molecular nitrogen is studied systematically in an ion trap mass spectrometer at 10² Pascal of nitrogen, the pressure of the Titan main haze layer. Nucleophilic addition of dinitrogen occurs and the nature of aryl group has a significant influence on the reactivity, through inductive effects and by changing the ground state spin multiplicity. The products of nitrogen activation, aryldiazonium ions, react with typical nitriles, aromatic amines, and alkynes (compounds that are relevant as possible Titan atmosphere constituents) to form covalently bonded heterocyclic products. Theoretical calculations at the level [DFT(B3LYP)/6-311++G(d,p)] indicate that the N₂ addition reaction is exothermic for the singlet aryl cations but endothermic for their triplet spin isomers. The –OH and –NH₂ substituted aryl ions are calculated to have triplet ground states, which is consistent with their decreased nitrogen addition reactivity. The energy needed for the generation of the aryl cations from their protonated precursors (ca. 340 kJ/mol starting with protonated aniline) is far less than that required to directly activate the nitrogen triple bond (the lowest energy excited state of N₂ lies ca. 600 kJ/mol above the ground state). The formation of aza-aromatics via arene ionization and subsequent reactions provide a conceivable route to the genesis of nitrogen-containing organic molecules in the interstellar medium and Titan haze layers.

Synthesis of N-Benzoyl-4-oxo-1,2,3,4-Tetrahydropyridine and its Ethylene Ketal

Recently we had need for large quantities of N-benzoyl-4-oxo-1,2,3,4-tetrahydropyridine (1), its ethylene ketal derivative 7, and potentially other N-acyl derivatives. Prior to our initial studies, the N-carboethoxy derivative 2 had been prepared by sodium borohydride reduction of N-carboethoxy-4-pyridone.¹.     

The stereochemistry of glycolipids. A key for understanding membrane functions?

A Commentary on the paper ”Studies on liquid‐crystalline glycosides" by Volkmar Vill, Thomas Böcker, Joachim Thiem and Fred Fischer. First published in Liquid Crystals, 6, 349‐356 (1989).     

Hexicon 2: Automated Processing of Hydrogen-Deuterium Exchange Mass Spectrometry Data with Improved Deuteration Distribution Estimation

Hydrogen–deuterium exchange (HDX) experiments analyzed by mass spectrometry (MS) provide information about the dynamics and the solvent accessibility of protein backbone amide hydrogen atoms. Continuous improvement of MS instrumentation has contributed to the increasing popularity of this method; however, comprehensive automated data analysis is only beginning to mature. We present Hexicon 2, an automated pipeline for data analysis and visualization based on the previously published program Hexicon (Lou et al. 2010). Hexicon 2 employs the sensitive NITPICK peak detection algorithm of its predecessor in a divide-and-conquer strategy and adds new features, such as chromatogram alignment and improved peptide sequence assignment. The unique feature of deuteration distribution estimation was retained in Hexicon 2 and improved using an iterative deconvolution algorithm that is robust even to noisy data. In addition, Hexicon 2 provides a data browser that facilitates quality control and provides convenient access to common data visualization tasks. Analysis of a benchmark dataset demonstrates superior performance of Hexicon 2 compared with its predecessor in terms of deuteration centroid recovery and deuteration distribution estimation. Hexicon 2 greatly reduces data analysis time compared with manual analysis, whereas the increased number of peptides provides redundant coverage of the entire protein sequence. Hexicon 2 is a standalone application available free of charge under http://hx2.mpimf-heidelberg.mpg.de.

Cyclodimerization versus Polymerization of Methyl Methacrylate Induced by N‐Heterocyclic Carbenes: A Combined Experimental and Theoretical Study

The activation behavior of two N‐heterocyclic carbenes (NHCs), namely, 1,3‐bis(isopropyl)imidazol‐2‐ylidene(NHCiPr) and 1,3‐bis(tert‐butyl) imidazol‐2‐ylidene (NHCtBu), as organic nucleophiles in the reaction with methyl methacrylate (MMA) is described. NHCtBu allows the polymerization of MMA in DMF at room temperature and in toluene at 50 °C, whereas NHCiPr reacts with two molecules of MMA, forming an unprecedented imidazolium–enolate cyclodimer (NHCiPr/MMA=1:2). It is proposed that the reaction mechanism occurs by initial 1,4‐nucleophilic addition of NHCiPr to MMA, generating a zwitterionic enolate 2 , followed by addition of 2 to a second MMA molecule, forming a linear imidazolium–enolate 3 (NHCiPr/MMA=1:2). Proton transfer, generating intermediate 5 , followed by cyclization and release of methanol yielded the aforementioned zwitterionic cyclodimer 1:2 adduct 7 , the molecular structure of which has been established by NMR spectroscopy, X‐ray diffraction, and mass spectrometry. This unexpected difference between NHCtBu and NHCiPr in the reaction with MMA (polymerization and cyclodimerization, respectively) can be rationalized by using DFT calculations. In particular, the nature of the NHC strongly influences the cyclodimerization pathway, the cyclization of 5 and the release of methanol are the discriminating step and limiting step, respectively. In the case of NHCtBu, both steps are strongly disfavoured compared with that of NHCiPr (energetic difference of around 14 and 9 kcal mol^?1, respectively), preventing the cyclization mechanism from a kinetic viewpoint. Moreover, addition of a third molecule of MMA in the polymerization pathway results in a lower activation barrier than that of the limiting step in the cyclodimerization pathway (difference of around 14 kcal mol^?1), in agreement with the formation of polymethyl methacrylate (PMMA) by using NHCtBu as nucleophile.     

Initiation of Protein Synthesis with Non-Canonical Amino Acids In Vivo

By transplanting identity elements into E. coli tRNA^fMet, we have engineered an orthogonal initiator tRNA (itRNA^Ty2) that is a substrate for Methanocaldococcus jannaschii TyrRS. We demonstrate that itRNA^Ty2 can initiate translation in vivo with aromatic non-canonical amino acids (ncAAs) bearing diverse sidechains. Although the initial system suffered from low yields, deleting redundant copies of tRNA^fMet from the genome afforded an E. coli strain in which the efficiency of non-canonical initiation equals elongation. With this improved system we produced a protein containing two distinct ncAAs at the first and second positions, an initial step towards producing completely unnatural polypeptides in vivo. This work provides a valuable tool to synthetic biology and demonstrates remarkable versatility of the E. coli translational machinery for initiation with ncAAs in vivo.     

Initiation of Protein Synthesis with Non‐Canonical Amino Acids In Vivo

By transplanting identity elements into E. coli tRNA^fMet, we have engineered an orthogonal initiator tRNA (itRNA^Ty2) that is a substrate for Methanocaldococcus jannaschii TyrRS. We demonstrate that itRNA^Ty2 can initiate translation in vivo with aromatic non‐canonical amino acids (ncAAs) bearing diverse sidechains. Although the initial system suffered from low yields, deleting redundant copies of tRNA^fMet from the genome afforded an E. coli strain in which the efficiency of non‐canonical initiation equals elongation. With this improved system we produced a protein containing two distinct ncAAs at the first and second positions, an initial step towards producing completely unnatural polypeptides in vivo. This work provides a valuable tool to synthetic biology and demonstrates remarkable versatility of the E. coli translational machinery for initiation with ncAAs in vivo.