Normal subgroup generated by a plane polynomial automorphism

We study the normal subgroup 〈f〉 _N generated by an element f ≠ id in the group G of complex plane polynomial automorphisms having Jacobian determinant 1. On the one hand, if f has length at most 8 relative to the classical amalgamated product structure of G, we prove that 〈f〉 _N = G. On the other hand, if f is a sufficiently generic element of even length at least 14, we prove that 〈f〉 _N ≠ G.     

Optimal control of a production-inventory system with customer impatience

We consider the control of a production-inventory system with impatient customers. We show that the optimal policy can be described using two thresholds: a production base-stock level that determines when production takes place and an admission threshold that determines when orders should be accepted. We describe an algorithm for computing the performance of the system for any choice of base-stock level and admission threshold. In a numerical study, we compare the performance of the optimal policy against several other policies.     

Thermodynamics of a continuous medium with electric and magnetic dipoles

The thermodynamics of an electrically charged, multicomponent fluid with spontaneous electric and magnetic dipoles is analysed in the presence of electromagnetic fields. Taking into account the chemical composition of the current densities and stress tensors leads to three types of irreversible terms: scalars, vectors and pseudo-vectors. The scalar terms account for chemical reactivities, the vectorial terms account for transport and the pseudo-vectorial terms account for relaxation. The linear phenomenological relations, derived from the irreversible evolution, describe notably the Lehmann and electric Lehmann effects, the Debye relaxation of polar molecules and the Landau-Lifshitz relaxation of the magnetisation. This formalism accounts for the thermal and electric magnetisation accumulations and magnetisation waves. It also predicts that a temperature gradient affects the dynamics of magnetic vortices and drives magnetisation waves.     

Critical reflexivity in financial markets: a Hawkes process analysis

We model the arrival of mid-price changes in the E-mini S&P futures contract as a self-exciting Hawkes process. Using several estimation methods, we find that the Hawkes kernel is power-law with a decay exponent close to ?1.15 at short times, less than ≈ 10³ s, and crosses over to a second power-law regime with a larger decay exponent ≈–1.45 for longer times scales in the range [10³ ,10⁶ ] seconds. More importantly, we find that the Hawkes kernel integrates to unity independently of the analysed period, from 1998 to 2011. This suggests that markets are and have always been close to criticality, challenging a recent study which indicates that reflexivity (endogeneity) has increased in recent years as a result of increased automation of trading. However, we note that the scale over which market events are correlated has decreased steadily over time with the emergence of higher frequency trading.     

Crises and Collective Socio-Economic Phenomena: Simple Models and Challenges

Financial and economic history is strewn with bubbles and crashes, booms and busts, crises and upheavals of all sorts. Understanding the origin of these events is arguably one of the most important problems in economic theory. In this paper, we review recent efforts to include heterogeneities and interactions in models of decision. We argue that the so-called Random Field Ising model (rfim) provides a unifying framework to account for many collective socio-economic phenomena that lead to sudden ruptures and crises. We discuss different models that can capture potentially destabilizing self-referential feedback loops, induced either by herding, i.e. reference to peers, or trending, i.e. reference to the past, and that account for some of the phenomenology missing in the standard models. We discuss some empirically testable predictions of these models, for example robust signatures of rfim-like herding effects, or the logarithmic decay of spatial correlations of voting patterns. One of the most striking result, inspired by statistical physics methods, is that Adam Smith’s invisible hand can fail badly at solving simple coordination problems. We also insist on the issue of time-scales, that can be extremely long in some cases, and prevent socially optimal equilibria from being reached. As a theoretical challenge, the study of so-called “detailed-balance” violating decision rules is needed to decide whether conclusions based on current models (that all assume detailed-balance) are indeed robust and generic.     

Analysis of high molecular mass proteins larger than 150 kDa using cyanogen bromide cleavage and conventional 2-DE

Proteomic approaches including high-resolution 2-DE are providing the tools needed to discover disease-associated biomarkers in complex biological samples. Although 2-DE is an extremely powerful approach to analyze the proteome, the separation of proteins with extreme molecular masses still remains an issue requiring improvement. Because high molecular mass (HMM) proteins larger than 150 kDa have already been observed to be differentially expressed in several pathologies such as cancer, we developed an original strategy to analyze this part of the proteome that is not easily separated by 2-DE in polyacrylamide gels. This strategy is based on the 2-DE separation of cyanogen bromide (CNBr) fragments of purified HMM protein fractions, and combines techniques including SEC fractionation, TCA precipitation, CNBr cleavage, 2-DE and MS analysis. The method was first tested on a model protein, the BSA. Preliminary results obtained using colonic tissues led to the identification of six HMM proteins with M(r) comprised between 163 and 533 kDa in their reduced state. These results demonstrated that our CNBr/2-DE approach should provide a powerful tool for identification of new biomarkers larger than 150 kDa.     

An expedient synthesis of the fibril binding compound FSB via sequential Pd-catalyzed coupling reactions

The styryl benzene derivative (E, E)-1-fluoro-2,5-bis(3-hydroxycarbonyl-4-hydroxy)styrylbenzene (FSB), well-known for its binding to beta-amyloid peptide fibrils, was synthesized in an efficient manner exploiting two sequential palladium(0)-catalyzed coupling reactions in a 34% overall yield. This is a substantial improvement to the previously reported synthesis of FSB in 1.1%.     

Liquid and gas chromatography coupled to isotope ratio mass spectrometry for the determination of 13C-valine isotopic ratios in complex biological samples

On-line gas chromatography-combustion-isotope ratio mass spectrometry (GC-C-IRMS) is commonly used to measure isotopic ratios at natural abundance as well as for tracer studies in nutritional and medical research. However, high-precision (13)C isotopic enrichment can also be measured by liquid chromatography-isotope ratio mass spectrometry (LC-IRMS). Indeed, LC-IRMS can be used, as shown by the new method reported here, to obtain a baseline separation and to measure (13)C isotopic enrichment of underivatised amino acids (Asp, Thr-Ser, Glu, Pro, Gly, Ala, Cys and Val). In case of Val, at natural abundance, the SD(delta(13)C) reported with this method was found to be below 1 per thousand . Another key feature of the new LC-IRMS method reported in this paper is the comparison of the LC-IRMS approach with the conventional GC-C-IRMS determination. To perform this comparative study, isotopic enrichments were measured from underivatised Val and its N(O, S)-ethoxycarbonyl ethyl ester derivative. Between 0.0 and 1.0 molar percent excess (MPE) (delta(13)C= -12.3 to 150.8 per thousand), the calculated root-mean-square (rms) of SD was 0.38 and 0.46 per thousand and the calculated rms of accuracy was 0.023 and 0.005 MPE, respectively, for GC-C-IRMS and LC-IRMS. Both systems measured accurately low isotopic enrichments (0.002 atom percent excess (APE)) with an SD (APE) of 0.0004. To correlate the relative (delta(13)C) and absolute (atom%, APE and MPE) isotopic enrichment of Val measured by the GC-C-IRMS and LC-IRMS devices, mathematical equations showing the slope and intercept of the curves were established and validated with experimental data between 0.0 to 2.3 MPE. Finally, both GC-C-IRMS and LC-IRMS instruments were also used to assess isotopic enrichment of protein-bound (13)C-Val in tibial epiphysis in a tracer study performed in rats. Isotopic enrichments measured by LC-IRMS and GC-C-IRMS were not statistically different (p>0.05). The results of this work indicate that the LC-IRMS was successful for high-precision (13)C isotopic measurements in tracer studies giving (13)C isotopic enrichment similar to the GC-C-IRMS but without the step of GC derivatisation. Therefore, for clinical studies requiring high-precision isotopic measurement, the LC-IRMS is the method of choice to measure the isotopic ratio.     

Studies on the Heck reaction with alkenyl phosphates: can the 1,2-migration be controlled? Scope and limitations

A catalyst system was identified which promotes the Heck coupling of nonactivated vinyl phosphates with electron deficient alkenes providing a new entry to diene products from simple and readily accessible starting materials. In contrast to our earlier work exploiting P(t-Bu)3 as the ligand in the presence of PdCl2(COD), the application of Buchwald's dialkylbiarylphosphines, X-Phos, effectively promoted the vinylic substitution with a wide range of alkenyl phosphates in the presence of 10 equiv of lithium chloride. Importantly, these reaction conditions suppressed 1,2-migration of the alkenyl palladium(II) intermediate. Further studies are also reported with the catalytic system which encourages isomerization in order to determine the range of vinyl phosphates that may participate in these coupling reactions. The extent of the 1,2-migration was dependent on the C1-substituent where best results were noted for substrates possessing a C1-alkyl quaternary carbon. Hence, with certain members of this class of alkenyl phosphates either the migrated or nonmigrated Heck products may be preferentially synthesized by selection of the phosphine ligand. Finally, competition experiments between an unactivated aryl chloride and a vinyl phosphate with a palladium catalyst possessing either X-Phos or P(t-Bu)3 as ligand demonstrated the ability to carry out Heck coupling reactions selectively with the aryl halide. Oxidative addition of the metal catalyst into the aryl chloride bond rather than the C-O bond of the alkenyl phosphate is therefore preferred.