Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals

High-order derivatives of analytic functions are expressible as Cauchy integrals over circular contours, which can very effectively be approximated, e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius of convergence is equal, numerical stability strongly depends on r. We give a comprehensive study of this effect; in particular we show that there is a unique radius that minimizes the loss of accuracy caused by round-off errors. For large classes of functions, though not for all, this radius actually gives about full accuracy; a remarkable fact that we explain by the theory of Hardy spaces, by the Wiman-Valiron and Levin-Pfluger theory of entire functions, and by the saddle-point method of asymptotic analysis. Many examples and non-trivial applications are discussed in detail.Comment: Version 4 has some references and a discussion of other quadrature rules added; 57 pages, 7 figures, 6 tables; to appear in Found. Comput. Mat

Interacting Preformed Cooper Pairs in Resonant Fermi Gases

We consider the normal phase of a strongly interacting Fermi gas, which can have either an equal or an unequal number of atoms in its two accessible spin states. Due to the unitarity-limited attractive interaction between particles with different spin, noncondensed Cooper pairs are formed. The starting point in treating preformed pairs is the Nozi\`{e}res-Schmitt-Rink (NSR) theory, which approximates the pairs as being noninteracting. Here, we consider the effects of the interactions between the Cooper pairs in a Wilsonian renormalization-group scheme. Starting from the exact bosonic action for the pairs, we calculate the Cooper-pair self-energy by combining the NSR formalism with the Wilsonian approach. We compare our findings with the recent experiments by Harikoshi {\it et al.} [Science {\bf 327}, 442 (2010)] and Nascimb\`{e}ne {\it et al.} [Nature {\bf 463}, 1057 (2010)], and find very good agreement. We also make predictions for the population-imbalanced case, that can be tested in experiments.Comment: 10 pages, 6 figures, accepted version for PRA, discussion of the imbalanced Fermi gas added, new figure and references adde

Sous-groupes alg\'ebriques du groupe de Cremona

We give a complete classification of maximal algebraic subgroups of the Cremona group of the plane and provide algebraic varieties that parametrize the conjugacy classes. ----- Nous donnons une classification compl\`ete des sous-groupes alg\'ebriques maximaux du groupe de Cremona du plan et explicitons les vari\'et\'es qui param\`etrent les classes de conjugaison.Comment: Text in French, Translated introduction, 35 pages, 1 figure, to appear in Transform. Group

The adipocyte: a model for integration of endocrine and metabolic signaling in energy metabolism regulation

The ability to ensure continuous availability of energy despite highly variable supplies in the environment is a major determinant of the survival of all species. In higher organisms, including mammals, the capacity to efficiently store excess energy as triglycerides in adipocytes, from which stored energy could be rapidly released for use at other sites, was developed. To orchestrate the processes of energy storage and release, highly integrated systems operating on several physiological levels have evolved. The adipocyte is no longer considered a passive bystander, because fat cells actively secrete many members of the cytokine family, such as leptin, tumor necrosis factor-alpha, and interleukin-6, among other cytokine signals, which influence peripheral fuel storage, mobilization, and combustion, as well as energy homeostasis. The existence of a network of adipose tissue signaling pathways, arranged in a hierarchical fashion, constitutes a metabolic repertoire that enables the organism to adapt to a wide range of different metabolic challenges, such as starvation, stress, infection, and short periods of gross energy excess

Physiological and molecular characterization of yeast cultures pre‐adapted for fermentation of lignocellulosic hydrolysate.

Economically feasible bioethanol process from lignocellulose requires efficient fermentation by yeast of all sugars present in the hydrolysate. However, when exposed to lignocellulosic hydrolysate, Saccharomyces cerevisiae is challenged with a variety of inhibitors that reduce yeast viability, growth, and fermentation rate, and in addition damage cellular structures. In order to evaluate the capability of S. cerevisiae to adapt and respond to lignocellulosic hydrolysates, the physiological effect of cultivating yeast in the spruce hydrolysate was comprehensively studied by assessment of yeast performance in simultaneous saccharification and fermentation (SSF), measurement of furaldehyde reduction activity, assessment of conversion of phenolic compounds and genome‐wide transcription analysis. The yeast cultivated in spruce hydrolysate developed a rapid adaptive response to lignocellulosic hydrolysate, which significantly improved its fermentation performance in subsequent SSF experiments. The adaptation was shown to involve the induction of NADPHdependent aldehyde reductases and conversion of phenolic compounds during the fed‐batch cultivation. These properties were correlated to the expression of several genes encoding oxidoreductases, notably AAD4, ADH6, OYE2/3, and YML131w. The other most significant transcriptional changes involved genes involved in transport mechanisms, such as YHK8, FLR1, or ATR1. A large set of genes were found to be associated with transcription factors (TFs) involved in stress response (Msn2p, Msn4p, Yap1p) but also cell growth and division (Gcr4p, Ste12p, Sok2p), and these TFs were most likely controlling the response at the post‐transcriptional level

Finite Hilbert stability of (bi)canonical curves

We prove that a generic canonically or bicanonically embedded smooth curve has semistable m-th Hilbert points for all m. We also prove that a generic bicanonically embedded smooth curve has stable m-th Hilbert points for all m \geq 3. In the canonical case, this is accomplished by proving finite Hilbert semistability of special singular curves with G_m-action, namely the canonically embedded balanced ribbon and the canonically embedded balanced double A_{2k+1}-curve. In the bicanonical case, we prove finite Hilbert stability of special hyperelliptic curves, namely Wiman curves. Finally, we give examples of canonically embedded smooth curves whose m-th Hilbert points are non-semistable for low values of m, but become semistable past a definite threshold. (This paper subsumes the previous submission and arXiv:1110.5960).Comment: To appear in Inventiones Mathematicae, 2012. The final publication is available at http://www.springerlink.co

Fibrinolysis in a lipid environment: modulation through release of free fatty acids

Background: Thrombolysis is conventionally regarded as dissolution of the fibrin matrix of thrombi by plasmin, but the structure of clots in vivo includes additional constituents (proteins, phospholipids) that modulate their solubilization. Objective: We examined the presence of free fatty acids in thrombi and their effects on distinct stages of fibrinolysis (plasminogen activation, plasmin activity). Methods and Results: Using the fluorescent probe acrylodated intestinal fatty acid-binding protein, variable quantities (up to millimolar concentrations) of free fatty acids were demonstrated in surgically removed human thrombi. Oleic acid at relevant concentrations reversibly inhibits more than 90% of the amidolytic activity of plasmin on a synthetic substrate (Spectrozyme PL), but only partially inhibits its fibrinolytic activity measured using turbidimetry. Chromogenic assays detecting the generated plasmin activity show that plasminogen activation by tissue-type plasminogen activator (t-PA) is completely blocked by oleic acid in the fluid phase, but is accelerated on a fibrin matrix. A recombinant derivative of t-PA (reteplase) develops higher fibrin specificity in the presence of oleic acid, because both the inhibition of plasminogen activation in free solution and its enhancement on fibrin template are stronger than with wild-type t-PA. Conclusion: Through the stimulation of plasminogen activation on a fibrin template and the inhibition of plasminogen activators and plasmin in the fluid phase, free fatty acids confine the action of fibrinolytic proteases to the site of clotting, where they partially oppose the thrombolytic barrier function of phospholipids

The A-B transition in superfluid helium-3 under confinement in a thin slab geometry

The influence of confinement on the topological phases of superfluid 3He is studied using the torsional pendulum method. We focus on the phase transition between the chiral A-phase and the time-reversal-invariant B-phase, motivated by the prediction of a spatiallymodulated (stripe) phase at the A-B phase boundary. We confine superfluid 3He to a single 1.08 {\mu}m thick nanofluidic cavity incorporated into a high-precision torsion pendulum, and map the phase diagram between 0.1 and 5.6 bar. We observe only small supercooling of the A-phase, in comparison to bulk or when confined in aerogel. This has a non-monotonic pressure dependence, suggesting that a new intrinsic B-phase nucleation mechanism operates under confinement, mediated by the putative stripe phase. Both the phase diagram and the relative superfluid fraction of the A and B phases, show that strong coupling is present at all pressures, with implications for the stability of the stripe phase.Comment: 6 figures, 1 table + supplemental informatio

The Proposed OECD Multilateral Instrument Amending Tax Treaties

In this article, the authors consider some of the practical issues relating to the introduction of the OECD multilateral instrument amending tax treaties, which has been proposed within the context of the OECD/G20 Base Erosion and Profit Shifting Project