Inference of an oscillating model for the yeast cell cycle

High-throughput techniques allow measurement of hundreds of cell components simultaneously. The inference of interactions between cell components from these experimental data facilitates the understanding of complex regulatory processes. Differential equations have been established to model the dynamic behavior of these regulatory networks quantitatively. Usually traditional regression methods for estimating model parameters fail in this setting, since they overfit the data. This is even the case, if the focus is on modeling subnetworks of, at most, a few tens of components. In a Bayesian learning approach, this problem is avoided by a restriction of the search space with prior probability distributions over model parameters.This paper combines both differential equation models and a Bayesian approach. We model the periodic behavior of proteins involved in the cell cycle of the budding yeast Saccharomyces cerevisiae, with differential equations, which are based on chemical reaction kinetics. One property of these systems is that they usually converge to a steady state, and lots of efforts have been made to explain the observed periodic behavior. We introduce an approach to infer an oscillating network from experimental data. First, an oscillating core network is learned. This is extended by further components by using a Bayesian approach in a second step. A specifically designed hierarchical prior distribution over interaction strengths prevents overfitting, and drives the solutions to sparse networks with only a few significant interactions.We apply our method to a simulated and a real world dataset and reveal main regulatory interactions. Moreover, we are able to reconstruct the dynamic behavior of the network.     

Optimal control and dependence modeling of insurance portfolios with Lévy dynamics

In this paper we are interested in optimizing proportional reinsurance and investment policies in a multidimensional Lévy-driven insurance model. The criterion is that of maximizing exponential utility. Solving the classical Hamilton-Jacobi-Bellman equation yields that the optimal retention level keeps a constant amount of claims regardless of time and the company’s wealth level.A special feature of our construction is to allow for dependencies of the risk reserves in different business lines. Dependence is modeled via an Archimedean Lévy copula. We derive a sufficient and necessary condition for an Archimedean Lévy generator to create a multidimensional positive Lévy copula in arbitrary dimension.Based on these results we identify structure conditions for the generator and the Lévy measure of an Archimedean Lévy copula under which an insurance company reinsures a larger fraction of claims from one business line than from another.     

Reactivite des carbanions benzyliques : VIII. Etude de la structure d'alkyl-9 lithio-10 dihydro-9,10 anthracenes par rmn du proton et spectrometrie d'absorption electronique; influence du substituant,du solvant et de la temperature

The structure of the 9,10-dihydroanthracenyl anion and of a series of 9-alkyl-10-lithio-9-10-dihydroanthracenes (9-R-10-LiDHA, I–V where R = H, Me, Et, i-Pr, t-Bu) was studied in solution by electronic absortion spectrometry and proton magnetic resonance. Our electronic absorption results, in addition to those of other authors, show that the contact ion pairs (c.i.p.) have an absorption at λ_max}- 400 nm (I–III) and 415 nm (V) whereas the loose ion pairs (l.i.p.) absorb at λmax}- 450 nm (I–V). In the NMR the chemical shift of the proton para with respect to the carbanionic center was examined as a function of solvent (THF, THF/HMPA, and in some cases ether or pure HMPA) and temperature (+20 to ?40°C). The para proton is shielded significantly with regard to the aromatic protons of the hydrocarbon (Δδ(H_para) ca. 1–1.7 ppm). The weakest shielding was observed in ether, in agreement with the existence of c.i.p. The largest shielding (THF/HMPA or pure HMPA) is in connection with the presence of l.i.p. where the negative charge is less localised at position 10. Moreover, in the same solvent, and at the same temperature, Δδ(H_para) was observed to increase with the substituent bulk, up to the point that there are only l.i.p. present. As found previously (namely for the fluorenyl anion) the l.i.p./c.i.p. ratio increases when temperature decreases. The results of this structural study allow to rationalize the protonation stereochemistry of 9-alkyl-10-lithio-9,10-dihydroanthracenes in the above-mentioned solvents.     

Mother and Child Emotions during Mathematics Homework

Mathematics is often thought of as a purely intellectual and unemotional activity. Recently, researchers have begun to question the validity of this approach, arguing that emotions and cognition are intertwined. The emotions expressed during mathematics work may be linked to mathematics achievement. We used behavioral measures to identify the emotions expressed by U.S. mothers and their 11-year-old children while solving pre-algebra tasks in the home. The most notable positive emotions displayed by mothers and children included positive interest, affection, joy, and pride, whereas the most notable negative emotions expressed included tension, frustration, and distress. Reflecting the social aspects of doing homework together, mothers' and children's emotions were highly correlated. Independent of pre-existing differences in knowledge, children's emotions were associated with their performance on a mathematics post-test: tension was linked to poorer performance while positive interest, humor, and pride were linked to better performance. We found no evidence of gender differences in the emotions while working the tasks, although boys responded with more tension following an incorrect solution than did girls.     

Ideals in a perfect closure, linear growth of primary decompositions, and tight closure

This paper is concerned with tight closure in a commutative Noetherian ring of prime characteristic , and is motivated by an argument of K. E. Smith and I. Swanson that shows that, if the sequence of Frobenius powers of a proper ideal of has linear growth of primary decompositions, then tight closure (of ) `commutes with localization at the powers of a single element'. It is shown in this paper that, provided has a weak test element, linear growth of primary decompositions for other sequences of ideals of that approximate, in a certain sense, the sequence of Frobenius powers of would not only be just as good in this context, but, in the presence of a certain additional finiteness property, would actually imply that tight closure (of ) commutes with localization at an arbitrary multiplicatively closed subset of .

Work of M. Katzman on the localization problem for tight closure raised the question as to whether the union of the associated primes of the tight closures of the Frobenius powers of has only finitely many maximal members. This paper develops, through a careful analysis of the ideal theory of the perfect closure of , strategies for showing that tight closure (of a specified ideal of ) commutes with localization at an arbitrary multiplicatively closed subset of and for showing that the union of the associated primes of the tight closures of the Frobenius powers of is actually a finite set. Several applications of the strategies are presented; in most of them it was already known that tight closure commutes with localization, but the resulting affirmative answers to Katzman's question in the various situations considered are believed to be new.

     

Mean‐risk optimization of electricity portfolios

We present a mathematical model with stochastic input data for mean‐risk optimization of electricity portfolios containing several physical components and energy derivative products. The model is designed for the optimization horizon of one year in hourly discretization. The aim consists in maximizing the mean book value of the portfolio at the end of the optimization horizon and, at the same time, in minimizing the risk of the portfolio decisions. The risk is measured by the conditional value‐at‐risk and by some multiperiod extension of CVaR, respectively.We present numerical results for a large‐scale realistic problem adapted to a municipal power utility and study the effects of varying weighting of risk. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Support Varieties for Selfinjective Algebras

Support varieties for any finite dimensional algebra over a field were introduced in (Proc. London Math. Soc. 88 (3) (2004) 705–732) using graded subalgebras of the Hochschild cohomology ring. We mainly study these varieties for selfinjective algebras under appropriate finite generation hypotheses. Then many of the standard results from the theory of support varieties for finite groups generalize to this situation. In particular, the complexity of the module equals the dimension of its corresponding variety, all closed homogeneous varieties occur as the variety of some module, the variety of an indecomposable module is connected, the variety of periodic modules are lines and for symmetric algebras a generalization of Webbs theorem is true. As a corollary of a more general result we show that Webbs theorem generalizes to finite dimensional cocommutative Hopf algebras.Received November 2003Mathematics Subject Classifications (2000) Primary: 16E40, 16G10, 16P10, 16P20; Secondary: 16G70.     

When random proportional subspaces are also random quotients

We discuss when a generic subspace of some fixed proportional dimension of a finite-dimensional normed space can be isomorphic to a generic quotient of some proportional dimension of another space. We show (in Theorem 4.1) that if this happens (for some natural random structures) then for any proportion arbitrarily close to 1, the first space has a lot of Euclidean subspaces and the second space has a lot of Euclidean quotients.