On the existence of Hopf bifurcations in the sequential and distributive double phosphorylation cycle

Protein phosphorylation cycles are important mechanisms of the post translational modification of a protein and as such an integral part of intracellular signaling and control. We consider the sequential phosphorylation and dephosphorylation of a protein at two binding sites. While it is known that proteins where phosphorylation is processive and dephosphorylation is distributive admit oscillations (for some value of the rate constants and total concentrations) it is not known whether or not this is the case if both phosphorylation and dephosphorylation are distributive. We study four simplified mass action models of sequential and distributive phosphorylation and show that for each of those there do not exist rate constants and total concentrations where a Hopf bifurcation occurs. To arrive at this result we use convex parameters to parameterize the steady state and Hurwitz matrices

Analytical parametrization of fusion barriers using proximity potentials

Using the three versions of proximity potentials, namely proximity 1977, proximity 1988, and proximity 2000, we present a pocket formula for fusion barrier heights and positions. This was achieved by analyzing as many as 400 reactions with mass between 15 and 296. Our parametrized formula can reproduced the exact barrier heights and positions within an accuracy of $\pm1$. A comparison with the experimental data is also in good agreement.Comment: 12 pages, 5 figure

Discrete Morse theory for computing cellular sheaf cohomology

Sheaves and sheaf cohomology are powerful tools in computational topology, greatly generalizing persistent homology. We develop an algorithm for simplifying the computation of cellular sheaf cohomology via (discrete) Morse-theoretic techniques. As a consequence, we derive efficient techniques for distributed computation of (ordinary) cohomology of a cell complex.Comment: 19 pages, 1 Figure. Added Section 5.

Order Reduction of the Radiative Heat Transfer Model for the Simulation of Plasma Arcs

An approach to derive low-complexity models describing thermal radiation for the sake of simulating the behavior of electric arcs in switchgear systems is presented. The idea is to approximate the (high dimensional) full-order equations, modeling the propagation of the radiated intensity in space, with a model of much lower dimension, whose parameters are identified by means of nonlinear system identification techniques. The low-order model preserves the main structural aspects of the full-order one, and its parameters can be straightforwardly used in arc simulation tools based on computational fluid dynamics. In particular, the model parameters can be used together with the common approaches to resolve radiation in magnetohydrodynamic simulations, including the discrete-ordinate method, the P-N methods and photohydrodynamics. The proposed order reduction approach is able to systematically compute the partitioning of the electromagnetic spectrum in frequency bands, and the related absorption coefficients, that yield the best matching with respect to the finely resolved absorption spectrum of the considered gaseous medium. It is shown how the problem's structure can be exploited to improve the computational efficiency when solving the resulting nonlinear optimization problem. In addition to the order reduction approach and the related computational aspects, an analysis by means of Laplace transform is presented, providing a justification to the use of very low orders in the reduction procedure as compared with the full-order model. Finally, comparisons between the full-order model and the reduced-order ones are presented

Sensitivity of exclusive proton knockout spin observables to different Lorentz invariant representations of the NN interaction

Within the framework of the relativistic plane wave impulse approximation, we study the observable consequences of employing a complete Lorentz invariant representation of the NN scattering matrix in terms of 44 independent amplitudes, as opposed to the previously-employed, but ambiguous, five-term Lorentz invariant parametrization of the NN scattering matrix, for the prediction of complete sets of exclusive ($\vec{p},2 \vec{p}$) polarization transfer observables. Two kinematic conditions are considered, namely proton knockout from the $3s_{1/2}$ state of $^{208}$Pb at an incident energy of 202 MeV for coplanar scattering angles ($28.0^{\circ}, -54.6^{\circ}$), as well as an incident energy of 392 MeV for the angle pair ($32.5^{\circ}, -80.0^{\circ}$). The results indicate that certain spin observables are ideal for discriminating between the two representations.Comment: 19 pages, 5 figures, Revtex, To be published in Phys. Rev.

Macaulay inverse systems revisited

Since its original publication in 1916 under the title "The Algebraic Theory of Modular Systems", the book by F. S. Macaulay has attracted a lot of scientists with a view towards pure mathematics (D. Eisenbud,...) or applications to control theory (U. Oberst,...).However, a carefull examination of the quotations clearly shows that people have hardly been looking at the last chapter dealing with the so-called "inverse systems", unless in very particular situations. The purpose of this paper is to provide for the first time the full explanation of this chapter within the framework of the formal theory of systems of partial differential equations (Spencer operator on sections, involution,...) and its algebraic counterpart now called "algebraic analysis" (commutative and homological algebra, differential modules,...). Many explicit examples are fully treated and hints are given towards the way to work out computer algebra packages.Comment: From a lecture at the International Conference : Application of Computer Algebra (ACA 2008) july 2008, RISC, LINZ, AUSTRI

Bounds on universal new physics effects from fermion-antifermion production at LEP2

We consider lepton-antilepton annihilation into a fermion-antifermion pair at variable c.m. energy. We propose for this process a simple parametrization of the virtual effects of the most general model of new physics of \underline{universal} type. This parametrization is based on a recent approach, that uses the experimental results of LEP1, SLC as theoretical input. It introduces \underline{three} functions whose energy dependence is argued to be smooth and, in first approximation, negligible. A couple of representative models of new physics are considered, as a support of the previous claim. Explicit bounds are then derived for this type of new physics from the available LEP2 data, and a discussion is given of the relevance in this respect of the different experimental measurements. The method is then extended to treat the case of two particularly simple models of {\it non universal} type, for which it is possible to draw analogous conclusions.Comment: 15 pages, 3 tables and 4 figures. e-mail: [email protected]

Soft and Collinear Radiation and Factorization in Perturbation Theory and Beyond

Power corrections to differential cross sections near a kinematic threshold are analysed by Dressed Gluon Exponentiation. Exploiting the factorization property of soft and collinear radiation, the dominant radiative corrections in the threshold region are resummed, yielding a renormalization-scale-invariant expression for the Sudakov exponent. The interplay between Sudakov logs and renormalons is clarified, and the necessity to resum the latter whenever power corrections are non-negligible is emphasized. The presence of power-suppressed ambiguities in the exponentiation kernel suggests that power corrections exponentiate as well. This leads to a non-perturbative factorization formula with non-trivial predictions on the structure of power corrections, which can be contrasted with the OPE. Two examples are discussed. The first is event-shape distributions in the two-jet region, where a wealth of precise data provides a strong motivation for the improved perturbative technique and an ideal situation to study hadronization. The second example is deep inelastic structure functions. In contrast to event shapes, structure functions have an OPE. However, since the OPE breaks down at large x, it does not provide a practical framework for the parametrization of power corrections. Performing a detailed analysis of twist 4 it is shown precisely how the twist-2 renormalon ambiguity eventually cancels out. This analysis provides a physical picture which substantiates the non-perturbative factorization conjecture.Comment: 11 pages, 6 postscript figures; talk presented at the XXXVII Rencontres de Moriond `QCD and high energy hadronic interactions', Les Arcs, France, and at the Workshop `Continuous Advances in QCD 2002/Arkadyfest', Minnesot