Reduction of Algebraic Parametric Systems by Rectification of their Affine Expanded Lie Symmetries

Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equations. We apply this principle by finding some \emph{affine derivations} that induces \emph{expanded} Lie point symmetries of considered system. By rewriting original problem in an invariant coordinates set for these symmetries, we \emph{reduce} the number of involved parameters. We present an algorithm based on this standpoint whose arithmetic complexity is \emph{quasi-polynomial} in input's size.Comment: Before analysing an algebraic system (differential or not), one can generally reduce the number of parameters defining the system behavior by studying the system's Lie symmetrie

Effective Invariant Theory of Permutation Groups using Representation Theory

Using the theory of representations of the symmetric group, we propose an algorithm to compute the invariant ring of a permutation group. Our approach have the goal to reduce the amount of linear algebra computations and exploit a thinner combinatorial description of the invariant ring.Comment: Draft version, the corrected full version is available at http://www.springer.com

Genotypic and phenotypic variation among Staphylococcus saprophyticus from human and animal isolates

<p>Abstract</p> <p>Background</p> <p>The main aim of this study was to examine the genotypic and phenotypic diversity of <it>Staphylococcus saprophyticus </it>isolates from human and animal origin.</p> <p>Findings</p> <p>In total, 236 clinical isolates and 15 animal isolates of <it>S. saprophyticus </it>were characterized in respect of the occurrence of 9 potential virulence genes and four surface properties. All strains were PCR positive for the regulatory genes <it>agr</it>, <it>sar</it>>it>A and <it>rot </it>as well as for the surface proteins UafA and Aas. Nearly 90% of the clinical isolates were found to possess the gene for the surface-associated lipase Ssp and 10% for the collagen binding MSCRAMM SdrI. All animal isolates were negative for<it>sdrI</it>. Lipolytic activity could be detected in 66% of the clinical and 46% of the animal isolates. Adherence to collagen type I was shown of 20% of the clinical strains and 6% of the strains of animal origin. Most <it>S. saprophyticus </it>strains showed hydrophobic properties and only few could agglutinate sheep erythrocytes.</p> <p>Conclusions</p> <p>We described a broad analysis of animal and human <it>S. saprophyticus </it>isolates regarding virulence genes and phenotypic properties such as lipase activity, hydrophobicity, and adherence. While <it>S. saprophyticus </it>strains from animal sources have prerequisites for colonization of the urinary tract like the D-serine-deaminase, out findings suggested that they need to acquire new genes e.g. MSCRAMMS for adherence like sdrI and to modulate their existing properties e.g. increasing the lipase activity or reducing hydrophobicity. These apparently important new genes or properties for virulence have to be further analyzed.</p

Ideal Interpolation, H-Bases and Symmetry

International audienceMultivariate Lagrange and Hermite interpolation are examples ofideal interpolation. More generally an ideal interpolation problemis defined by a set of linear forms, on the polynomial ring, whosekernels intersect into an ideal.For an ideal interpolation problem with symmetry, we addressthe simultaneous computation of a symmetry adapted basis of theleast interpolation space and the symmetry adapted H-basis ofthe ideal. Beside its manifest presence in the output, symmetry isexploited computationally at all stages of the algorithm

On the Mathematics of the Law of Mass Action

In 1864,Waage and Guldberg formulated the "law of mass action." Since that time, chemists, chemical engineers, physicists and mathematicians have amassed a great deal of knowledge on the topic. In our view, sufficient understanding has been acquired to warrant a formal mathematical consolidation. A major goal of this consolidation is to solidify the mathematical foundations of mass action chemistry -- to provide precise definitions, elucidate what can now be proved, and indicate what is only conjectured. In addition, we believe that the law of mass action is of intrinsic mathematical interest and should be made available in a form that might transcend its application to chemistry alone. We present the law of mass action in the context of a dynamical theory of sets of binomials over the complex numbers.Comment: 40 pages, no figure

Resonances in a spring-pendulum: algorithms for equivariant singularity theory

A spring-pendulum in resonance is a time-independent Hamiltonian model system for formal reduction to one degree of freedom, where some symmetry (reversibility) is maintained. The reduction is handled by equivariant singularity theory with a distinguished parameter, yielding an integrable approximation of the Poincaré map. This makes a concise description of certain bifurcations possible. The computation of reparametrizations from normal form to the actual system is performed by Gröbner basis techniques.

A convex polynomial that is not sos-convex

A multivariate polynomial $p(x)=p(x_1,...,x_n)$ is sos-convex if its Hessian $H(x)$ can be factored as $H(x)= M^T(x) M(x)$ with a possibly nonsquare polynomial matrix $M(x)$. It is easy to see that sos-convexity is a sufficient condition for convexity of $p(x)$. Moreover, the problem of deciding sos-convexity of a polynomial can be cast as the feasibility of a semidefinite program, which can be solved efficiently. Motivated by this computational tractability, it has been recently speculated whether sos-convexity is also a necessary condition for convexity of polynomials. In this paper, we give a negative answer to this question by presenting an explicit example of a trivariate homogeneous polynomial of degree eight that is convex but not sos-convex. Interestingly, our example is found with software using sum of squares programming techniques and the duality theory of semidefinite optimization. As a byproduct of our numerical procedure, we obtain a simple method for searching over a restricted family of nonnegative polynomials that are not sums of squares.Comment: 15 page

Study of the 22^{22}Mg waiting point relevant for x-ray burst nucleosynthesis via the 22^{22}Mg(α\alpha,pp)25^{25}Al reaction

The $^{22}$Mg($\alpha$,$p$)$^{25}$Al reaction rate has been identified as a major source of uncertainty for understanding the nucleosynthesis flow in Type-I x-ray bursts (XRBs). We report a direct measurement of the energy- and angle-integrated cross sections of this reaction in a 3.3-6.9 MeV center-of-mass energy range using the MUlti-Sampling Ionization Chamber (MUSIC). The new $^{22}$Mg($\alpha$,$p$)$^{25}$Al reaction rate is a factor of $\sim$4 higher than the previous direct measurement of this reaction within temperatures relevant for XRBs, resulting in the $^{22}$Mg waiting point of x-ray burst nucleosynthesis flow to be significantly bypassed via the ($\alpha,p$) reactionComment: 6 pages, 3 figures, 1 tabl

Direct Determination of Fission-Barrier Heights Using Light-Ion Transfer in Inverse Kinematics

We demonstrate a new technique for obtaining fission data for nuclei away from $\beta$-stability. These types of data are pertinent to the astrophysical \textit{r-}process, crucial to a complete understanding of the origin of the heavy elements, and for developing a predictive model of fission. These data are also important considerations for terrestrial applications related to power generation and safeguarding. Experimentally, such data are scarce due to the difficulties in producing the actinide targets of interest. The solenoidal-spectrometer technique, commonly used to study nucleon-transfer reactions in inverse kinematics, has been applied to the case of transfer-induced fission as a means to deduce the fission-barrier height, among other variables. The fission-barrier height of $^{239}$U has been determined via the $^{238}$U($d$,$pf$) reaction in inverse kinematics, the results of which are consistent with existing neutron-induced fission data indicating the validity of the technique