On the Complexity of Solving Zero-Dimensional Polynomial Systems via Projection

Given a zero-dimensional polynomial system consisting of n integer polynomials in n variables, we propose a certified and complete method to compute all complex solutions of the system as well as a corresponding separating linear form l with coefficients of small bit size. For computing l, we need to project the solutions into one dimension along O(n) distinct directions but no further algebraic manipulations. The solutions are then directly reconstructed from the considered projections. The first step is deterministic, whereas the second step uses randomization, thus being Las-Vegas. The theoretical analysis of our approach shows that the overall cost for the two problems considered above is dominated by the cost of carrying out the projections. We also give bounds on the bit complexity of our algorithms that are exclusively stated in terms of the number of variables, the total degree and the bitsize of the input polynomials

Minimal distance transformations between links and polymers: Principles and examples

The calculation of Euclidean distance between points is generalized to one-dimensional objects such as strings or polymers. Necessary and sufficient conditions for the minimal transformation between two polymer configurations are derived. Transformations consist of piecewise rotations and translations subject to Weierstrass-Erdmann corner conditions. Numerous examples are given for the special cases of one and two links. The transition to a large number of links is investigated, where the distance converges to the polymer length times the mean root square distance (MRSD) between polymer configurations, assuming curvature and non-crossing constraints can be neglected. Applications of this metric to protein folding are investigated. Potential applications are also discussed for structural alignment problems such as pharmacophore identification, and inverse kinematic problems in motor learning and control.Comment: Submitted to J. Phys.:Condens. Matte

Fermi Detection of the Pulsar Wind Nebula HESS J1640-465

We present observations of HESS J1640-465 with the Fermi-LAT. The source is detected with high confidence as an emitter of high-energy gamma-rays. The spectrum lacks any evidence for the characteristic cutoff associated with emission from pulsars, indicating that the emission arises primarily from the pulsar wind nebula. Broadband modeling implies an evolved nebula with a low magnetic field resulting in a high gamma-ray to X-ray flux ratio. The Fermi emission exceeds predictions of the broadband model, and has a steeper spectrum, possibly resulting from a distinct excess of low energy electrons similar to what is inferred for both the Vela X and Crab pulsar wind nebulae.Comment: 6 pages, 5 figures, accepted for publication in Ap

Meta-Plaquette Expansion for the Triplet Excitation Spectrum in CaV4_4O9_9

We study antiferromagnetic, $S=1/2$ Heisenberg models with nearest and second neighbor interactions on the one-fifth depleted square lattice which describes the spin degrees of freedom in the spin-gap system CaV$_4$O$_9$. The meta-plaquette expansion for the triplet excitation spectrum is extended to fifth order, and the results are compared with experimental data on CaV$_4$O$_9$. We attempt to locate the phase boundary between magnetically ordered and gapped phases.Comment: 4 figure

Pulsar Wind Nebulae in the SKA era

Neutron stars lose the bulk of their rotational energy in the form of a pulsar wind: an ultra-relativistic outflow of predominantly electrons and positrons. This pulsar wind significantly impacts the environment and possible binary companion of the neutron star, and studying the resultant pulsar wind nebulae is critical for understanding the formation of neutron stars and millisecond pulsars, the physics of the neutron star magnetosphere, the acceleration of leptons up to PeV energies, and how these particles impact the interstellar medium. With the SKA1 and the SKA2, it could be possible to study literally hundreds of PWNe in detail, critical for understanding the many open questions in the topics listed above.Comment: Comments: 10 pages, 3 figures, to be published in: "Advancing Astrophysics with the Square Kilometre Array", Proceedings of Science, PoS(AASKA14

On bi-Hamiltonian deformations of exact pencils of hydrodynamic type

In this paper we are interested in non trivial bi-Hamiltonian deformations of the Poisson pencil \omega_{\lambda}=\omega_2+\lambda \omega_1=u\delta'(x-y)+\f{1}{2}u_x\delta(x-y)+\lambda\delta'(x-y). Deformations are generated by a sequence of vector fields $\{X_2, X_4,...\}$, where each $X_{2k}$ is homogenous of degree $2k$ with respect to a grading induced by rescaling. Constructing recursively the vector fields $X_{2k}$ one obtains two types of relations involving their unknown coefficients: one set of linear relations and an other one which involves quadratic relations. We prove that the set of linear relations has a geometric meaning: using Miura-quasitriviality the set of linear relations expresses the tangency of the vector fields $X_{2k}$ to the symplectic leaves of $\omega_1$ and this tangency condition is equivalent to the exactness of the pencil $\omega_{\lambda}$. Moreover, extending the results of [17], we construct the non trivial deformations of the Poisson pencil $\omega_{\lambda}$, up to the eighth order in the deformation parameter, showing therefore that deformations are unobstructed and that both Poisson structures are polynomial in the derivatives of $u$ up to that order.Comment: 34 pages, revised version. Proof of Theorem 16 completely rewritten due to an error in the first versio

Classical nonlinear response of a chaotic system: Langevin dynamics and spectral decomposition

We consider the classical response of a strongly chaotic Hamiltonian system. The spectrum of such a system consists of discrete complex Ruelle-Pollicott (RP) resonances which manifest themselves in the behavior of the correlation and response functions. We interpret the RP resonances as the eigenstates and eigenvalues of the Fokker-Planck operator obtained by adding an infinitesimal noise term to the first-order Liouville operator. We demonstrate how the deterministic expression for the linear response is reproduced in the limit of vanishing noise. For the second-order response we establish an equivalence of the spectral decomposition with infinitesimal noise and the long-time asymptotic expansion for the deterministic case.Comment: 16 pages, 1 figur

Dimer Expansion Study of the Bilayer Square Lattice Frustrated Quantum Heisenberg Antiferromagnet

The ground state of the square lattice bilayer quantum antiferromagnet with nearest ($J_1$) and next-nearest ($J_2$) neighbour intralayer interaction is studied by means of the dimer expansion method up to the 6-th order in the interlayer exchange coupling $J_3$. The phase boundary between the spin-gap phase and the magnetically ordered phase is determined from the poles of the biased Pad\'e approximants for the susceptibility and the inverse energy gap assuming the universality class of the 3-dimensional classical Heisenberg model. For weak frustration, the critical interlayer coupling decreases linearly with $\alpha (= J_2/J_1)$. The spin-gap phase persists down to $J_3=0$ (single layer limit) for 0.45 \simleq \alpha \simleq 0.65. The crossover of the short range order within the disordered phase is also discussed.Comment: 4 pages, 6 figures, One reference adde

Modulation of p53 activity by IκBα: Evidence suggesting a common phylogeny between NF-κB and p53 transcription factors

BACKGROUND: In this work we present evidence that the p53 tumor suppressor protein and NF-κB transcription factors could be related through common descent from a family of ancestral transcription factors regulating cellular proliferation and apoptosis. P53 is a homotetrameric transcription factor known to interact with the ankyrin protein 53BP2 (a fragment of the ASPP2 protein). NF-κB is also regulated by ankyrin proteins, the prototype of which is the IκB family. The DNA binding sequences of the two transcription factors are similar, sharing 8 out of 10 nucleotides. Interactions between the two proteins, both direct and indirect, have been noted previously and the two proteins play central roles in the control of proliferation and apoptosis. RESULTS: Using previously published structure data, we noted a significant degree of structural alignment between p53 and NF-κB p65. We also determined that IκBα and p53 bind in vitro through a specific interaction in part involving the DNA binding region of p53, or a region proximal to it, and the amino terminus of IκBα independently or cooperatively with the ankyrin 3 domain of IκBα In cotransfection experiments, κBα could significantly inhibit the transcriptional activity of p53. Inhibition of p53-mediated transcription was increased by deletion of the ankyrin 2, 4, or 5 domains of IκBα Co-precipitation experiments using the stably transfected ankyrin 5 deletion mutant of κBα and endogenous wild-type p53 further support the hypothesis that p53 and IκBα can physically interact in vivo. CONCLUSION: The aggregate results obtained using bacterially produced IκBα and p53 as well as reticulocyte lysate produced proteins suggest a correlation between in vitro co-precipitation in at least one of the systems and in vivo p53 inhibitory activity. These observations argue for a mechanism involving direct binding of IκBα to p53 in the inhibition of p53 transcriptional activity, analogous to the inhibition of NF-κB by κBα and p53 by 53BP2/ASPP2. These data furthermore suggest a role for ankyrin proteins in the regulation of p53 activity. Taken together, the NFκB and p53 proteins share similarities in structure, DNA binding sites and binding and regulation by ankyrin proteins in support of our hypothesis that the two proteins share common descent from an ancestral transcriptional factor

On the Extended Emission Around the Anomalous X-ray Pulsar 1E 1547.0-5408

We present an analysis of the extended emission around the anomalous X-ray pulsar 1E 1547.0-5408 using four XMM-Newton observations taken with the source in varying states of outburst as well as in quiescence. We find that the extended emission flux is highly variable and strongly correlated with the flux of the magnetar. Based on this result, as well as on spectral and energetic considerations, we conclude that the extended emission is dominated by a dust-scattering halo and not a pulsar wind nebula (PWN), as has been previously argued. We obtain an upper limit on the 2-10 keV flux of a possible PWN of 4.7e-14 erg/s/cm^2, three times less than the previously claimed value, implying an efficiency for conversion of spin-down energy into nebular luminosity of <9e-4 (assuming a distance of 4 kpc). We do, however, find strong evidence for X-ray emission from the supernova remnant shell surrounding the pulsar, as previously reported.Comment: 16 pages, 3 tables, 4 figures, published in the Astrophysical Journa