Computational algebraic methods in efficient estimation

A strong link between information geometry and algebraic statistics is made by investigating statistical manifolds which are algebraic varieties. In particular it it shown how first and second order efficient estimators can be constructed, such as bias corrected Maximum Likelihood and more general estimators, and for which the estimating equations are purely algebraic. In addition it is shown how Gr\"obner basis technology, which is at the heart of algebraic statistics, can be used to reduce the degrees of the terms in the estimating equations. This points the way to the feasible use, to find the estimators, of special methods for solving polynomial equations, such as homotopy continuation methods. Simple examples are given showing both equations and computations. *** The proof of Theorem 2 was corrected by the latest version. Some minor errors were also corrected.Comment: 21 pages, 5 figure

Fabrication of magnetometers with multiple-SQUID arrays

We have designed and fabricated magnetometers with multiple-SQUID arrays to achieve higher signal to noise ratio compared to that for a single SQUID. In our directly coupled scheme, ten SQUIDs are connected in parallel with the same pickup coil composed of four parallel rectangular loops. Each SQUID having inductance of 70 pH and junctions of 1.5 /spl mu/m width was fabricated from an Au/YBa/sub 2/Cu/sub 3/O/sub 7-/spl delta// thin film on a SrTiO/sub 3/ bicrystal substrate with 30/spl deg/ misorientation angle. To avoid forming superconducting loops between junctions of adjoining SQUIDs, a Au wiring layer interrupts a current bias line. The obtained critical current of 20I/sub c/ and normal resistance of R/sub n//20 including contact resistance for the Au wiring layer are 350 /spl mu/A and 0.4 /spl Omega/, respectively. The modulation voltage of 25 /spl mu/V for multiple-SQUIDs is the same level as for a single SQUID. On the other hand, the modulation current of 40 /spl mu/A is several times larger than that for a single SQUID, but rather smaller than the expected value when all SQUIDs have equal parameters. A flux noise level of 15 /spl mu//spl Phi//sub 0//Hz/sup 1/2/ at 100 Hz, including preamplifier noise, was observed by using flux-locked loop electronics in a magnetically shielded room

Photon generation by laser-Compton scattering at the KEK-ATF

We performed a photon generation experiment by laser-Compton scattering at the KEK-ATF, aiming to develop a Compton based polarized positron source for linear colliders. In the experiment, laser pulses with a 357 MHz repetition rate were accumulated and their power was enhanced by up to 250 times in the Fabry-Perot optical resonant cavity. We succeeded in synchronizing the laser pulses and colliding them with the 1.3 GeV electron beam in the ATF ring while maintaining the laser pulse accumulation in the cavity. As a result, we observed 26.0 +/- 0.1 photons per electron-laser pulse crossing, which corresponds to a yield of 10^8 photons in a second.Comment: 3 pages, 5 figures, Preprint submitted to TIPP09 Proceedings in NIM

Design of a Polarised Positron Source Based on Laser Compton Scattering

We describe a scheme for producing polarised positrons at the ILC from polarised X-rays created by Compton scattering of a few-GeV electron beam off a CO2 or YAG laser. This scheme is very energy effective using high finesse laser cavities in conjunction with an electron storage ring.Comment: Proposal submitted to the ILC workshop, Snowmass 2005. v2: note number adde

Static Friction as a Function of Waiting Time Probed by Dynamics of Driven Vortices in La2-xSrxCuO4 Thin Films

We investigated the dynamics of driven vortices in high-$T_c$ superconductor as an ideal model system to study the physics of friction. The waiting-time dependence of the maximum static friction force, $F_s(t_w)$, was measured in La$_{2-x}$Sr$_x$CuO$_4$ thin films with different structures, sample sizes and pinning force. We found various kinds of $F_s(t_w)$ in the $B$-$T$ phase diagram and in different types of samples. The results suggest that the relaxation by thermal fluctuation is strongly affected by the pinning strength, the vortex bundle size and the system size. Based on these results, we found crucial conditions to determine the validity of the Amontons-Coulomb's law, and proposed a criterion.Comment: 5 pages, 1 table, 3 figures, submitted to Phys. Rev. Let

High-Tc SQUID magnetometers for use in moderatemagnetically-shielded room

We have fabricated and characterized high-Tc planar SQUID magnetometers and first derivative gradiometers with directly-coupled pickup loops. The devices were made from single layer of YBa2Cu3O7-δ thin film on LSAT bicrystal substrate with 30° or 24° misorientation angle. Magnetic properties were investigated by applying a magnetic field B0 for the SQUID magnetometer patterned with holes to reduce the maximum structural width. We found an increasing low frequency noise with cooling fields B0 larger than 1.5 μT. This value consists with the threshold field estimated from the maximum structural width. A magnetic field noise level of 500 fT/Hz1/2 at 10 Hz was observed by using FLL electronics with a bias current reversal in a moderate magnetically-shielded room consisting of only two 1 mm thick layers of permalloy. Measurements of magnetocardiograms demonstrate the suitability of this magnetometer for biomagnetic applications. On the other hand, the gradiometer with two symmetric pickup loops was operated without any shielding. The performance obtained was a field gradient resolution of about 1 pT/cmHz1/2 at 1 kHz and 10 pT/cmHz1/2 at 1 Hz, with a baseline of 4 mm. The imbalance of this gradiometer was around 0.7%, limited by the sensitivity to homogeneous field of the SQUID itself

The CLIC positron source based on compton schemes

The CLIC polarized positron source is based on a positron production scheme in which polarized photons are produced by a Compton process. In one option, Compton backscattering takes place in a so-called “Compton ring”, where an electron beam of 1 GeV interacts with circularly-polarized photons in an optical resonator. The resulting circularly-polarized gamma photons are sent on to an amorphous target, producing pairs of longitudinally polarized electrons and positrons. The nominal CLIC bunch population is 4.2x109 particles per bunch at the exit of the Pre-Damping Ring (PDR). Since the photon flux coming out from a "Compton ring" is not sufficient to obtain the requested charge, a stacking process is required in the PDR. Another option is to use a Compton Energy Recovery Linac (ERL) where a quasicontinual stacking in the PDR could be achieved. A third option is to use a "Compton Linac" which would not require stacking. We describe the overall scheme as well as advantages and constraints of the three options