Computations on Sofic S-gap Shifts

Let $S=\{s_{n}\}$ be an increasing finite or infinite subset of $\mathbb N \bigcup \{0\}$ and $X(S)$ the $S$-gap shift associated to $S$. Let $f_{S}(x)=1-\sum\frac{1}{x^{s_{n}+1}}$ be the entropy function which will be vanished at $2^{h(X(S))}$ where $h(X(S))$ is the entropy of the system. Suppose $X(S)$ is sofic with adjacency matrix $A$ and the characteristic polynomial $\chi_{A}$. Then for some rational function $Q_{S}$, $\chi_{A}(x)=Q_{S}(x)f_{S}(x)$. This $Q_{S}$ will be explicitly determined. We will show that $\zeta(t)=\frac{1}{f_{S}(t^{-1})}$ or $\zeta(t)=\frac{1}{(1-t)f_{S}(t^{-1})}$ when $|S|<\infty$ or $|S|=\infty$ respectively. Here $\zeta$ is the zeta function of $X(S)$. We will also compute the Bowen-Franks groups of a sofic $S$-gap shift.Comment: This paper has been withdrawn due to extending results about SFT shifts to sofic shifts (Theorem 2.3). This forces to apply some minor changes in the organization of the paper. This paper has been withdrawn due to a flaw in the description of the adjacency matrix (2.3

Registration of retinal images from Public Health by minimising an error between vessels using an affine model with radial distortions

In order to estimate a registration model of eye fundus images made of an affinity and two radial distortions, we introduce an estimation criterion based on an error between the vessels. In [1], we estimated this model by minimising the error between characteristics points. In this paper, the detected vessels are selected using the circle and ellipse equations of the overlap area boundaries deduced from our model. Our method successfully registers 96 % of the 271 pairs in a Public Health dataset acquired mostly with different cameras. This is better than our previous method [1] and better than three other state-of-the-art methods. On a publicly available dataset, ours still better register the images than the reference method

QSO clustering and the AAT 2dF redshift survey

We review previous results on the clustering and environments of QSOs. We show that the correlation length for QSOs derived from existing surveys is r~5/h Mpc, similar to the observed correlation length for field galaxies at the present epoch. The galaxy environment for z<1 radio-quiet QSOs is also consistent with field galaxies. The evolution of the QSO correlation length with redshift is currently uncertain, largely due to the small numbers of QSOs (~2000) in surveys suitable for clustering analysis. We report on intial progress with the AAT 2dF QSO redshift survey, which, once completed will comprise almost 30000 QSOs. With over 1000 QSOs already observed, it is already the largest single homogeneous QSO survey. We discuss prospects for deriving limits on cosmological parameters from this survey, and on the evolution of large-scale structure in the Universe.Comment: Invited talk at RS meeting on 'Large Scale Structure in the Universe' held at the Royal Society on 25-26 March 1998 14 pages, 11 figre

Discovery of a Clustered Quasar Pair at z ~ 5: Biased Peaks in Early Structure Formation

We report a discovery of a quasar at z = 4.96 +- 0.03 within a few Mpc of the quasar SDSS 0338+0021 at z = 5.02 +- 0.02. The newly found quasar has the SDSS i and z magnitudes of ~ 21.2, and an estimated absolute magnitude M_B ~ -25.2. The projected separation on the sky is 196 arcsec, and the redshift difference Delta z = 0.063 +- 0.008. The probability of finding this quasar pair by chance in the absence of clustering in this particular volume is ~ 10^-4 to 10^-3. We conclude that the two objects probably mark a large-scale structure, possibly a protocluster, at z ~ 5. This is the most distant such structure currently known. Our search in the field of 13 other QSOs at z >~ 4.8 so far has not resulted in any detections of comparable luminous QSO pairs, and it is thus not yet clear how representative is this structure at z ~ 5. However, along with the other evidence for clustering of quasars and young galaxies at somewhat lower redshifts, the observations are at least qualitatively consistent with a strong biasing of the first luminous and massive objects, in agreement with general predictions of theoretical models. More extensive searches for clustered quasars and luminous galaxies at these redshifts will provide valuable empirical constraints for our understanding of early galaxy and structure formation.Comment: Latex file, 8 pages, 3 eps figures, sty files included. To appear in the Ap

Acoustic power delivery to pipeline monitoring wireless sensors

The use of energy harvesting for powering wireless sensors is made more challenging in most applications by the requirement for customi zation to each specific application environment because of specificities of the availab le energy form, such as precise location, direction and motion frequency, as well a s the temporal variation and unpredictability of the energy source. Wireless pow er transfer from dedicated sources can overcome these difficulties, and in this work, the use of targeted ultrasonic power transfer as a possible method for remote powering o f sensor nodes is investigated. A powering system for pipeline monitoring sensors is described and studied experimentally, with a pair of identical, non6inert ial piezoelectric transducers used at the transmitter and receiver. Power transmission of 18 mW (Root6Mean6Square) through 1 m of a 118 mm diameter cast iron pipe, wi th 8 mm wall thickness is demonstrated. By analysis of the delay between tran smission and reception, including reflections from the pipeline edges, a transmission speed of 1000 m/s is observed, corresponding to the phase velocity of the L(0,1) a xial and F(1,1) radial modes of the pipe structure. A reduction of power delivery with water6filling is observed, yet over 4 mW of delivered power through a fully6filled pipe i s demonstrated. The transmitted power and voltage levels exceed the requirements fo r efficient power management, including rectification at cold6starting conditions , and for the operation of low6power sensor nodes. The proposed powering technique may a llow the implementation of energy autonomous wireless sensor systems for monit oring industrial and network pipeline infrastructure