Finite dimensional semigroup quadratic algebras with the minimal number of relations

A quadratic semigroup algebra is an algebra over a field given by the generators x_1, . . . , x_n and a finite set of quadratic relations each of which either has the shape x_j x_k = 0 or the shape x_j x_k = x_l x_m . We prove that a quadratic semigroup algebra given by n generators and d=(n^2+n)/4 relations is always infinite dimensional. This strengthens the Golod–Shafarevich estimate for the above class of algebras. Our main result however is that for every n, there is a finite dimensional quadratic semigroup algebra with n generators and d_n relations, where d_n is the first integer greater than (n^2+n)/4 . That is, the above Golod–Shafarevich-type estimate for semigroup algebras is sharp.

Design and test of a bit parallel 2nd order IIR filter structure

Test procedures for a pipelined bit-parallel IIR filter chip which maximally exploit its regularity are described. It is shown that small modifications to the basic architecture result in significant reductions in the number of test patterns required to test such chips. The methods used allow 100% fault coverage to be achieved using less than 1000 test vectors for a chip which has 12 bit data and coefficients.

Programmable high-performance IIR filter chip

The paper presents a state-of-the-art commercial demonstrator chip for infinite impulse response (IIR) filtering. The programmable IIR filter chip contains eight multiplier/accumulators that can be configured in one of five different modes to implement up to a 16th-order IIR filter. The multiply-accumulate block is based on a highly regular systolic array architecture and uses a redundant number system to overcome problems of pipelining in the feedback loop. The chip has been designed using the GEC Plessey Semiconductors CLA 78000 series gate array, operates on 16-bit two's complement data and has a clock speed of 30 MHz. Issues such as overflow detection and design for testability have also been addressed and are described.

Selectable linear or quadratic coupling in an optomechanical system

There has been much interest recently in the analysis of optomechanical systems incorporating dielectric nano- or microspheres inside a cavity field. We analyse here the situation when one of the mirrors of the cavity itself is also allowed to move. We reveal that the interplay between the two oscillators yields a cross-coupling that results in, e.g., appreciable cooling and squeezing of the motion of the sphere, despite its nominal quadratic coupling. We also discuss a simple modification that would allow this cross-coupling to be removed at will, thereby yielding a purely quadratic coupling for the sphere.

The outcome of the functioning filter after subsequent cataract extraction

OBJECTIVE: To evaluate and compare the outcome of functioning filtration surgery followed by cataract surgery with posterior intraocular lens implantation by both phacoemulsification and extracapsular cataract extraction (ECCE) techniques in glaucomatous eyes. PATIENTS AND METHODS: We retrospectively evaluated the clinical course of 77 eyes (68 patients) that after successful trabeculectomy, underwent cataract surgery by either phacoemulsification or ECCE techniques. We determined the frequency of partial and absolute failure following cataract surgery by either phacoemulsification or ECCE in eyes with functioning trabeculectomies. Partial failure of intraocular pressure (IOP), control after cataract extraction was defined as the need for an increased number of antiglaucoma medications or argon laser trabeculoplasty to maintain IOP =21mm Hg. Complete failure of IOP control after cataract surgery was defined as an IOP >21 mm Hg on at least two consecutive measurements one or more weeks apart or the performance of additional filtration surgery. Failure rates were calculated using the Kaplan-Meier actuarial method. Failure rates between phacoemulsification and ECCE subgroups were compared using the log rank test. RESULTS: The probability of partial failure by the third postoperative year after cataract surgery was 39.5% in the phacoemulsification subgroup and 37.3% in the ECCE subgroup. This small difference is not statistically significant (P = 0.48). The probability of complete failure by the fourth postoperative year after cataract surgery was 12.0% in the phacoemulsification subgroup and 12.5% in the ECCE subgroup. This difference is also not statistically significant (P = 0.77). At the 6-month follow-up visit, visual acuity of both groups improved one or more lines in 87.0% of patients, and worsened one or more lines in 3.9% of patients. Sixty-one percent achieved visual acuity of 20/40 or better. The most frequent complication was posterior capsular opacification requiring laser capsulotomy that occurred in 31.2% of patients. CONCLUSION: Cataract extraction by either phacoemulsification or ECCE following trabeculectomy surgery may be associated with a partial loss of the previously functioning filter and the need for more antiglaucoma medications to control IOP.

Invariant Information Local Sub-map Filter (IILSF) for Efficient Simultaneous Localisation and Mapping of Large Environments

This paper presents an Invariant Information Local Sub-map Filter (IILSF) as a technique for consistent Simultaneous Localisation and Mapping (SLAM) in a large environment. It harnesses the benefits of sub-map technique to improve the consistency and efficiency of Extended Kalman Filter (EKF) based SLAM. The IILSF makes use of invariant information obtained from estimated locations of features in independent sub-maps, instead of incorporating every observation directly into the global map. Then the global map is updated at regular intervals. Applying this technique to the EKF based SLAM algorithm: (a) reduces the computational complexity of maintaining the global map estimates and (b) simplifies transformation complexities and data association ambiguities usually experienced in fusing sub-maps together. Simulation results show that the method was able to accurately fuse local map observations to generate an efficient and consistent global map, in addition to significantly reducing computational cost and data association ambiguities.

An in vitro study of the radiobiological effects of flattening filter free radiotherapy treatments

Flattening filter free (FFF) linear accelerators allow for an increase in instantaneous dose-rate of the x-ray pulses by a factor of 2-6 over the conventional flattened output. As a result, radiobiological investigations are being carried out to determine the effect of these higher dose-rates on cell response. The studies reported thus far have presented conflicting results, highlighting the need for further investigation. To determine the radiobiological impact of the increased dose-rates from FFF exposures a Varian Truebeam medical linear accelerator was used to irradiate two human cancer cell lines in vitro, DU-145 prostate and H460 non-small cell lung, with both flattened and FFF 6 MV beams. The fluence profile of the FFF beam was modified using a custom-designed Nylon compensator to produce a similar dose profile to the flattened beam (6X) at the cell surface but at a higher instantaneous dose-rate. For both cell lines there appeared to be no significant change in cell survival. Curve fitting coefficients for DU145 cells irradiated with constant average dose-rates were 6X: alpha = 0.09 +/- 0.03, beta = 0.03 +/- 0.01 and 6FFF: alpha = 0.14 +/- 0.13, beta = 0.03 +/- 0.02 with a significance of p = 0.75. For H460 cells irradiated with the same instantaneous dose-rate but different average dose-rate the fit coefficients were 6FFF (low dose-rate): alpha = 0.21 +/- 0.11, 0.07 +/- 0.02 and 6FFF (high dose-rate): alpha = 0.21 +/- 0.16, 0.07 +/- 0.03, with p = 0.79. The results indicate that collective damage behaviour does not occur at the instantaneous dose-rates investigated here and that the use of either modality should result in the same clinical outcome, however this will require further validation in vivo.

Transmit and receive filter design for OFDM based WLAN systems

We analyze the effect of different pulse shaping filters on the orthogonal frequency division multiplexing (OFDM) based wireless local area network (LAN) systems in this paper. In particular, the performances of the square root raised cosine (RRC) pulses with different rolloff factors are evaluated and compared. This work provides some guidances on how to choose RRC pulses in practical WLAN systems, e.g., the selection of rolloff factor, truncation length, oversampling rate, quantization levels, etc.

Octavius 4D characterization for flattened and flattening filter free rotational deliveries

Purpose: In this study the Octavius detector 729 ionization chamber (IC) array with the Octavius 4D phantom was characterized for flattening filter (FF) and flattening filter free (FFF) static and rotational beams. The device was assessed for verification with FF and FFF RapidArc treatment plans.

Methods: The response of the detectors to field size, dose linearity, and dose rate were assessed for 6 MV FF beams and also 6 and 10 MV FFF beams. Dosimetric and mechanical accuracy of the detector array within the Octavius 4D rotational phantom was evaluated against measurements made using semiflex and pinpoint ionization chambers, and radiochromic film. Verification FF and FFF RapidArc plans were assessed using a gamma function with 3%/3 mm tolerances and 2%/2 mm tolerances and further analysis of these plans was undertaken using film and a second detector array with higher spatial resolution.

Results: A warm-up dose of >6 Gy was required for detector stability. Dose-rate measurements were stable across a range from 0.26 to 15 Gy/min and dose response was linear, although the device overestimated small doses compared with pinpoint ionization chamber measurements. Output factors agreed with ionization chamber measurements to within 0.6% for square fields of side between 3 and 25 cm and within 1.2% for 2 x 2 cm(2) fields. The Octavius 4D phantom was found to be consistent with measurements made with radiochromic film, where the gantry angle was found to be within 0.4. of that expected during rotational deliveries. RapidArc FF and FFF beams were found to have an accuracy of >97.9% and >90% of pixels passing 3%/3 mm and 2%/2 mm, respectively. Detector spatial resolution was observed to be a factor in determining the accurate delivery of each plan, particularly at steep dose gradients. This was confirmed using data from a second detector array with higher spatial resolution and with radiochromic film.

Conclusions: The Octavius 4D phantom with associated Octavius detector 729 ionization chamber array is a dosimetrically and mechanically stable device for pretreatment verification of FF and FFF RapidArc treatments. Further improvements may be possible through use of a detector array with higher spatial resolution (detector size and/or detector spacing). (C) 2013 American Association of Physicists in Medicine.