4-Engel groups are locally nilpotent

Questions about nilpotency of groups satisfying Engel conditions have been considered since 1936, when Zorn proved that finite Engel groups are nilpotent. We prove that 4-Engel groups are locally nilpotent. Our proof makes substantial use of both hand and machine calculations.

Acceptability of short term neo-adjuvant androgen deprivation in patients with locally advanced prostate cancer

Purpose: To determine the acceptability of short term neo-adjuvant maximal androgen deprivation (MAD) to patients treated with external beam radiation for locally advanced prostate cancer. Methods: Between 1996 and 2000, 818 patients with locally advanced, but non-metastatic, prostate cancer were entered into a randomised clinical trial (TROG 96.01), which compared radiation treatment alone with the same radiation treatment and 3 or 6 months neo-adjuvant MAD with goserelin and flutamide. Relevant symptoms, and how troublesome they were to the patient, were scored using a self-assessment questionnaire. This was completed by the patient at registration, and at specified times during and after treatment. Patients taking flutamide had liver function tests checked at regular intervals. Results: All patients have completed at least 12 months follow-up after treatment. Nearly all patients completed planned treatment with goserelin, but 27% of patients in the 6-month MAD treatment arm, and 20% in the 3-month arm, had to stop flutamide early. This was mainly due to altered liver function (up to 17% patients) and bowel side effects (up to 8% patients). However, although flutamide resulted in more bowel symptoms for patients on MAD, there was significant reduction in some urinary symptoms on this treatment. Acute bowel and urinary side effects at the end of radiation treatment were similar in all treatment arms. Side effect severity was unrelated to radiation target volume size, which was reduced by MAD, but symptomatology prior to any treatment was a powerful predictor. Of the 36% of patients who were sexually active before any treatment, the majority became inactive whilst on MAD. However, sexual activity at 12 months after radiation treatment was similar in all treatment arms, indicating that the effects of short term MAD on sexual function are reversible. Conclusion: Despite temporary effects on sexual activity, and compliance difficulties with flutamide, short-term neo-adjuvant MAD was not perceived by patients to be a major inconvenience. If neo-adjuvant MAD in the way tested can be demonstrated to lead to improved biochemical control and/or survival, then patients would view these therapeutic gains as worthwhile. Compliance with short-term goserelin was excellent, confirming that LH-RH analogues have a potential role in more long-term adjuvant treatment. However, for more protracted androgen deprivation, survival advantages and deleterious effects need to be assessed in parallel, in order to determine the optimal duration of treatment. (C) 2003 Elsevier Ireland Ltd. All fights reserved.

Utility functions on locally connected spaces

We investigate the role of local connectedness in utility theory and prove that any continuous total preorder on a locally connected separable space is continuously representable. This is a new simple criterion for the representability of continuous preferences, and is not a consequence of the standard theorems in utility theory that use conditions such as connectedness and separability, second countability, or path-connectedness. Finally we give applications to problems involving the existence of value functions in population ethics and to the problem of proving the existence of continuous utility functions in general equilibrium models with land as one of the commodities. (C) 2003 Elsevier B.V. All rights reserved.

Demonstrating superior discrimination of locally prepared states using nonlocal measurements

We experimentally demonstrate the superior discrimination of separated, unentangled two-qubit correlated states using nonlocal measurements, when compared with measurements based on local operations and classical communications. When predicted theoretically, this phenomenon was dubbed quantum nonlocality without entanglement. We characterize the performance of the nonlocal, or joint, measurement with a payoff function, for which we measure 0.72 +/- 0.02, compared with the maximum locally achievable value of 2/3 and the overall optimal value of 0.75.

Promising results of a cooperative group phase II trial of preoperative chemoradiation for locally advanced rectal cancer (TROG 9801)

PURPOSE: This article reports the overall survival, failure-free survival, local failure, and late radiation toxicity of a phase II trial of preoperative radiotherapy with continuous infusion 5-fluorouracil for rectal cancer after a minimum 3.5 years of follow-up. METHODS: Eligible patients were those with newly diagnosed localized adenocarcinoma of the rectum, within 12 cm of the anal verge, staged T3-T4 and deemed suitable for curative resection. Radiotherapy (50.4 Gy in 28 fractions in five weeks and three days) was given with continuous infusion 5-fluorouracil throughout the course of radiotherapy. RESULTS: A total of 82 patients were accrued in 13 months. The median follow-up time was 4.1 (range, 2.3-4.5) years. There were 55 males (67 percent) and the median age was 59 (range, 27-87) years. Patients were staged pretreatment as T3 (89 percent) and resectable T4 (11 percent). Endorectal ultrasound was performed in 70 percent and magnetic resonance imaging in another 5 percent. The four-year overall and failure-free survival rates were 82 percent (95 percent Cl: 72-89) and 69 percent (95 percent Cl: 58-78), respectively. The cumulative incidence of local failure at four years was 3.9 percent (95 percent CI: 1.3-11). Risk of failures, local and distant, has not reached a plateau phase. CONCLUSION: This regimen can be delivered safely and without leading to a significant increase in late toxicity. It provides excellent local control and favorable overall survival. There is a need for longer follow-up than has commonly been used for the proper evaluation of failures after an effective regimen of preoperative chemoradiation.

Unified derivations of measurement-based schemes for quantum computation

We present unified, systematic derivations of schemes in the two known measurement-based models of quantum computation. The first model (introduced by Raussendorf and Briegel, [Phys. Rev. Lett. 86, 5188 (2001)]) uses a fixed entangled state, adaptive measurements on single qubits, and feedforward of the measurement results. The second model (proposed by Nielsen, [Phys. Lett. A 308, 96 (2003)] and further simplified by Leung, [Int. J. Quant. Inf. 2, 33 (2004)]) uses adaptive two-qubit measurements that can be applied to arbitrary pairs of qubits, and feedforward of the measurement results. The underlying principle of our derivations is a variant of teleportation introduced by Zhou, Leung, and Chuang, [Phys. Rev. A 62, 052316 (2000)]. Our derivations unify these two measurement-based models of quantum computation and provide significantly simpler schemes.