text:
Radiation Oncology/Breast/Randomized

Randomized evidence for breast cancer (in progress)

Surgery +/- RT

 * NSABP B-17
 * Randomized. 818 women with DCIS, SM-. Treated with lumpectomy or lumpectomy + RT 50Gy (no boost)
 * 2001 PMID 11498833 -- "Prevention of invasive breast cancer in women with ductal carcinoma in situ: an update of the national surgical adjuvant breast and bowel project experience." (Fisher B, Semin Oncol. 2001 Aug;28(4):400-18.) Update on B-17 and B-24. F/U 12 years
 * 10-year IBTR: 30.8% vs. 14.9% (51% reduction);Invasive 16.4% to 7.1% (57% reduction)
 * No difference in distant recurrence or contralateral breast cancers.
 * UKCCCR (1990-1998)
 * Randomized. 1701 women with DCIS. 2x2 factorial: BCS followed by 1) observation, 2) RT alone, 3) tamoxifen alone, or 4) RT + Tamoxifen. RT to 50 Gy, TAM 20mg qd x5 years
 * 2003 PMID 12867108 -- "Radiotherapy and tamoxifen in women with completely excised ductal carcinoma in situ of the breast in the UK, Australia, and New Zealand: randomised controlled trial." (Houghton J, Lancet. 2003 Jul 12;362(9378):95-102.). Mean F/U 4.4 years
 * Tamoxifen: no impact on invasive IBTR, benefit for DCIS IBTR (HR 0.68)
 * RT: benefit for invasive IBTR (HR 0.45), and benefit for DCIS IBTR (HR 0.36). New breast events reduced 16% to 7% (SS)
 * No synergy between tamoxifen and RT

 * Swedish DCIS Trial (1987-1999) -- RT vs No RT
 * Randomized. 1046 women, DCIS on sector resection, target clinical surgical margin 1 cm but microscopically negative SM not required; clinically N0. Arm 1) RT 50/25 vs Arm 2) no RT
 * 2008 PMID 18250350 -- "Absolute risk reductions for local recurrence after postoperative radiotherapy after sector resection for ductal carcinoma in situ of the breast." (Holmberg L, J Clin Oncol. 2008 Mar 10;26(8):1247-52. Epub 2008 Feb 4.)
 * Outcome: IBTR RT+ 12.1% vs RT- 27.1% (RR 0.4, SS), invasive recurrence ~50%. No difference in DMFS. Age effect: women <50 RR 0.7, age >50 RR ~0.3. No group defined by stratification variables that had low risk without RT
 * Conclusion: RT decreases risk by ~50%, though younger women have low protective effect and older women benefit substantially

 * EORTC 10853 (1986-1996)
 * Randomized. 1010 women with DCIS. Size <=5cm. SM- (intraop evaluation of margins, re-excision if needed). Lumpectomy alone to lumpectomy + RT 50 Gy
 * 2006 PMID 16801628 — "Breast-Conserving Treatment With or Without Radiotherapy in Ductal Carcinoma In Situ: Ten-Year Results of European Organisation for Research and Treatment of Cancer Randomized Phase III Trial 10853--A Study by the EORTC Breast Cancer Cooperative Group and EORTC Radiotherapy Group." (Bijker N, J Clin Oncol. 2006 Jul 20;24(21):3381-7.). Median F/U 10.5 yrs.
 * 10-year LR: 26% BCS alone vs 15% BCS+RT (SS), 47% reduction. All subgroups benefited.
 * 10-year LR: invasive 13% vs. 8% (SS), 42% reduction; DCIS 14% vs. 7% (SS), 48% reduction
 * Increased risk for LR: age <40, grade 2 or 3, cribiform or solid growth pattern, doubtful margin, and LE alone. Size not a prognostic factor
 * No difference in OS or distant mets

Surgery + RT +/- Tamoxifen

 * NSABP B-24
 * Randomized, double-blind. N=1804 women with DCIS or LCIS, involved margins included. BCS + RT with or without tamoxifen. RT 50 Gy (no boost), TAM 20mg QD
 * 1999 PMID 10376613 -- "Tamoxifen in treatment of intraductal breast cancer: National Surgical Adjuvant Breast and Bowel Project B-24 randomised controlled trial." (Fisher B, Lancet. 1999 Jun 12;353(9169):1993-2000.) Median F/U 6.2 years
 * 5-year BCA events: 13.4% vs tamoxifen 8.2% (SS), ipsilateral 9.5% vs. 6.0% (SS), contralateral 3.4% vs. 2.0% (SS)
 * 5-year invasive: 7.2% vs 4.1% (SS), ipsilateral 4.2% vs. 2.1% (SS), 2.3% vs. 1.8% (NS)
 * Younger patients are at higher risk.
 * Conclusion: Tamoxifen of benefit for further reduction of invasive breast cancer recurrences. There was no difference in regional or distant metastases.

 * UKCCCR (1990-1998)
 * Randomized. 1701 women with DCIS. 2x2 factorial: BCS followed by 1) observation, 2) RT alone, 3) tamoxifen alone, or 4) RT + Tamoxifen. RT to 50 Gy, TAM 20mg qd x5 years
 * 2003 PMID 12867108 -- "Radiotherapy and tamoxifen in women with completely excised ductal carcinoma in situ of the breast in the UK, Australia, and New Zealand: randomised controlled trial." (Houghton J, Lancet. 2003 Jul 12;362(9378):95-102.). Mean F/U 4.4 years
 * Tamoxifen: no impact on invasive IBTR, benefit for DCIS IBTR (HR 0.68)
 * RT: benefit for invasive IBTR (HR 0.45), and benefit for DCIS IBTR (HR 0.36). New breast events reduced 16% to 7% (SS)
 * No synergy between tamoxifen and RT
 * Note: No benefit of tamoxifen differs from B-24 trial: authors suggest it may be due to differences in the patient population. In B-24 33.5% of patients were under 50 compared to only 9.5% in the UK/ANZ trial.

Extent of Surgery

 * NSABP B-04 (1971-1974) -- radical mastectomy vs. total mastectomy + RT vs. total mastectomy alone
 * Randomized, 2 separate randomizations. 1665 women. For further information, please see page at Axilla
 * 1079 women with clinically LN-: Arm 1) radical mastectomy vs. Arm 2) total mastectomy + RT vs. Arm 3) total mastectomy alone
 * 586 women with clinically LN+: Arm 1) radical mastectomy vs. Arm 2) total mastectomy + RT
 * 25-years, 2000 PMID 12192016 -- "Twenty-five-year follow-up of a randomized trial comparing radical mastectomy, total mastectomy, and total mastectomy followed by irradiation." (Fisher B, N Engl J Med. 2002 Aug 22;347(8):567-75.)
 * No difference in DFS, RFS, DM, or OS
 * Conclusion: No advantage to radical mastectomy. Also no survival advantage to removing occult positive nodes at surgery or to RT

 * Denmark DBCG (1951-1957) -- extended radical mastectomy vs. simple mastectomy + RT
 * Randomized. 666 consecutive patients with untreated primary breast CA randomized, 425 patients underwent surgery (majority of those excluded were not surgical candidates). Arm 1) extended radical mastectomy (radical mastectomy + dissection of axilla, infraclavicular, supraclavicular, and 2nd-4th intercostal spaces) vs. Arm 2) simple mastectomy + RT. RT given with opposing tangential fields including internal mammary LN + anterior/posterior fields to axilla supraclavicular region. Energy 180 kV - 400 kV, dose 42-45 Gy given in 6 days/week
 * 50-years; 2008 PMID 18465331 -- "Extended radical mastectomy versus simple mastectomy followed by radiotherapy in primary breast cancer. A fifty-year follow-up to the Copenhagen Breast Cancer randomised study." (Johansen H, Acta Oncol. 2008;47(4):633-8.)
 * Outcome: 5-year OS ERM 1% vs. SM + RT 1% (NS); 30-year OS 11% vs. 9% (NS). 25-year DFS 18% vs. 14% (NS)
 * Predictors: Stage I better vs. Stage II-III; premenopausal better vs. postmenopausal. Excess mortality due to breast CA demonstrable up to 20-25 years after primary diagnosis
 * Toxicity: lymphedema ERM 12% vs. SM + RT 4%
 * Conclusion: Mutilating extended radical mastectomy can be safely substituted by simple mastectomy with radiation; no difference in OS or DFS

Breast Conservation Surgery +/- RT

 * NSABP B-06 (1976-84)
 * See above for more details. Total mastectomy vs lumpectomy vs lumpectomy + RT. Chemo in N+ melphalan + 5-FU
 * 20-year LR: No RT 39.2% vs RT 14.3%. No difference in survival
 * Node negative subgroup showed survival advantage (unpublished)

 * Uppsala-Orebro (1981-88)
 * 381 patients. Stage I (<2cm, N0). "Sector resection" and ALND, +/- RT 54/27 without boost. No systemic therapy
 * 5-years, 1994 PMID 8158702 -- "Sector resection with or without postoperative radiotherapy for stage I breast cancer: five-year results of a randomized trial. Uppsala-Orebro Breast Cancer Study Group." (Liljegren G, J Natl Cancer Inst. 1994 May 4;86(9):717-22.)
 * Local recurrence 18% vs 2%. No survival difference.
 * 10-years, 1999 PMID 10561294 -- "10-Year results after sector resection with or without postoperative radiotherapy for stage I breast cancer: a randomized trial." (Liljegren G, J Clin Oncol. 1999 Aug;17(8):2326-33.)
 * 10-year LR: no RT 24% vs. RT 8.5% (SS); no difference in OS at 77%
 * Low risk: >55 and no comedo/LCIS - no RT 11% vs. RT 6% (NS)

 * St. George's (1981-1990)
 * 418 patients treated with wide local excision, adjuvant chemo (tamoxifen if ER+ or CMF if ER-), +/- RT
 * 5-years, 1996 PMID 8846860 -- "The importance of the resection margin in conservative surgery for breast cancer." (Renton SC, Eur J Surg Oncol. 1996 Feb;22(1):17-22.)
 * Local recurrence: no RT 35% vs. RT 13%. LR strictly related to margin status; if SM+ LR 17% with RT
 * Conclusion: RT cannot compensate for inadequate surgery

 * Ontario (1984-89)
 * Randomized. 837 patients, <4cm, LN-. Lumpectomy and axillary dissection +/- RT. RT 40/16 + boost 12.5/5 No systemic therapy
 * Original, 1992 PMID 1314910 (1992)
 * 8-years, 1996 PMID 8931610 -- "Randomized clinical trial of breast irradiation following lumpectomy and axillary dissection for node-negative breast cancer: an update. Ontario Clinical Oncology Group." (Clark RM, J Natl Cancer Inst. 1996 Nov 20;88(22):1659-64.). Median F/U 7.6 years
 * Ipsilateral recurrence: No RT 35% vs. RT 11% (SS). OS: 24% vs. 21% (NS). Bigger tumors on average
 * Predictors for relapse: age <50, size >2cm, poor grade
 * Conclusion: Reduced recurrence, but no survival difference. No subgroups identified

 * Scottish (1985-1991)
 * 585 patients. BCA <4cm, <70 y/o. Local excision + 1cm margin, ALND/SLN. Tamoxifen or CMF. Randomized to RT 50/20 or 50/25 + boost (20-30 IR implant or 10-15 e-boost) vs. observation. If no ALND, RT 45/20 to axilla given
 * 6-years, 1996 PMID 8806289 -- "Randomised controlled trial of conservation therapy for breast cancer: 6-year analysis of the Scottish trial. Scottish Cancer Trials Breast Group." (Forrest AP, Lancet. 1996 Sep 14;348(9029):708-13.) Median F/U 5.7 years
 * Local recurrence: no RT 24% vs. RT 6%; no difference in survival
 * Conclusion: RT advisable, even if chemotherapy given

 * Tokyo (1985-1993)
 * 113 patients. Stage I-II. Sector resection +/- RT, systemic therapy
 * 8-years, 1996 PMID 11091552 -- "Local Control and Cosmetic Outcome after Sector Resection with or without Radiation Therapy for Early Breast Cancer." (Inoue M, Breast Cancer. 1996 Mar 29;3(1):39-46.). Median F/U 4.6 years
 * Local recurrence: no RT 9.4% vs. RT 7.1
 * Conclusion: Sector resection without RT reasonable for some patients

 * St. Petersburg (1985-1996)
 * 360 patients. T1-2N0, <2.5cm. Quadrantectomy. +/- RT, systemic therapy
 * 5-years, 1998 PMID 9807204 -- "[Preliminary results of the randomized trial "The role of adjuvant radiotherapy in organ-preserving treatment of breast cancer"] - [Article in Russian]" (Semiglazov VF, Vopr Onkol. 1998;44(4):414-21.)
 * Local recurrence: no RT 17% vs. RT 4% (SS); no difference on OS

 * Milan 3 (1987-1989)
 * 579 pts. Size < 2.5 cm. 32% N+. Quadrantectomy, ALND +/- RT 50/25 + boost 10/5. Systemic in N+ (premenopausal, postmenopausal and ER- chemo, postmenopausal ER+ tamoxifen)
 * 3-years, 1993 PMID 8387637 — "Radiotherapy after breast-preserving surgery in women with localized cancer of the breast." Veronesi U et al. N Engl J Med. 1993 Jun 3;328(22):1587-91.
 * Median f/u 39 months. LR 8.8% (no RT) vs 0.3% (RT). Low rate of recurrence in pts older than 55 yrs. No difference in survival.
 * 10-years PMID 11521809 -- "Radiotherapy after breast-conserving surgery in small breast carcinoma: long-term results of a randomized trial." (Veronesi U, Ann Oncol. 2001 Jul;12(7):997-1003.)
 * Local recurrence: no RT 23% vs. RT 6% (SS); women <45 43% vs. 9%; women >65 4% vs. 4%
 * Node positive: death rate no RT 34/100 vs. RT 19/100 (SS); no difference in N0
 * Conclusion: RT indicated for <=55 years old, N+, or EIC, not indicated if >65

 * NSABP B-21 (1989-1998)
 * 1009 women. Tumors <=1cm. Lumpectomy + ALND. Randomized to RT, TAM, or RT + TAM. RT 50/25, boost at discretion
 * 8-years, 2002 PMID 12377957 -- "Tamoxifen, radiation therapy, or both for prevention of ipsilateral breast tumor recurrence after lumpectomy in women with invasive breast cancers of one centimeter or less." (Fisher B, J Clin Oncol. 2002 Oct 15;20(20):4141-9.)
 * Local recurrence: TAM 16% vs. RT 9% vs. RT+TAM 3%; no difference in DM or survival
 * Contralateral BCA: no TAM 5.4% vs. TAM 2.2%
 * Conclusion: Even in tumors <=1cm, should consider RT and TAM

 * Finland (1990-1995)
 * 152 women. <2cm, G1-2, no EIC, DNA diploid, S-phase <=7. SM 1cm. Lumpectomy. +/- RT 50/25. No systemic therapy
 * 7-years, 2001 PMID 11161371 -- "Lumpectomy with or without postoperative radiotherapy for breast cancer with favourable prognostic features: results of a randomized study." (Holli K, Br J Cancer. 2001 Jan;84(2):164-9.). Median F/U 6.7 years
 * Local recurrence: no RT 18% vs. RT 7% (SS); no difference in DM or OS, or breast preservation
 * Conclusion: RT beneficial even in women with small tumors with favorable biology

 * SweBCG (1991-1997)
 * 1187 women. Stage I-II, N0. Median tumor 12mm, 65% detected by mammography. Sector resection + ALND. +/- RT 48-54 Gy. Adjuvant chemo not regulated, given in 9%
 * 5-years, 2003 PMID 12888363 -- "Breast conservation surgery, with and without radiotherapy, in women with lymph node-negative breast cancer: a randomised clinical trial in a population with access to public mammography screening." (Malmstrom P, Eur J Cancer. 2003 Aug;39(12):1690-7.)
 * Local control: no RT 14% vs. RT 4% (SS). DFS 77% vs. 88%

 * German GBSG (1991-1998) -- 2x2 factorial BCS +/- RT +/- TAM
 * Randomized. Stopped prematurely due to slow accrual. 2x2 factorial. 347 out of target 700 patients with pT1N0, ER+, Grade I-II, EIC-, LVI-, SM-, ALND with minimum 10 LNs. Age 45-75 (>=60 in 54%). Randomized to +/- RT and to +/- TAM. RT 50/25 + boost 10-12 Gy. TAM 30 mg x2 years
 * 10-years; 2009 PMID 19879131 -- "Radiation therapy and tamoxifen after breast-conserving surgery: Updated results of a 2x2 randomised clinical trial in patients with low risk of recurrence." (Winzer KJ, Eur J Cancer. 2009 Oct 28. [Epub ahead of print]). Median F/U 9.9 years
 * Outcome: 10-year ITBR BCS 34% vs. BCS+RT 10% vs. BCS+TAM 7% vs. BCS+RT+TAM 5% (SS); regional failure 0% vs 1% vs 0% vs 0%; 8-year EFS 48% vs. 78% (RR 0.36) vs. 78% (RR 0.33) vs. 78% (RR 0.32) (SS). No difference for DMFS
 * Conclusion: In patients with favorable prognosis, avoidance of RT and TAM increases local recurrence substantially. Not powered to distinguish between RT, TAM, and RT+TAM

 * Canada multi-institutional (1992-2000) - 50 years or older, pT1-2N0
 * 769 pts. Randomized to tamoxifen +/- RT. Median age 68. BCS, pN staging 83%. Almost all had positive receptors (81%) or unknown receptor status (13%). RT 40/16 + boost 12.5/5
 * 2004 PMID 15342804 — "Tamoxifen with or without breast irradiation in women 50 years of age or older with early breast cancer." Fyles AW et al. N Engl J Med. 2004 Sep 2;351(10):963-70. Median F/U 5.6 years
 * 5-yr local: LR tamoxifen 7.7% vs TAM+RT 0.6% (SS); DFS 84% vs 91%. Planned subset outcome (T1 ER+): LR 5.9% vs 0.4% (SS).
 * 5-year regional: axillary relapse 2.5% vs. 0.5% (SS). No difference in DM or OS.
 * Conclusion: RT in addition to tamoxifen significantly reduces local and axillary recurrence

 * CALGB 9343 (Intergroup trial, RTOG 97-02, ECOG) (1994-99) - 70 years or older, T1N0, ER+.
 * 636 pts. Randomized to tamoxifen +/- RT. 56% >75 y/o. BCS, ALND 37%. RT 45/25 + boost 14/7
 * 2004 PMID 15342805 — "Lumpectomy plus tamoxifen with or without irradiation in women 70 years of age or older with early breast cancer." Hughes KS et al. N Engl J Med. 2004 Sep 2;351(10):971-7. Median F/U 5 years
 * 5-yr outcome: LR tamoxifen 4% vs TAM+RT 1% (SS). No difference in rate of mastectomy, distant mets, or 5-yr OS (87% vs 86%)
 * Side effects:
 * Physicians: cosmesis, breast pain, edema, hyperpigmentation worse at 1 year; no differences at 4 years
 * Patients: breast pain, fibrosis worse at 1 year; breast pain, arm/shoulder stiffness worse at 4 years
 * Conclusion: lumpectomy + tamoxifen alone is acceptable for women 70 years or older with T1N0 ER+ tumors

 * EBCTCG Oxford meta-analysis(1985 onwards)
 * 7300 patients in 10 trials for the BCS +/- RT subset of the analysis.
 * 2005 PMID 16360786 — "Effects of radiotherapy and of differences in the extent of surgery for early breast cancer on local recurrence and 15-year survival: an overview of the randomised trials." Clarke M et al. Lancet. 2005 Dec 17;366(9503):2087-106.
 * 5-yr LR 7% vs. 26%, respectively
 * 15-yr breast cancer-specific mortality 30.5% vs. 35.9%, respectively
 * 15-yr overall mortality 35.2% vs. 40.5%, respectively
 * Conclusion: For every four LRs prevented by the addition of RT after BCS, one death is prevented.

BCS + Tamoxifen +/- RT

 * Austrian ABCSG 8A (1996-2004)
 * 869 patients. Early breast cancer, <3 cm, G1-2, N0, ER or PR positive. Treated by lumpectomy with Arimidex or Tamoxifen. Randomized to whole breast RT 50 Gy (+/- 10 Gy boost) vs no RT. Median age 66 yrs.
 * 2005 ASTRO 2005 Plenary #3 (Abstract only) - No PMID Webcast — "Lumpectomy Plus Tamoxifen or Arimidex With or Without Whole Breast Irradiation in Women with Favorable Early Breast Cancer." Poetter R et al. IJROBP Volume 63, Supplement 1, 1 October 2005, Page S2.
 * Median f/u 3.5 years. LR 0.2% vs 3.1%. Overall recurrence 4.4% vs 6.7%.
 * 5-years, 2007 PMID 17363187 -- "Lumpectomy plus tamoxifen or anastrozole with or without whole breast irradiation in women with favorable early breast cancer." (Potter R, Int J Radiat Oncol Biol Phys. 2007 Jun 1;68(2):334-40. Epub 2007 Mar 23.). Median F/U 4.5 years
 * 5-year outcome: LR: no RT 0.4% vs. RT 5.1% (SS); Overall relapse 2.1% vs. 6.1% (SS); DM/OS NS
 * Conclusion: RT leads to significant reduction in local and overall relapse

 * Intergroup (CALGB 9343, RTOG 97-02, ECOG) (1994-99) - 70 years or older, T1N0, ER+.
 * 636 pts. Randomized to tamoxifen +/- RT. 56% >75 y/o. ALND 37%. RT 45/25 + boost 14/7
 * 5-years, 2004 PMID 15342805 — "Lumpectomy plus tamoxifen with or without irradiation in women 70 years of age or older with early breast cancer." Hughes KS et al. N Engl J Med. 2004 Sep 2;351(10):971-7. Median F/U 5 years
 * 5-yr outcome: LR tamoxifen 4% vs TAM+RT 1% (SS). No difference in rate of mastectomy, distant mets, or 5-yr OS (87% vs 86%)
 * Side effects:
 * Physicians: cosmesis, breast pain, edema, hyperpigmentation worse at 1 year; no differences at 4 years
 * Patients: breast pain, fibrosis worse at 1 year; breast pain, arm/shoulder stiffness worse at 4 years
 * Conclusion: lumpectomy + tamoxifen alone is acceptable for women 70 years or older with T1N0 ER+ tumors

 * Canada (1992-2000) - 50 years or older, pT1-2N0
 * 769 pts. Randomized to tamoxifen +/- RT. Median age 68. pN staging 83%. Almost all had positive receptors (81%) or unknown receptor status (13%). RT 40/16 + boost 12.5/5
 * 5-years, 2004 PMID 15342804 — "Tamoxifen with or without breast irradiation in women 50 years of age or older with early breast cancer." Fyles AW et al. N Engl J Med. 2004 Sep 2;351(10):963-70. Median F/U 5.6 years
 * 5-yr local: LR tamoxifen 7.7% vs TAM+RT 0.6% (SS); DFS 84% vs 91%. Planned subset outcome (T1 ER+): LR 5.9% vs 0.4% (SS).
 * 5-year regional: axillary relapse 2.5% vs. 0.5% (SS). No difference in DM or OS.
 * Conclusion: RT in addition to tamoxifen significantly reduces local and axillary recurrence

 * NSABP B-21 (1989-1998)
 * 1009 women. Tumors <=1cm. Lumpectomy + ALND. Randomized to RT, TAM, or RT + TAM. RT 50/25, boost at discretion
 * 8-years, 2002 PMID 12377957 -- "Tamoxifen, radiation therapy, or both for prevention of ipsilateral breast tumor recurrence after lumpectomy in women with invasive breast cancers of one centimeter or less." (Fisher B, J Clin Oncol. 2002 Oct 15;20(20):4141-9.)
 * Local recurrence: TAM 16% vs. RT 9% vs. RT+TAM 3%; no difference in DM or survival
 * Contralateral BCA: no TAM 5.4% vs. TAM 2.2%
 * Conclusion: Even in tumors <=1cm, should consider RT and TAM

RT: Hypofractionation vs. standard fractionation

 * MRC START B (1999-2001) -- 50/25 vs. 40/15 over 3 weeks
 * Randomized. 2215 patients. Operable invasive BCA, pT1-3a N0-1, requiring RT after surgery. Surgery either BCS or mastectomy (8%). Arm 1) 50/25 vs. Arm 2) 40/15 over 3 weeks. Boost given at discretion (43%) 10/5. Regional RT 14%.
 * Concurrently, patients enrolled on photographic assessment substudy, QoL substudy and health economic studies.
 * 2008 PMID 18355913 -- "The UK Standardisation of Breast Radiotherapy (START) Trial B of radiotherapy hypofractionation for treatment of early breast cancer: a randomised trial." (START Trialists' Group, Lancet. 2008 Mar 29;371(9618):1098-107. Epub 2008 Mar 19.) Median F/U 6 years
 * Outcome: LRR 50 Gy 3% vs. 40 Gy 2% (NS); DM, DSF and OS all better (SS) in 40 Gy group
 * Toxicity: Lower rate of late toxicity in 40 Gy group (SS)
 * Conclusion: 40 Gy over 3 weeks has at least as favorable control and toxicity as 50 Gy over 5 weeks

 * MRC START A (1998-2002) -- 50/25 vs. 41.6/13 vs. 39/13 over 5 weeks
 * Randomized. 2236 patients. Operable invasive BCA, pT1-3a N0-1, requiring RT after surgery. Surgery either BCS or mastectomy (15%). Arm 1) 50/25 vs. Arm 2) 41.6/13 vs. Arm 3) 39/13; all arms given over 5 weeks to eliminate treatment time variable. Boost given at discretion (61%) 10/5. Regional RT 14%.
 * Concurrently, patients enrolled on photographic assessment substudy, QoL substudy and health economic studies.
 * 2008 PMID 18356109 -- "The UK Standardisation of Breast Radiotherapy (START) Trial A of radiotherapy hypofractionation for treatment of early breast cancer: a randomised trial." (START Trialsists' Group, Lancet Oncol. 2008 Apr;9(4):331-41. Epub 2008 Mar 19.) Median F/U 5.1 years
 * Outcome: 5-year LRR 50 Gy 4%, 41.6 Gy 4%, 39 Gy 5% (NS).
 * Cosmesis: Lower rate of late adverse effects in 39 Gy, same in 41.6 Gy compared with 50 Gy
 * Alpha/beta estimate: tumor control 4.6 Gy, late breast changes 3.4 Gy
 * Conclusion: Breast cancer and normal breast tissues respons similarly to fraction size. No difference in local control

10 year followup of START A and START B: http://www.ncbi.nlm.nih.gov/pubmed/24055415

 * Ontario (Canada) (1993-96)
 * Randomized. 1234 patients with invasive T1-2 N0, SM-. Treated with 1) 42.5/16 (2.66 Gy/fx) or 2) 50/25; No boost.
 * 10-years; 2010 PMID 20147717 -- "Long-Term Results of Hypofractionated Radiation Therapy for Breast Cancer" (Whelan TJ, 2010 Feb 11; N Engl J Med 362(6):513-20). Min F/U 10 years
 * Outcome: 10-year local recurrence: Hypo-fx 7.4% (invasive 6.2%) vs control 7.5% (invasive 6.7%) (NS). No difference in 10-year DFS or OS. Subgroup analysis high grade tumors hypo-fx 16% vs. control 5% (SS). 10-year DSS both groups 87% (NS); OS both groups 84% (NS)
 * Toxicity: No Grade 4 toxicity. Grade 3 skin toxicity hypo-fx 2.5% vs. control 2.7% (NS); Grade 3 subcutaneous toxicity 2.5% vs 3.6% (NS). Grade 2 skin toxicity 6.4% vs. 5.0% (NS); Grade 2 subcutaneous toxicity 9.4% vs 6.8% (NS). Excellent/good cosmetic outcome hypo-fx 70% vs. 71% (NS)
 * Conclusion: Accelerated hypofractionated WBRT was not inferior to standard WBRT

 * Royal Marsden (UK) (1986-1998)
 * Randomized. 1410 patients with T1-3N0-1 (max 1 positive node), treated with 1) 50/25, or 2) 39/13 (3.0 Gy/fx), or 3) 42.9/13 (3.3 Gy/fx) all over 5 weeks. Primary outcome late side effects; trial extended to allow power for LR evaluation but then stopped early due to start of START trial
 * RT: WBRT; 25% randomly assigned to no boost, 26% randomly assigned to boost, 50% boost at MD discretion (comparable in all 3 groups)
 * 2006 PMID 16750496 -- "Effect of radiotherapy fraction size on tumour control in patients with early-stage breast cancer after local tumour excision: long-term results of a randomised trial." (Owen JR, Lancet Oncol. 2006 Jun;7(6):467-71.). Median F/U 9.7 years
 * 10-year IBTR: 12% vs. 14.8% vs. 9.6% (NS vs 50/25, but SS between 39/13 and 42.9/13)
 * Estimate of LR-based a/b = 4.0 Gy (and possibly as low as 3.0 Gy)
 * 2005 PMID 15878095 -- "Fractionation sensitivity and dose response of late adverse effects in the breast after radiotherapy for early breast cancer: long-term results of a randomised trial." (Yarnold J, Radiother Oncol. 2005 Apr;75(1):9-17.) Minimum F/U 5 years
 * Long-term side effects equivalent among groups
 * Estimate of long-term side-effects a/b: 3.1 Gy

 * Egypt NCI, 2004 PMID 15959551 -- "Hypofractionation versus conventional fractionation radiotherapy after conservative treatment of breast cancer: early skin reactions and cosmetic results." (Taher AN, J Egypt Natl Canc Inst. 2004 Sep;16(3):178-87.)
 * Randomized. 30 patients with T1-2N0, treated with A) 50/25 vs. B) 42.5/16 (2.66 Gy/fx). Primary outcome early reaction and late cosmesis. Median F/U 22 months
 * Acute reactions: no difference, but group B 2 weeks earlier (3rd week vs. 5th week)
 * Late reactions: preliminary - no difference

 * Hopital Necker, France (1982-1984) -- 45/25 vs 23/4
 * Randomized. 230 patients (T1 22%, T2 61%, cN+ 28%), surgery in 79%, neoadjuvant chemo + RT 21%. Arm 1) 45/25 vs Arm 2) 23/4 over 17 days (D1, D3, D15, D17)
 * 1990 PMID 2254102 -- "The use of a specific hypofractionated radiation therapy regimen versus classical fractionation in the treatment of breast cancer: a randomized study of 230 patients." (Baillet F, Int J Radiat Oncol Biol Phys. 1990 Nov;19(5):1131-3.) Min F/U 4 years
 * Outcome: 5-year OS no difference. LRR hypofx 7% vs conventional 5% (NS)
 * Toxicity: hypofx 23% vs conventional 19%; fibrosis 18% vs 9%
 * Conclusion: No difference in effectiveness and rate of complications

RT Boost vs. no boost

 * Budapest (Hungary)(1995-1998)
 * Randomized. 604 women, T1-2 N0-1 BCA, s/p BCS + ALND and whole breast RT 50/25. Arm 1) observation vs. Arm 2) tumor bed boost. Boost given as electron boost 16/8 (50% patients) or Ir-192 HDR brachytherapy with 3-9 needles to 12/3 initially and then 14.25/3 (50% patients)
 * 5-years; 2002 PMID 12426672 -- "Electron and high-dose-rate brachytherapy boost in the conservative treatment of stage I-II breast cancer first results of the randomized Budapest boost trial." (Polgar C, Strahlenther Onkol. 2002 Nov;178(11):615-23.) Median F/U 5.3 years
 * Outcome: LR no boost 15% vs. boost 7% (SS), tumor bed recurrence 12% vs. 4% (SS), CSS 90% vs. 82% (p=0.053). No difference between electron and HDR boost
 * Predictors for LR: age <40, close/positive SM, high mitotic activity
 * Toxicity: excellent/good no boost 91% vs. boost 86% (NS); but Grade 2-3 side effects 8% vs. 17% (SS). No difference between electron and HDR boost
 * Conclusion: Boost dose significantly improves local control and relapse-free survival; cosmetic outcome comparable

 * Lyon (France) (1986-92)
 * 1024 pts. Tumor <=3cm. Lumpectomy 82%/quadrantectomy 16%. N+ 27%. SM- 2%. Treated with 50/20 +/- 10/4 boost to tumor bed.
 * 5-years, 1997 — PMID 9060534 "Role of a 10-Gy boost in the conservative treatment of early breast cancer: results of a randomized clinical trial in Lyon, France." Romestaing P et al. J Clin Oncol. 1997 Mar;15(3):963-8.
 * Local recurrence: 3.6% (boost) vs 4.5% (no boost)
 * Cosmesis: telangiectasia 12.4% vs. 5.9%, but no difference in self-assessment of cosmesis
 * Conclusion: boost provides significant benefit without much impact on cosmesis

 * EORTC 22881/10882, 2001 (1989-96) - boost vs no boost.
 * 5318 patients. Stage I-II. Lumpectomy + ALND + 50/25 Gy to breast. 21% N+. If SM-, randomized to +/- 16 Gy boost. Boost was to lumpectomy + 1.5 cm margin. 28% adjuvant systemic therapy
 * Cosmesis, 1999 PMID 10524422 -- "The influence of the boost in breast-conserving therapy on cosmetic outcome in the EORTC "boost versus no boost" trial." (Vrieling C, Int J Radiat Oncol Biol Phys. 1999 Oct 1;45(3):677-85.)
 * Panel evaluation of cosmesis (731 patient photographs), digitizer measurements of nipple displacement pre-RT (3000 patients) and 3 years later (1141 patients)
 * Pre-RT cosmesis: no difference
 * 3-year cosmesis: excellent/good results in 86% no boost vs. 71% boost (SS)
 * Conclusion: Boost had adverse effect on cosmesis
 * 5-years, 2001 PMID 11794170 Full Text — "Recurrence Rates after Treatment of Breast Cancer with Standard Radiotherapy with or without Additional Radiation" Bartelink H et al. N Engl J Med. 2001 Nov 8;345(19):1378-87.
 * 5-year LR: Overall Boost 4.3% vs no boost 7.3%. (reduction of 40%). Women <40 the most benefit (10% vs 20%). Women >60 minimal benefit (2.5% vs. 4%)
 * No difference in rate of metastases or OS.
 * 10-years, 2007 PMID 17577015 -- "Impact of a Higher Radiation Dose on Local Control and Survival in Breast-Conserving Therapy of Early Breast Cancer: 10-Year Results of the Randomized Boost Versus No Boost EORTC 22881-10882 Trial." (Bartelink H, J Clin Oncol. 2007 Jun 18; [Epub ahead of print])
 * 10-year outcome: LR: boost 6% vs. no boost 10% (SS); if age <40 24% vs. 13% (SS). Salvage mastectomy reduced by 41%. Survival 82% in both arms (NS)
 * Toxicity: severe fibrosis boost 4.4% vs. no boost 1.6% (SS)
 * Conclusion: Improved local control in all age groups, but no difference in survival

Sequencing RT with hormonal therapy

 * CO-HO-RT, France/Switzerland (2005-2007) -- concurrent vs sequential RT + letrozole
 * Randomized, Phase II. 150 postmenopausal women, early stage BCA, s/p BCT. Arm 1) concurrent RT and letrozole (starting 3 weeks prior to RT) vs Arm 2) sequential RT and letrozole (starting 3 weeks post RT). Whole breast RT 50/25, SCV/IM as necessary. Letrozole 2.5 mg QD x5 years
 * 2010 PMID 20138810 -- "Concurrent or sequential adjuvant letrozole and radiotherapy after conservative surgery for early-stage breast cancer (CO-HO-RT): a phase 2 randomised trial." (Azria D, Lancet Oncol. 2010 Mar;11(3):258-65. Epub 2010 Feb 6.) Median F/U 2.2 years
 * Acute toxicity: Skin Grade 2+ concurrent 41% vs sequential 41% (NS); Dermatitis Grade 3 in 5% vs 8%
 * Late toxicity: Fibrosis Grade 2+ in 3% vs 3% (NS)
 * Conclusion: Letrozole can be safely delivered concurrent with RT

PMRT vs PMRT + Chemo vs Chemo Alone

 * Scotland (1976-1982) -- PMRT alone vs PMRT + Chemo vs Chemo Alone
 * Randomized, 3 arms. 322 women, age ≤ 70, operable breast cancer, pN+. Arm 1) PMRT vs Arm 2) PMRT followed by CMF vs Arm 3) CMF alone
 * 2010 PMID 20673353 -- "Adjuvant radiotherapy and chemotherapy in breast cancer: 30 year follow-up of survival." (McArdle CS, BMC Cancer. 2010 Jul 30;10:398.) Median F/U 27 years (25-31 years)
 * Outcome: Deaths 81%, BCA deaths 63%. No difference in OS or CSS between the 3 arms (if RT+CMF baseline, HR for CSS for RT alone 1.24 (p=0.3) and HR for chemo alone 1.43 (p=0.08). CSS 10-years 41%, 20-years 34%, 30-years 33%.
 * Conclusion: No difference in long-terms survival between the different adjuvant regimens

Hypofractionated PMRT

 * INMOL, Pakistan -- PMRT 27/5 vs 35/10 vs 40/15
 * Randomized. 300 patients, BCA Stage T2-4N+. Arm 1) 27/5 in one week vs Arm 2) 35/10 in 2 weeks vs Arm 3) 40/15 in 3 weeks. Delivered using Co-60 with 4 fields
 * 2009 PMID 19438129 -- "Post mastectomy adjuvant radiotherapy in breast cancer: a comparision of three hypofractionated protocols." (Shahid A, J Pak Med Assoc. 2009 May;59(5):282-7.)
 * Outcome: LRR 27/5 was 11%, 35/10 was 12%, and 40/15 was 10% (NS); OS 83% vs 82% vs 80% (NS).
 * Toxicity: Grade 3-5 skin 37% vs. 28% vs. 14% (SS); cardiac toxicity 5% vs 6% vs 5%; pulmonary toxicity 4% vs 5% vs 5% (NS). No rib fractions
 * Conclusion: All 3 protocols equally effective, with similar toxicity, and were helpful in reducing work load

Neoadjuvant chemo -> mastectomy -> normal vs. hyperfractionated PMRT

 * MD Anderson, 2006 (1985-1989) PMID 16750325 -- "Fifteen-year results of a randomized prospective trial of hyperfractionated chest wall irradiation versus once-daily chest wall irradiation after chemotherapy and mastectomy for patients with locally advanced noninflammatory breast cancer." (Buchholz TA, Int J Radiat Oncol Biol Phys. 2006 Jul 15;65(4):1155-60.)
 * Randomized. 200 patients with clinical Stage III, no inflammatory BCA. Treated with neoadjuvant chemo; if CR then mastectomy and randomized to standard PMRT (60/30) vs. hyperfractionated PMRT (72/60 in 1.2 Gy BID). SCV treated in both arms to 50/25. Median F/U 15 years
 * 15-year LRR: standard 7% vs. hyperfractionated 12% (NS)
 * Toxicity: acute similar, moist desquammation standard 28% vs. hyperfractionated 42% (NS); late similar 6% vs. 11% (NS)
 * Conclusion: No evidence of clinical advantage for hyperfractionated regimen

Extent of surgical dissection

 * NSABP B-32 (1999-2004) -- SLN + ALND vs. SLN alone
 * Randomized. 5611 women with operable invasive breast cancer and clinically negative axillary LNs (T1 80%, T2 18%; lumpectomy 86%). Arm 1) SLN followed by immediate completion ALND vs. Arm 2) SLN alone, if SLN-; full ALND if no SLN identified or if SLN+. Identification included technetium scan, blue dye, and clinically suspicious lymph nodes
 * Technical Outcomes; 2007 PMID 17851130 -- "Technical outcomes of sentinel-lymph-node resection and conventional axillary-lymph-node dissection in patients with clinically node-negative breast cancer: results from the NSABP B-32 randomised phase III trial." (Krag DN, Lancet Oncol. 2007 Oct;8(10):881-8.)
 * Technical outcome: Technical success in 97%. Location in Level I/II in 99% (Level I 83%, Level II 16%, Level III 0.5%, IM 0.5%, SCV 0.1%. Mean number removed 2.1
 * Clinical outcome: SLN+ in both groups 26% (NS). If SLN- (74%), ALND- 96% and ALND+ 4% (false negative rate 10%). Overall accuracy 97%. If only one SLN removed, false negative rate 18%. In the 26% of SLN+ patients, 61% had no further LN disease on completion ALND
 * Conclusion: Success of SLN resection is high

 * Sentinella/GIVOM (Italy)(1999-2004) -- SLN vs. ALND
 * Randomized. Stopped early due to increasing preference for SLN. 697/1498 patients, breast cancer <=3 cm, clinically negative axilla. Arm 1) SLN + ALND vs. Arm 2) SLN alone, if SLN+ completion ALND. Radioactive tracer used. ALND was at least Level I-II. If BCS, adjuvant RT 50 Gy.
 * 5-years; 2008 PMID 18216523 -- "A Randomized clinical trial on sentinel lymph node biopsy versus axillary lymph node dissection in breast cancer: results of the Sentinella/GIVOM trial." (Zavagno G, Ann Surg. 2008 Feb;247(2):207-13.) Median F/U 4.7 years
 * Technical outcome: SLN identified in 95%. SLN+ in ALND 27% vs SLN 30%. False negative rate 17% (1 LN+ in 78%, 2 LN+ in 11%)
 * Clinical outcome: LR ALND 1% vs. SLN 5%. Axilla recurrence 0 patients vs. 1 patient. SCV recurrence 0 patients vs. 3 patients. 5-year DFS 90% vs. 88% (NS)
 * Toxicity: SLN group significantly less lymphedema, restrictions of shoulder mobility, and numbness. No impact on psychologic well-being
 * Conclusion: SLN is effective and well tolerated. Safety should be confirmed in larger randomized trials
 * Comment: Small size due to early stoppage, no formal training required for SLN, inclusion of small hospitals, which may explain high false positive rate, but may also be true of clinical practice

 * ALMANAC (UK)(1999-2003) -- SLN vs. ALND
 * Randomized. 'Stopped early due to perceived loss of equipoise, with better QoL in SLN arm. 991/1260 patients, operable breast cancer, no size restriction, multicentric disease excluded. Arm 1) SLN, if SLN+ then delayed axillary surgery or axillary RT (depending on institutional practice) vs. Arm 2) standard axillary surgery (either full Level I-III ALND (75%) or 4 node sampling (25%), depending on institutional practice). Radioactive tracer and blue dye used. Primary outcome arm/shoulder morbidity and QoL
 * 2006 PMID 16670385 -- "Randomized multicenter trial of sentinel node biopsy versus standard axillary treatment in operable breast cancer: the ALMANAC Trial." (Mansel RE, J Natl Cancer Inst. 2006 May 3;98(9):599-609.)
 * Technical outcome: SLN identified in 98%. SLN+ in ALND 23% vs. SLN 26%. If SLN+, delayed axillary clearance 69%, axillary RT 27%
 * Clinical outcome: Lymphedema SLN 5% vs. ALND 13% (SS), numbness 11% vs. 31% (SS). QoL and arm functioning scores significantly better for SLN group. No increase in anxiety level. 1-year axillary failure SLN 1 patient vs. ALND 4 patients
 * Conclusion: SLN is associated with reduced arm morbidity and better quality of life

 * Milan SLN (1998-1999) -- SLN + ALND vs. SLN alone
 * Randomized. 516/532 patients, T1-T2, breast conserving surgery. Multicentric cancer excluded. Arm 1) SLN + ALND vs. Arm 2) SLN without ALND, if SLN+ completion ALND; if no SLN identified, patient not eligible. ALND included Levels I-III. Radioactive tracer used. Adjuvant RT to ipsilateral breast 50 Gy + boost 10 Gy. Adjuvant chemotherapy as per institutional protocol (50% hormones, 7% chemotherapy, 40% chemotherapy + hormones, 3% none)
 * 7-years; 2006 PMID 17138219 -- "Sentinel-lymph-node biopsy as a staging procedure in breast cancer: update of a randomised controlled study." (Veronesi U, Lancet Oncol. 2006 Dec;7(12):983-90.) Median F/U 6.6 years
 * Technical outcome: SLN+ in ALND 32% vs. SLN 35% (NS). If SLN- (68%), ALND- 95% and ALND+ 5% (false negative rate 9%). Overall accuracy 97%. If LVI+, 70% had SLN+
 * Clinical outcome: Axillary failure ALND 0% vs SLN 0.004% (1 patient), SCV failure 0.008% (2 patients) vs. 0%, DM 5% vs. 4%. 5-year OS 96% vs. 98% (NS)
 * Toxicity: SLN patients less pain, numbness, better arm mobility, and less swelling
 * Conclusion: SLND allows patients with SLN- to avoid ALND, while reducing morbidity and cost of hospital stay

 * Kyoto (Japan)(1995-1997) -- ALND Level I vs. Level III
 * Randomized. 522 patients. T1-3N0-1b. BCS or mastectomy. Randomized to Level I vs. Level III dissection. All oral 5-FU day 1 and tamoxifen x2 years
 * 10-years; 2006 "Ten-year follow-up results of a randomised controlled study comparing level-I vs level-III axillary lymph node dissection for primary breast cancer." (Kodama H, Br J Cancer. 2006 Oct 9;95(7):811-6.)
 * 10-year outcome: OS 77% vs. 74% (NS); DFS 90% vs. 88% (NS)
 * Toxicity: shorter surgery, less blood loss, no difference in edema or shoulder problems
 * Conclusion: Level III dissection not recommended

 * Showa University, 2004 (Japan)(1991-1993) -- ALND Level II vs. Level III
 * Randomized. 1209 women with Stage II BCA. Mastectomy + Level II vs. Level III dissection.
 * 10-years; 2004 PMID 14716791 -- "Randomized clinical trial comparing level II and level III axillary node dissection in addition to mastectomy for breast cancer." (Tominaga T, Br J Surg. 2004 Jan;91(1):38-43.) F/U 10 years
 * 10-year outcome: OS 87% vs. 86% (NS); DFS 73% vs. 78% (NS)
 * Toxicity: Level II surgery shorter with less blood loss. No difference in patients' symptoms
 * Conclusion: Level III resection does not improve OS or DFS

ALND vs. Axillary RT

 * NSABP B-04 (Fisher), 1985 (1971-4) - radical mastectomy (including axillary dissection) vs total mastectomy (no axillary dissection) + XRT to chest wall and lymphatics.
 * 1665 pts, operable, potentially curable cancer confined to the breast and axilla; nodes not fixed.
 * For clinically N+ pts, randomized to radical mastectomy vs total mastectomy + RT.
 * For clinically N- pts, randomized to radical mastectomy vs total mastectomy vs total mastectomy + RT. Pts treated without axillary dissection or regional RT who later developed biopsy-proven axillary disease then went on to axillary dissection. These pts were not considered to have a LR (unless the nodes were unresectable, only in 1 pt).
 * Dose was 50 Gy / 25 fx to chest wall, with 10-20 Gy boost for LN+ pts. 45 Gy to SCLV and IM nodes.
 * No systemic therapy was given.
 * 25-years, 2000: PMID 12192016 Full text — "Twenty-five-year follow-up of a randomized trial comparing radical mastectomy, total mastectomy, and total mastectomy followed by irradiation." Fisher B et al. N Engl J Med. 2002 Aug 22;347(8):567-75.
 * 82% of pts had an event. Most common event was recurrence (57% LN+, 37% LN-) followed by death without evidence of cancer (25%) followed by second primary cancer (6%) and contralateral breast cancer (6%). Most recurrences (74%) were distant. 30% of LN- pts had a distant recurrence and 42% of LN+. 5% had local recurrence, and 4% had regional recurrence.  Note the continued relapses even after 10 years.
 * Summary: No difference in DFS or RFS among the three LN- groups or among the two LN+ groups.
 * Conclusion: Failed to show a benefit of axillary dissection for clinically node-negative pts (compared with a wait-and-watch approach).

 * Institut Curie (France)(1982-1987) - lumpectomy + axillary surgery vs lumpectomy + axillary XRT
 * Randomized. 658 pts. Clinically N0, T < 3cm, randomized to axillary dissection or axillary XRT. All patients received lumpectomy + XRT to the breast, 55 Gy + 10-15 Gy boost (total 65-70 Gy).
 * Pts randomized to axillary surgery had axillary dissection (level I and lower level II nodes inferior to axillary vein) and had XRT to SCLV and IM nodes if they had positive axillary nodes, and IM node XRT if they had a central or medially located tumor.
 * Pts randomized to axillary XRT received RT to axilla and IMN. Dose to axilla was 50 Gy; dose to SCLV and IM nodes was 45 Gy.
 * 21% of the surgery group had LN+. Pts with more than one positive LN were allowed either hormonal therapy or CMF chemotherapy; some pts in XRT group received chemo. Chemotherapy in ~5% of surgery group, 3% of XRT group. Tamoxifen was allowed. Hormonal therapy given in 3-5% of patients (more in surgery group).
 * 15-years, 2004 PMID 14701770 Full text — "Axillary treatment in conservative management of operable breast cancer: dissection or radiotherapy? Results of a randomized study with 15 years of follow-up." (Louis-Sylvestre C et al. J Clin Oncol. 2004 Jan 1;22(1):97-101.)
 * No difference in OS or DFS. 10-year OS 86% vs 83%; 15-year OS 75% vs 75%. 5-year DFS 83%; 10-year 72%; 15-year 64%.  5-year distant mets, 10-12%; 10-year DM 18-21%; 15-year DM 25%.  Ipsilateral breast recurrence at 5-years 7%, at 10 years 12%, at 15 years 17%.  Isolated axillary recurrence (without breast recurrence) 1% vs 3% at 15 years (p=0.04).
 * Summary: with longer followup, no difference. Data agree with results from B-04

ALND vs. Axillary RT vs. Observation

 * NSABP B-04 (Fisher), 1985 (1971-4) - radical mastectomy (including axillary dissection) vs total mastectomy (no axillary dissection) + XRT to chest wall and lymphatics.
 * 1665 pts, operable, potentially curable cancer confined to the breast and axilla; nodes not fixed.
 * For clinically N+ pts, randomized to radical mastectomy vs total mastectomy + RT.
 * For clinically N- pts, randomized to radical mastectomy vs total mastectomy vs total mastectomy + RT. Pts treated without axillary dissection or regional RT who later developed biopsy-proven axillary disease then went on to axillary dissection. These pts were not considered to have a LR (unless the nodes were unresectable, only in 1 pt).
 * Dose was 50 Gy / 25 fx to chest wall, with 10-20 Gy boost for LN+ pts. 45 Gy to SCLV and IM nodes.
 * No systemic therapy was given.
 * 25-years, 2000: PMID 12192016 Full text — "Twenty-five-year follow-up of a randomized trial comparing radical mastectomy, total mastectomy, and total mastectomy followed by irradiation." Fisher B et al. N Engl J Med. 2002 Aug 22;347(8):567-75.
 * 82% of pts had an event. Most common event was recurrence (57% LN+, 37% LN-) followed by death without evidence of cancer (25%) followed by second primary cancer (6%) and contralateral breast cancer (6%). Most recurrences (74%) were distant. 30% of LN- pts had a distant recurrence and 42% of LN+. 5% had local recurrence, and 4% had regional recurrence.  Note the continued relapses even after 10 years.
 * Summary: No difference in DFS or RFS among the three LN- groups or among the two LN+ groups.
 * Conclusion: Failed to show a benefit of axillary dissection for clinically node-negative pts (compared with a wait-and-watch approach).

ALND vs. Tangents Only RT

 * International Breast Cancer Study Group Trial 10-93, 2006 (1993-2002) - PMID 16344321 — "Randomized Trial Comparing Axillary Clearance Versus No Axillary Clearance in Older Patients With Breast Cancer: First Results of International Breast Cancer Study Group Trial 10-93." IBCSG (Rudenstam CM). J Clin Oncol. 2006 Jan 20;24(3):337-44.
 * 473 pts. Women >= 60 yrs, clinically node negative, operable, eligible for tamoxifen. Randomized to primary surgery + axillary clearance vs surgery without axillary clearance. Both groups received tamoxifen. Primary end point was quality of life. Axillary staging was clinical; no sentinel lymph node biopsy was performed. RT was tangents, no axillary RT.
 * Median f/u 6.6 yrs. 42% had 2 cm or larger tumors. 20% of pts (of those dissected) had 1-3 LN, 8% had 4 or more LN. Largest difference in QOL was before first post-op visit. Differences disappeared by 6-12 months. At median f/u, similar DFS and OS. 2% axillary recurrence rate (same in both arms).
 * Avoiding axillary clearance leads to similar efficacy and better early QOL.

Whole Breast 2D vs. IMRT
Randomized
 * Canada (2003-2005) -- 2D vs. IMRT
 * Randomized. 331 patients, early-stage BCA (no >=4 LN+) treated with breast-only RT. Arm 1) 2D tangent + wedge vs. Arm 2) IMRT. RT dose 50/25 + optional 16 Gy electron boost.
 * 2008 PMID 18285602 -- "A Multicenter Randomized Trial of Breast Intensity-Modulated Radiation Therapy to Reduce Acute Radiation Dermatitis." (Pignol JP, J Clin Oncol. 2008 Feb 19 [Epub ahead of print])
 * IMRT associated with decreased moist desquamation ), in inframammary fold (26% vs 43%). The breast volume (V95) is associated with acute skin toxicity.
 * Outcome: Dose distribution: IMRT better. Moist desquamation anywhere in breast: IMRT 31% vs 2D 48% (SS), 26% vs. 43% (SS), no difference in pain 23% vs. 25% (NS) or QoL
 * Conclusion: Breast IMRT reduced occurrence of moist desquamation

 * Royal Marsden -- 2D vs. IMRT
 * Randomized. 240/306 patients. Early stage. Treated with Arm 1) IMRT vs. Arm 2) 2D using standard wedges. Dose 50/25 + boost 11.1/5.
 * 2007 PMID 17224195 -- "Randomised trial of standard 2D radiotherapy (RT) versus intensity modulated radiotherapy (IMRT) in patients prescribed breast radiotherapy." (Donovan E, Radiother Oncol. 2007 Mar;82(3):254-64.) Minimum F/U 5 years
 * Change in breast: IMRT 40% vs. 2D 58% (SS); significantly fewer developed palpable induration. No difference in pain, hardness, or QoL
 * Conclusion: Minimisation of inhomogeneity reduces late adverse effects

APBI vs. Whole Breast RT

 * University of Florence (2005-2008) -- WBRT vs APBI 30/5
 * Randomized. Ongoing. 259 patients out of planned 520. Arm 1) WBRT 50/25 using conventional tangents vs Arm 2) IMRT APBI 30/5. Mean CTV 44 cm3, mean PTV 123 cm3, mean PTV/breast volume 21%
 * 2009 PMID 19700248 -- "Accelerated Partial Breast Irradiation with IMRT: New Technical Approach and Interim Analysis of Acute Toxicity in a Phase III Randomized Clinical Trial." (Livi L, Int J Radiat Oncol Biol Phys. 2009 Aug 21. [Epub ahead of print])
 * Toxicity: Skin toxicity Grade 2 WBRT 19% vs. IMRT 1%
 * Conclusion: APBI is feasible, with very low acute toxicity

 * Hungary (1998-2004) -- partial breast RT vs WBRT
 * Randomized. Trial stopped prematurely, since patients offered entry onto GEC-ESTRO Phase III APBI trial. 258 of expected 570 patients with T1N0-1mic, G1-2 nonlobular BCA, no EIC, SM-. WLE + ALND/SLND. Arm 1) WBI 50/25 vs. Arm 2) PBI 36.4/7 @ 5.2 Gy/fx BID multicatheter HDR (69%) or limited field electron PBI 50/25 if unsuitable for HDR (tumor bed + 2cm margin). Primary endpoint 5-year LR, noninferiority was 6% difference. Adjuvant chemo/hormones 72%
 * 5-years; 2007 PMID 17531400 -- "Breast-conserving treatment with partial or whole breast irradiation for low-risk invasive breast carcinoma-5-year results of a randomized trial." (Polgar C, Int J Radiat Oncol Biol Phys. 2007 Nov 1;69(3):694-702.). Median F/U 5.5 years
 * Outcome: 5-year LR WBI 3.4% vs. PBI 4.7% (NS); no difference in DFS or OS
 * Toxicity: excellent/good cosmesis WBI 63% vs. PBI 78% (SS); HDR 81% and EB-APBI 70%
 * Conclusion: Similar outcomes, better cosmesis with HDR APBI

 * Yorkshire Breast Cancer Group (1986-1990) -- WBRT 40/15 vs PBI
 * Randomized. Trial closed prematurely due to non-accrual. 174 out of expected 400 patients. pT1-T2, pN0-N1. SM-. Arm 1) conventional WBRT 40/15 vs Arm 2) APBI 55/20 (tangents, appositional Co-60 teletherapy, appositional Cs-137 teletherapy, electrons)
 * 2005 PMID 16372487 -- "A randomised study of whole-breast vs tumour-bed irradiation after local excision and axillary dissection for early breast cancer." (Dodwell DJ, Clin Oncol (R Coll Radiol). 2005 Dec;17(8):618-22.)
 * Outcome: IBTR WBRT 4% vs. APBI 12% (NS). LRF 24% vs 9% (NS). No difference in DM and OS
 * Conclusion: Conclusions are limited due to failure to complete accrual

 * Christie Hospital (1982-1987) -- electron tumor bed RT vs WBRT
 * Randomized. 708 patients. Tumor <4cm, SM-. No ALND. No systemic therapy. Randomized to tumor bed electron RT (Dose 40-42.5/8, majority 10 MeV, majority 8x6 cm field) or 4 field whole breast with regional LNs, no IMN (40/15). No adjuvant therapy
 * 8-years; 1996 PMID 8783398 -- "Prognostic factors for breast recurrence after conservative breast surgery and radiotherapy: results from a randomised trial." (Magee B, Radiother Oncol. 1996 Jun;39(3):223-7.)
 * Outcome: 8-year local recurrence tumor bed 25% vs. WBRT 13% (SS). Majority of recurrences within treated quadrant. 8-year DSS 72% vs 73% (NS). IDC 22% vs 12%; ILC 43% vs 17%. Axillary failure 24% vs 12% (SS), supraclav failure 6% vs 5%
 * Predictors for recurrence: field size, grade, LVI
 * Conclusion: Clear superiority for whole breast radiation therapy

Acute Dermatitis

 * Please see the Supportive Care/Acute Radiation Dermatitis randomized data page for further information

Hot Flashes

 * Please see the Supportive Care/Hot Flashes randomized data page for relevant studies

Exercise & Yoga

 * Please see the Supportive Care/Exercise randomized data page for relevant studies

Neoadjuvant chemotherapy

 * NSABP B-27 (1995-2000) - Preop AC alone vs Preop ACT vs. Preop AC + postop docetaxel
 * Randomized, 3 arms. 2353 women, only palpable disease allowed (breast or axilla). If primary breast, >1cm (T1c-T3N0-1); any size with axillary adenopathy (T1-3N1. Arm 1) Neoadjuvant AC x4 cycles vs. Arm 2) Neoadjuvant AC x4 then neoadjuvant docetaxel x4 vs. Arm 3) Neoadjuvant AC x4 followed by surgery then adjuvant docetaxel x4. Surgery was lumpectomy + ALDN or mastectomy. All pts received tamoxifen x 5 yrs regardless of ER/PR status. Measurement of tumor (by physical exam) prior to each chemo and before surgery. PMRT not permitted.
 * 8-years; 2008 PMID 18258986 -- "Preoperative chemotherapy: updates of National Surgical Adjuvant Breast and Bowel Project Protocols B-18 and B-27." (Rastogi P, J Clin Oncol. 2008 Feb 10;26(5):778-85.) Median F/U 8.5 years
 * Outcome: pCR AC (AC and AC-S-T) 13% vs. ACT 26% (SS); OS 5-year 82-83% (NS), 8-year 74-75% (NS); DFS 5-year 68-71% (NS); 8-year 59-62% (NS). Having pCR significant predictor for DFS and OS
 * Recurrence: IBTR AC 7% vs. ACT 6% vs. AC-S-T 5% (NS); chest wall 4% vs. 2% vs. 3% (NS); regional 3% vs. 2% vs. 3%. Overall taxotere regimens had (SS) fewer first local recurrences
 * Conclusion: Addition of docetaxel no impact on DFS or OS, improved pCR and first LF rate

 * NSABP B-18 (1988-1993) - neoadjuvant AC versus postop AC
 * Randomized. 1523 patients. T1-3N0-1 "operable, palpable, non-fixed" (Stage I-IIIA but no cN2 disease). Arm 1) ADJ: Surgery (lumpectomy + ALND or radical mastectomy) followed by 4 cycles doxorubicin and cyclophosphamide (AC) every 21 days, vs. Arm 2) NEO: Same chemotherapy neoadjuvantly, followed by surgery. Surgeons required to state intended surgical procedure at randomization. Tamoxifen x 5 years for age 50+, regardless of ER/PR. In NEO group, pts received breast and lymph node measurement by physical exam before each chemo cycle and before surgery. For lumpectomy group, XRT was given after surgery in the preop group and after chemo in the postop group. No PMRT allowed. cT1 ~30%, cN0 ~75%
 * 16-years; 2008 PMID 18258986 -- "Preoperative chemotherapy: updates of National Surgical Adjuvant Breast and Bowel Project Protocols B-18 and B-27." (Rastogi P, J Clin Oncol. 2008 Feb 10;26(5):778-85.) Median F/U 16 years
 * Outcome: Ability to undergo BCS NEO 68% vs. ADJ 60% (SS); pCR 13%; OS 5-year 81% vs. 80% (NS), 8-year both 72% (NS), 16-year both 55%; DFS 5-year both 67% (NS), 8-year 58% vs. 55 (NS), 16-year 42% vs. 39% (NS). Having pCR significant predictor for DFS and OS
 * By subset: age <50 trend for improved survival with neoadjuvant 16-years 61% vs. 55% (p=0.06); age >50 trend for improved survival with adjuvant 16-year 50% vs. 55% (p=0.07)
 * Recurrence: IBTR (only if lumpectomy) NEO 13% vs. 10% (NS); chest wall both 3% (NS); regional 4% vs. 5% (NS); contralateral 5% vs. 6% (NS)
 * Conclusion: Neoadjuvant chemotherapy comparable to adjuvant therapy, and may allow BCS for patients who may not otherwise be candidates

Hyperthermia

 * International Collaborative Hyperthermia Group (1988-1991) -- combined results from 5 PIII trials
 * Randomized. 5 trials merged due to slow accrual, closed early after benefit. 306 patients. Advanced primary or recurrent BCA; 50% active disease outside treatment area. Could have had prior RT. Trials: Dutch Hyperthermia Group (DHG), Medical Research Council (MRC BrI and BrR), European Society of Hyperthermic Oncology (ESHO), and Princes Margaret (PMH). Target hyperthermia 43C. RT given in various fractions.
 * 1996 PMID 8690639 -- "Radiotherapy with or without hyperthermia in the treatment of superficial localized breast cancer: results from five randomized controlled trials. International Collaborative Hyperthermia Group." (Vernon CC, Int J Radiat Oncol Biol Phys. 1996 Jul 1;35(4):731-44.)
 * Outcome: CR RT 41% vs. RT+HT 59% (SS); greatest effect in recurrent lesions in previous RT, where re-irradiation dose was low. 2-year OS ~40% (NS), 74% patients progressed outside HT area during follow-up
 * Conclusion: Combined result demonstrated efficacy of hyperthermia as adjunct to RT for treatment of recurrence

Palliative RT and Zoledronic Acid

 * Turkey (2003-2005) -- Zoledronic acid + RT 30/10 vs. Zoledronic acid + RT 15/5
 * Randomized. 100 patients, at least one bone metastasis, life expectancy >6 months. Excluded pathologic fractures, prior RT to that area, prior treatment with zoledronic acid, brain mets. Zoledronic acid 4 mg Q28 days, starting day 1 of RT. Used objective measure (MRI, bone scan) and subjective end points (pain, analgesic score, visual analog score)
 * 2009 PMID 19484483 -- "Zoledronic acid concurrent with either high- or reduced-dose palliative radiotherapy in the management of the breast cancer patients with bone metastases: a phase IV randomized clinical study." (Atahan L, Support Care Cancer. 2009 May 31. [Epub ahead of print]). Minimum F/U 6 months
 * Outcome: No difference in time-to-first skeletal event, rate of first-skeleta-event, time-to-response, rate of response, or duration of response. Higher satisfaction in shorter 15/5 arm
 * Conclusion: Concomitant use of zoledronic acid and RT safe

Erythropoietin

 * Canada; 2005 PMID 16087945 -- "Maintaining normal hemoglobin levels with epoetin alfa in mainly nonanemic patients with metastatic breast cancer receiving first-line chemotherapy: a survival study." (Leyland-Jones B, J Clin Oncol. 2005 Sep 1;23(25):5960-72. Epub 2005 Aug 8.)
 * Randomized. Stopped early due to adverse outcomes. 939 patients. Arm 1) placebo vs. Arm 2) Epo to maintain Hgb 12-14 g/dL, and initiated if Hgb <13 g/dL
 * Outcome: 1-year OS placebo 76% vs. Epo 70% (SS); no difference in tumor response
 * Conclusion: Epo use to maintain high Hgb was associated with decreased survival

title: Radiation Oncology/Breast/Randomized


text:
English for B2 Students/Unit 8

= The film had already started when we arrived =

Aim of this lesson: Learn about and use the Past Perfect and understand the difference between the tense and Past Simple. Vocabulary that will be taught is related to cinema.

Speaking about films
''Work with a partner, if you can, and ask/answer these questions. If you're on your own you should think about these questions and write your answers instead.''

 * What's your favourite kind of film?
 * What films have you seen this year?
 * Who is your favourite male or female actor?
 * What's the best film you've ever seen?
 * Do you prefer watching films at home or at the cinema?

Grammar - Past Perfect
Past perfect is used in English to indicate that an event occurred before another past event.

Further examples of past simple and past perfect

 * How many hours had you slept for when your alarm clock went off this morning?
 * My mother was angry because I had crashed her car.
 * She didn't realise that she had forgotten her credit card until she got to the cash machine.
 * I had only walked 100 metres when it started raining.

Vocabulary - Entertainment
Look at the table below. Do you know the correct definitions for this vocabulary related to cinema? Click on the 'show' button on the right for the correct answers.

Exercises
Try these questions to see if you know how to use past simple and past perfect correctly. The answers can be found here.

Complete the following sentences using the verb in brackets in the correct form:

 * 1) The burglars ____________ (escape) when the police __________ (arrive).
 * 2) When she __________ (arrive), the party ____________ (finish).
 * 3) When they __________ (get) to the hospital, she __________ (give) birth.
 * 4) Before we __________ (come) to London, we __________ (live) in 10 different cities.
 * 5) He __________ (be) on a plane, so he __________ (be) tired.

Grammar Reference
For further information about using past perfect and past simple see ../Tenses and Forms/.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: English for B2 Students/Unit 8


text:
English for B2 Students/Further Reading

What should you read in English?
By this stage you should be able to understand the main idea and key words of many articles. You will still have difficulty recognising and using many words but you should not let this prevent you from attempting to read in English. The following newspapers can be read online. Newspapers like The Guardian are considered to be broadsheet newspapers and articles are usually longer and may use more formal vocabulary. Newspapers like The Sun are tabloid newspapers and their articles are often shorter, with more pictures but they may use very informal language, idioms and phrasal verbs which may be a challenge for non-native speakers to read. English varies around the world so you should try to read articles from many different countries

 * Guardian Online (British)
 * The Independent (British)
 * The Sun (British)
 * Cape Times (South African)
 * Strait Times (Singaporean)
 * Washington Post (American)

title: English for B2 Students/Further Reading


text:
Cookbook:Yellow Split Pea Soup

Ingredients

 * 1 pound (½ kilogram) dry yellow split peas
 * 2 chicken or beef bouillon cubes
 * 1 small onion, chopped
 * 1 medium carrot, diced
 * 1 stalk celery, chopped
 * 6 cups (1½ liters) water
 * Salt and pepper to taste

Procedure

 * 1) Soak split peas up to six hours in cold water if you wish. This is not necessary, but will shorten cooking time.
 * 2) Put all ingredients into a 6 or 8 quart stock pot or Dutch oven
 * 3) Bring to a boil, then simmer covered until peas are tender, 1–2 hours.

Notes, tips, and variations

 * Watch water level and top up with hot water if necessary.
 * Croutons are good on top!

title: Cookbook:Yellow Split Pea Soup


text:
Cookbook:Water

Water is both added to food as an ingredient and used to transfer heat for cooking.

For both such purposes, the water should be generally drinkable. Water is a common source of disease organisms. Boiling water for about 5 minutes should take care of this problem. Baked goods containing water also need to be kept at a boiling temperature to prevent the spread of disease.

Water-based cooking methods include:

 * blanching
 * boiling
 * poaching
 * simmering
 * steaming

Water for fermenting
When adding water to a fermented food, it is generally best to use water with little or no chlorine. Chlorine is added to water to kill harmful microbes such as bacteria, and as such, can change how well a fermentation progresses, by slowing it down or even by ruining it.

Commercial yeast ferments like beer are not as sensitive to chlorine as yeast / bacteria ferments like sourdough, but often still benefit from chlorine-free water as it also affects the taste of the final product.

Chlorine can be removed from tap water by boiling for a few minutes and leaving to cool. Also, leaving uncovered overnight (e.g. in the refrigerator) will reduce chlorine. However, some water suppliers are now using the more stable chloramine instead, which cannot be boiled out and will remain stable in water for longer periods. Many water filters will remove both chlorine and chloramine.

Potable
Potable means "drinking" quality. Making water potable involves several steps.
 * 1) Remember, some contaminants cannot be removed except with a reverse osmosis filter, for example, heavy metals, or poisons that, in trace amounts, are still toxic, like dioxin.
 * 2) Gross physical contaminants should be removed, by pulling them out, coarse filtration with screens or sand, or settling in a quiet pond.
 * 3) Fine physical contaminants (haziness or cloudiness) may be removed by fine filtration, filtering through activated charcoal, or by settling with agents, such as diatomaceous earth.
 * 4) Biological purification should be performed on any natural water source on the surface. This may be chemical, with chlorine bleach or iodine (will stain clothing), or boiling for 5 minutes at an actively rolling boil.
 * 5) After boiling, the water often tastes flat, and this can usually be remedied by pouring the purified water from pan to pan (they must be clean!) for several minutes to put dissolved air back into the liquid.
 * 6) Distillation can often be used to make water potable but volatiles, such as petroleum products will usually distill along with the water. After distillation, the water will taste flat.

title: Cookbook:Water


text:
Cookbook:Pesto II

Pesto is a sauce which is added mainly, but by no means exclusively to pasta. Pesto is purely the Italian version of this delicious sauce, with other names for the same (or similar) sauce from other countries. Another famous national variant to pesto is pistou, which is the French equivalent.

Ingredients

 * High-quality olive oil
 * 1 packet of pine nuts or walnuts
 * 2 large plants worth of fresh basil
 * 7 garlic cloves
 * Freshly grated Parmesan cheese (not Pecorino)

Procedure

 * 1) Whatever you may have been told, use a electric blender or a liquidiser to make pesto. Faffing about with a pestle and mortar is for the birds.
 * 2) Again, whatever you have been told, put a good quantity of olive oil in the blender first and start it running, otherwise the blades will gum up and you risk burning the basil.
 * 3) Drop basil leaves through the top into the olive oil so that they are mulched up by the blades.
 * 4) Add some nuts so they are also mulched up.
 * 5) When the developing pesto sticks and becomes too thick, simply add more olive oil until the whole lot starts to mulch again. Continue adding basil leaves, nuts and the garlic cloves, always making sure the mixture remains fluid.
 * 6) Once you begin to run out of basil leaves and nuts, add a handful of Parmesan cheese (though not too much; remember the taste should be predominantly of basil). The end result should be a wondrous smelling, glutinous mass of green, which should be then emptied out of the blender into its own container.

Notes, tips and variations

 * If you like your pesto a little rough, add a small extra quantity of pine nuts and some grated Parmesan cheese to the finished pesto and mix in well. You're ready to go.
 * Fresh pesto can be stirred into pasta (penne in a good choice), added as a topping to crostini, or eaten, with eyes closed and a smile on your face, off a spoon, entirely on its own.
 * Greek olive oil is actually better for this recipe than either French or Italian as it has a stronger taste.
 * Pine nuts give the pesto a blander flavour, walnuts a more robust flavour.

title: Cookbook:Pesto II


text:
User:Wknight8111/monobook.js

//import_script('User:Whiteknight/gadgets.js'); //import_script('User:Whiteknight/pagetester.js'); import_script('User:Whiteknight/gadgetscore.js'); //import_script('User:Whiteknight/designer.js'); import_script('User:Whiteknight/bookpage.js'); import_script('User:Whiteknight/pageheading.js'); import_script('User:Whiteknight/designer3.js'); //import_script('User:Whiteknight/printversion.js'); import_script('User:Whiteknight/categorize.js'); //import_script('User:Whiteknight/remotetalk.js'); //import_script('User:Whiteknight/editinsert.js');

title: User:Wknight8111/monobook.js


text:
User:Whiteknight/Remotetalk Gadget

Remote Talk Gadget (Version 3.01)

Accessing the Gadget
Once you have installed the necessary javascript and properly configured it (see below), you can access the remote talk gadget by coming to this page or by transcluding this page into another page where you want it to appear (such as your user or user talk page). To do this, add this to the appropriate page:

How to Configure
To configure this gadget to look at the correct pages, you need to create a 2-D array named "Alias" to contain the parameters:

var Alias = new Array(  [LANG, PROJECT, USERNAME, LINKNAME],   [LANG, PROJECT, USERNAME, LINKNAME],   ...);

The LANG is the 2 or 3 letter language code (such as "en"). PROJECT is the name of the project using all lower-case letters. The URL is created by:

LANG.PROJECT.org

So if you want to make a link to a page at meta, you would say:

['meta', 'wikimedia', ...],

The USERNAME is your username on that project. LINKNAME is the words that you want to appear as the hyperlink. For instance, the following code: var Alias = new Array(  ['en', 'wikipedia', 'TimmyWikibookian', 'Me at Wikipedia'] ); import_script('User:Whiteknight/remotetalk2.js');

Will produce a link that says "Me At Wikipedia", and loads the page at en.wikipedia.org/wiki/User:TimmyWikibookian". If you leave one of the fields blank, or if you do not create an Alias array at all, defaults will be provided for you.

 * Note:I am working on an easier way to install the gadget. Future versions will hopefully be easier to install.

About this Gadget
This gadget is used to view the talk pages of multiple user accounts on other projects from a single location. It uses IFRAME elements for the page loads, instead of AJAX, so that the server can be remote. You must install the script and properly configure it before use.

To Do

 * Figure out why it doesnt work in safari

Version History

 * 3.01 Fixed for complete compatibility with IE
 * 3.00 Complete rewrite using new gadgets framework.
 * 2.00 Major rewrite, integrated into my gadgets framework, allowed default parameters for various fields.
 * 1.00 First stable version

title: User:Whiteknight/Remotetalk Gadget


text:
Chess Opening Theory/1. e4/1...b6

= 1. e4 b6 Owen's Defense=

1...b6
The Owen's Defence, named after John Owen, is a very rare and uncommon response to the King’s pawn game as white can easily control the center with 2. d4 and usually black fianchettos the dark-squared bishop, the Owen’s defence is still popular among club players and this opening can be transposed to an English opening or other lines.

White generally responds to Owen's Defence with 2. d4, preparing to take over the centre.

Theory table
1.e4 b6

title: Chess Opening Theory/1. e4/1...b6


text:
Template talk:German/Table

flags
The current flags (German, Austrian, Swiss) don't make much sense to me because the English translation isn't related to these flags. Moreover, in Switzerland you would always use "ss" instead of "ß". Moreover, the flags aren't used anywhere else; thus, maybe it's best to get rid of them. --Martin Kraus (talk) 08:27, 8 June 2010 (UTC)

title: Template talk:German/Table


text:
Gothic/2/Cases

What is a Case?
In the simplest terms, a case determines the function of a word in a sentence. Gothic has five cases: the nominative, genitive, dative, accusative, and vocative.
 * The Nominative Case indicates the subject of a sentence. Generally, the noun "that is doing something" is in the nominative. Example: The man went to the store.
 * The Genitive Case indicates an attributive relationship of one noun to the other noun, or in simpler terms, the genitive case indicates to whom an object belongs. Example: This is the man's store.
 * The Dative Case indicates the indirect object of a sentence. Example: The man gave the money to the storekeeper.
 * The Accusative Case indicates the direct object of a sentence or transitive verb. Example: The man bought food.
 * The Vocative Case is used when you directly talk to someone, for example: "My brother, listen to me!" or "My friend, go with me".

Certain Gothic verbs, pronouns, and adjectives must modify a case.

title: Gothic/2/Cases


text:
This Quantum World/Implications and applications/Why energy is quantized

< PREVIOUS

Why energy is quantized
Limiting ourselves again to one spatial dimension, we write the time independent Schrödinger equation in this form:

{d^2\psi(x)\over dx^2}=A(x)\,\psi(x),\qquad A(x)={2m\over\hbar^2}\Big[V(x)-E\Big]. $$ Since this equation contains no complex numbers except possibly $$\psi$$ itself, it has real solutions, and these are the ones in which we are interested. You will notice that if $$V>E,$$ then $$A$$ is positive and $$\psi(x)$$ has the same sign as its second derivative. This means that the graph of $$\psi(x)$$ curves upward above the $$x$$ axis and downward below it. Thus it cannot cross the axis. On the other hand, if $$V<E,$$ then $$A$$ is negative and $$\psi(x)$$ and its second derivative have opposite signs. In this case the graph of $$\psi(x)$$ curves downward above the $$x$$ axis and upward below it. As a result, the graph of $$\psi(x)$$ keeps crossing the axis — it is a wave. Moreover, the larger the difference $$E-V,$$ the larger the curvature of the graph; and the larger the curvature, the smaller the wavelength. In particle terms, the higher the kinetic energy, the higher the momentum.

Let us now find the solutions that describe a particle "trapped" in a potential well — a bound state. Consider this potential:

Observe, to begin with, that at $$x_1$$ and $$x_2,$$ where $$E=V,$$ the slope of $$\psi(x)$$ does not change since $$d^2\psi(x)/dx^2=0$$ at these points. This tells us that the probability of finding the particle cannot suddenly drop to zero at these points. It will therefore be possible to find the particle to the left of $$x_1$$ or to the right of $$x_2,$$ where classically it could not be. (A classical particle would oscillates back and forth between these points.)

Next, take into account that the probability distributions defined by $$\psi(x)$$ must be normalizable. For the graph of $$\psi(x)$$ this means that it must approach the $$x$$ axis asymptotically as $$x\rightarrow\pm\infty.$$

Suppose that we have a normalized solution for a particular value $$E.$$ If we increase or decrease the value of $$E,$$ the curvature of the graph of $$\psi(x)$$ between $$x_1$$ and $$x_2$$ increases or decreases. A small increase or decrease won't give us another solution: $$\psi(x)$$ won't vanish asymptotically for both positive and negative $$x.$$ To obtain another solution, we must increase $$E$$ by just the right amount to increase or decrease by one the number of wave nodes between the "classical" turning points $$x_1$$ and $$x_2$$ and to make $$\psi(x)$$ again vanish asymptotically in both directions.

The bottom line is that the energy of a bound particle — a particle "trapped" in a potential well — is quantized: only certain values $$E_k$$ yield solutions $$\psi_k(x)$$ of the time-independent Schrödinger equation:

NEXT >


text:
User talk:75.4.207.92

Hello, and welcome to Wikibooks! Please feel free to wander around and poke at things... but of course, constructively!

I am one of the editors over at the Muggle's Guide, and I note that you have been playing with the series timeline; and I wonder why you chose to put Riddle's application for the DADA teacher's job as late as you did. I'm not saying it's wrong, mind -- we have no information that I can see that would suggest either way when the application was... but I'm interested in why you chose the date you did. Would you be so kind as to go to the Discussion tab on the Timeline page and fill in something about your reasoning? Thank you very much... Chazz (talk) 06:28, 8 June 2007 (UTC)

title: User talk:75.4.207.92


text:
Logic for Computer Scientists/Predicate Logic/Herbrand Theories

Herbrand Theories
Until now we considered arbitrary interpretations of formulae in predicate logics. In particular we sometimes used numbers as interpretation domain and functions, like addition or successor. In the following, we will concentrate on a special case, the Herbrand interpretation and we will discuss their relation to the general case.

Definition 11
Let $$S$$ be a set of clauses. The Herbrand universe $$U_H$$ for $$S$$ is given by:
 * All constants which occur in $$S$$ are in $$U_H$$ (if no   constant appears in $$S$$, we assume a single constant, say $$a$$ to be in $$U_H$$).
 * For every $$n$$-ary function symbol $$f$$ in $$S$$ and every $$t_1, \cdots,t_n \in U_H $$, $$f(t_1, \cdots, t_n)\in U_H$$.

Examples: Given the clause set $$S_1 = \{ P(a),  \lnot P(x) \lor P(f(x))\}$$, we construct the Herbrand universe $$ U_H = \{ a, f(a), f(f(a)), f(f(f(a))), \cdots \} $$ For the clause set $$S_2 = \{ P(x)\lor Q(x), R(z)\}$$ we get the Herbrand universe $$U_H =\{a\}$$.

Definition 12
Let $$S$$ be a set of clauses. An interpretation $$\mathcal{I} = (U_\mathcal{I}, A_\mathcal{I})$$ is an Herbrand interpretation iff
 * $$U_\mathcal{I} = U_H$$
 * For every $$n$$-ary function symbol ($$n\geq 0$$) $$f$$ and $$t_1,  \cdots, t_n \in U_H$$  $$ f^\mathcal{I} (t_1, \cdots, t_n) =f(t_1,\cdots , t_n) $$

Note, that there is no restriction on the assignments of relations to predicate symbols (except, that, of course, they have  to be relations over the Herbrand universe $$U_H$$).

In order to discuss the interpretation of predicate symbols, we need the notion of Herbrand basis.

Definition 13
A ground atom or a ground term is an atom or a term without an occurrence of a variable. The Herbrand basis for a set of clauses $$S$$ is the set of ground atoms $$p(t_1, \ldots, t_n)$$, where $$p$$ is a $$n$$-ary predicate symbol from $$S$$ and $$t_1, \ldots, t_n \in U_H$$

We will notate the assignments of relations to predicate symbols by simply giving a set $$I = \{ m_1, m_2, \cdots, m_n, \cdots \}$$, where each element is a literal with its atom is from the Herbrand basis.

Examples:

 * $$S= \{p(x) \lor q(x), r(f(y))\} $$
 * $$U_H = \{ a, f(a), f(f(a)), \ldots\} $$
 * $$I = \{ p(a), q(a), r(a), p(f(a)), q(f(a)), r(f(a)), \cdots \} $$

Definition 14
Let $$\mathcal{I} =( U_\mathcal{I}, A_\mathcal{I} )$$ be an interpretation for a set of clauses $$S$$; the Herbrand interpretation $$\mathcal{I}^*$$ corresponding to $$\mathcal{I}$$ is a Herbrand interpretation satisfying the following condition: Let $$t_1,\ldots, t_n $$ be Elements from the Herbrand universe $$U_H$$ for $$S$$. By the interpretation $$\mathcal{I}$$ every $$t_i$$ is mapped to a $$d_i \in U_\mathcal{I}$$. If $$p^\mathcal{I}(d_1, \ldots, d_n) = true (false)$$, then $$p(t_1, \ldots, t_n) $$ have to be assigned $$true (false)$$ in $$\mathcal{I}^*$$.

Let us now state a simple, very obvious lemma, which will help us, to focus on Herbrand interpretation in the following.

Lemma 4
If $$\mathcal{I} $$ is a model for a set of clauses, then every corresponding Herbrand interpretation $$\mathcal{I}^*$$ is a model for $$S$$

Theorem 4
A set of clauses $$S$$ is unsatisfiable iff there is no Herbrand model for $$S$$.

Proof: If $$S$$ is unsatisfiable, there is obviously no Herbrand model for $$S$$. Assume that there is no Herbrand model for $$S$$ and that $$S$$ is satisfiable. Then, there is a model $$\mathcal{I}$$ for $$S$$ and according to lemma 4 the corresponding Herbrand interpretation $$\mathcal{I}^*$$ is a model for $$S$$, which is a contradiction.


text:
Logic for Computer Scientists/Predicate Logic/Semantic Trees

Semantic Trees
In this section we introduce the concept of semantic trees, which then can be used to proof completeness of resolution. For this we assume familiarity with the concepts of trees, binary trees and paths in trees.

Definition 15
A semantic tree for a set of clauses $$S$$ is a binary tree $$T$$ with root $$N_0$$, such that the edges are label with literals, built from elements from the Herbrand basis of $$S$$, such that:
 * If $$N$$ is an inner node, its two outgoing edges are label with complementary literals $$A$$ and $$\lnot A$$.
 * Every path to a node  $$N$$  in $$T$$ does not contain  complementary literals in $$I(N)$$, where $$I(N)$$ is the set of   literals which are labels  along the edges of the path.

Definition 16
A semantic tree is called complete, if every path contains every atom from the Herbrand basis either positive or negative.

Example: $$S = \{ p(x), q(f(x))\} $$ with Herbrand basis $$ \{p(a), q(a), p(f(a)), q(f(a)), p(f(f(a))), \ldots\} $$ Note, that for a semantic tree $$T$$ and a node $$N$$ the set $$I(N)$$ can be seen as an assignment of truth-values to ground atoms, as it is done in an Herbrand interpretation. Hence we call $$I(N)$$ a partial interpretation. A complete semantic tree corresponds to an exhaustive "enumeration" of interpretations.

Definition 17

 * A node $$N$$ of a semantic tree $$T$$ is a failure node if $$I(N)$$ falsifies some ground instance of a clause in $$S$$, but $$I(N')$$  does not falsifiy any ground instance of a clause in $$S$$ for every ancestor node $$N'$$ of $$N$$.
 * A semantic tree $$T$$ is called closed if every path contains a failure node.
 * A node $$N$$ of a closed semantic tree is called an inference node, if both immediate descendant nodes are failure nodes.

Example: $$S = \{ p(x), \lnot p(x) \lor q(f(x)), \lnot q(f(a))\} $$ with Herbrand basis $$\{ p(a), q(a), p(f(a)), q(f(a)), p(f(f(a))), \ldots\} $$

Let $$T$$ be a complete semantic tree, than we call $$T'$$ the corresponding closed tree, if it is obtainable from $$T$$ by cutting all branches at a failure node.

Theorem 5 (Herbrand's Theorem - Version 1)
A set $$S$$ of clauses is unsatisfiable, iff for every complete semantic tree for $$S$$ there is a corresponding finite closed semantic tree.

Proof: Assume $$S$$ to be unsatisfiable and $$T$$ a complete semantic tree for $$S$$. For every path $$P$$ we have the set of labels $$I_B$$, which is an interpretation, because the tree is complete. Hence, $$I_B$$ falsifies a ground instance $$C'$$ of a clause $$C \in S$$, because $$S$$ is unsatisfiable. Since there are only finitely many literals in $$C'$$, there must be a failure node $$N_B$$ in a finite distance from the root. Since every path has such a failure node, there is a corresponding closed semantic tree $$T'$$, which is finite.

For the opposite direction, assume that for every complete semantic tree $$T$$ there is a finite closed corresponding tree $$T'$$. Then, every path contains a failure node, and hence, every interpretation falsifies $$S$$; hence $$S$$ is unsatisfiable.

Theorem 6 (Herbrand's Theorem - Version 2)
A set $$S$$ of clauses is unsatisfiable, iff there is a finite unsatisfiable set $$S'$$ of ground instances of clauses in $$S$$.

Proof: Assume $$S$$ to be unsatisfiable and $$T$$ a complete semantic tree for $$S$$. By Herbrand's theorem, version 1, there is a finite closed semantic tree $$T'$$ for $$S$$. Let $$S'$$ be the set of ground instances of clauses, which are falsified at all failure nodes of $$T'$$. $$S'$$ is finite and is falsified by every interpretation and hence unsatisfiable. The opposite direction we show by contraposition:

Note, that this version of Herbrand's theorem can be turned directly into a proof procedure: Given a set of clauses $$S$$, for which we want to proof unsatisfiability.

 * Generate $$S_1', \ldots, S_n', \ldots $$ sets of ground instances of clauses of $$S$$. Perform a propositional test for unsatisfiability  on each of them.
 * According to Herbrand's theorem, there is a finite $$S_N'$$ which is unsatisfiable, if $$S$$ is unsatisfiable.

Problem 10 (Predicate)
Assume the following set of clauses: $$ M_0 = \{ \{p(x)\}, \{q(x,f(x)),\lnot p(x)\},\{\lnot q(g(y),z)\} \} $$ $$\Box$$
 * 1) Indicate (a) the Herbrand-universe and (b) the Herbrand-basis for $$M_0$$!
 * 2) Give a closed semantic tree for $$M_0$$!

Problem 11 (Predicate)
The following formulae $$F$$ and $$G$$ are given. $$ F =  \forall y  p(y) \land \exists z  \lnot p(z)$$ $$ G =  r(a) \land \forall x (r(x) \to r(f(x))) $$

Give for $$F$$ and $$G$$ (a) a finate and (b) an infinite Herbrand model, or argument if this  is not possible. $$\Box$$

Problem 12 (Predicate)
The following sets of clauses are  given: Give for each of them (a) a Herbrand universe, (b)  Herbrand model and (c) a non-Herbrand model. $$\Box$$
 * 1) $$M_1 = \big\{ \{ p(a,x) \}, \{ \lnot p(y,b), q(y) \} \big\}$$
 * 2) $$M_2 = \big\{ \{ r(x), r(f(x)) \} \big\}$$


text:
This Quantum World/Implications and applications/A quantum bouncing ball

< PREVIOUS

A quantum bouncing ball
As a specific example, consider the following potential:

V(z)=mgz\quad\hbox{if}\quad z>0\quad\hbox{and}\quad V(z)=\infty\quad\hbox{if}\quad z<0. $$ $$g$$ is the gravitational acceleration at the floor. For $$z<0,$$ the Schrödinger equation as given in the previous section tells us that $$d^2\psi(z)/dz^2=\infty$$ unless $$\psi(z)=0.$$ The only sensible solution for negative $$z$$ is therefore $$\psi(z)=0.$$ The requirement that $$V(z)=\infty$$ for $$z<0$$ ensures that our perfectly elastic, frictionless quantum bouncer won't be found below the floor.

Since a picture is worth more than a thousand words, we won't solve the time-independent Schrödinger equation for this particular potential but merely plot its first eight solutions:

Where would a classical bouncing ball subject to the same potential reverse its direction of motion? Observe the correlation between position and momentum (wavenumber).

All of these states are stationary; the probability of finding the quantum bouncer in any particular interval of the $$z$$ axis is independent of time. So how do we get it to move?

Recall that any linear combination of solutions of the Schrödinger equation is another solution. Consider this linear combination of two stationary states:

\psi(t,x)=A\,\psi_1(x)\,e^{-i\omega_1t}+B\,\psi_2(x)\,e^{-i\omega_2t}. $$ Assuming that the coefficients $$A,B$$ and the wave functions $$\psi_1(x),\psi_2(x)$$ are real, we calculate the mean position of a particle associated with $$\psi(t,x)$$:

\int\!dx\,\psi^*x\psi=\int\!dx\,(A\psi_1e^{i\omega_1t}+B\psi_2e^{i\omega_2t})\,x\,(A\psi_1e^{-i\omega_1t}+B\psi_2e^{-i\omega_2t})$$
 * $$=A^2\int\!dx\,\psi_1^2\,x+B^2\int\!dx\,\psi_2^2\,x+AB(e^{i(\omega_1-\omega_2)t}+e^{i(\omega_2-\omega_1)t})\int\!dx\,\psi_1x\psi_2.

$$ The first two integrals are the (time-independent) mean positions of a particle associated with $$\psi_1(x)\,e^{i\omega_1t}$$ and $$\psi_2(x)\,e^{i\omega_2t},$$ respectively. The last term equals

2AB\cos(\Delta\omega\,t)\int\!dx\,\psi_1x\psi_2, $$ and this tells us that the particle's mean position oscillates with frequency $$\Delta\omega= \omega_2-\omega_1$$ and amplitude $$2AB\int\!dx\,\psi_1x\psi_2$$ about the sum of the first two terms.

Visit this site to watch the time-dependence of the probability distribution associated with a quantum bouncer that is initially associated with a Gaussian distribution.

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text:
Logic for Computer Scientists/Predicate Logic/Resolution

Resolution
In the propositional case we defined the resolution inference rule by "cutting away" a pair of complementary literals in two clauses which are resolved upon. In the first order case however this is not always sufficient: $$\begin{matrix} C_1: & p(x) \lor q(x) \\

C_2: & \lnot p(f(x)) \end{matrix}$$ In these two clauses there are no complementary literals, however, after substituting the term $$f(a)$$ for the variable $$x$$ in $$C_1$$ and $$a$$ for $$x$$ in $$C_2$$ we arrive at: $$\begin{matrix} C_1': & p(f(a)) \lor q(f(a)) \\

C_2': & \lnot p(f(a)) \end{matrix}$$ Now we can apply the inference rule from propositional logic and arrive at the resolvent $$q(f(a))$$.

Another possibility is to substitute $$f(x')$$ for $$x$$ in $$C_1$$ to get $$ C_1'': p(f(x')) \lor q(f(x')) $$ and then we can have the resolvent $$q(f(x'))$$ from $$C_1''$$ and $$C_2$$, which is in a certain sense more general then the resolvent derived previously.

Definition 18
A substitution $$\sigma$$ is a function, which maps variables to terms and which is the identical mapping almost everywhere. Hence it can be represented as $$\sigma =\{x_1 / t_1, \cdots, x_n / t_n\}$$ If $$t_1, \cdots, t_n$$ are groundterms, we call $$\sigma$$ a ground substitution. The empty substitution is notated by $$\epsilon$$.

Definition 19
Let $$\theta = \{ x_1 / t_1, \cdots, x_n / t_n\}$$ be a substitution and $$E$$ an expression (i.e. a literal or a term), then $$E\theta$$ is the expression, obtained from $$E$$ by replacing simultaneously each occurrence of $$X_i, 1 \leq i \leq n$$ in $$E$$ by the term $$t_i$$.

Example: With $$\theta = \{ x/a, y/f(b), z/e\}$$  and $$E = p(x, y, z)$$, we get $$E\theta = p(a,f(b),c)$$

Definition 20
Let $$\sigma = \{ x_1 / t_1, \cdots, x_n / t_n\}$$ and $$ \lambda = \{ y_1/s_1,\cdots , y_m/s_m\}$$ be substitutions. Then the composition of substitutions, denoted by $$ \sigma \circ \lambda $$, is the substitution, which is obtained from $$ \{ x_1 / t_1 \lambda, \cdots,x_n / t_n \lambda, y_1/s_1,\cdots, y_m/s_m \}$$ by deleting any element $$x_j/t_j \lambda$$ for which $$ t_j \lambda = x_j$$ and any element $$y_i/s_i$$ such that $$y_i \in\{ x_1, \cdots, x_n\}$$. Example:

Definition 21
Let $$ \{E_1, \cdots, E_n\}$$ be a set of expressions and $$\theta$$ a substitution, $$\theta$$ is unifier for  $$ \{E_1, \cdots, E_n\}$$ iff $$E_1\theta = E_2\theta = \cdots E_n\theta $$.

A unifier $$\theta$$ is called most general unifier iff for every unifier $$\sigma$$ there is a substitution $$\lambda$$ such that $$ \sigma = \theta \circ \lambda$$.

In the following we discuss an algorithm for computing most general unifiers. For this we assume a set of terms  $$ \{t_1, \cdots, t_n\}$$ to be unified. First we transform this into a set of equations by introducing a new variable not yet occurring in this set, say $$y$$ and by defining the set of equations $$N = \{ y = t_1, \cdots, y = t_n\} $$ We will now transform this set such that its unifiers stay invariant, where a $$\sigma$$ is a unifier of a set of $$ \{s_1 = t_1, \cdots, s_n = t_n\}$$ if $$ \{s_1 \sigma = t_1 \sigma, \cdots , s_n\sigma  = t_n\sigma \}$$ holds.

Theorem 7
Let $$N$$ be a set of expressions. The above unification algorithm terminates. If it returns $$FAIL$$, there is no unifier for $$N$$, otherwise $$N$$ is transformed into a set of equation  $$\{y_1 = u_1, \cdots, y_m = u_m\}$$, which represents the most general unifier for $$N$$.

Definition 22
Let two or more literals of a clause $$C$$ have a unifier $$\sigma$$, then $$C\sigma$$ is called a factor of $$C$$. Example: With $$ C= \{p(x), p(f(y)), \lnot q(x)\}$$ and $$\sigma = \{ x/f(y)\}$$ we get the factor $$C\sigma = \{p(f(y)), \lnot q(f(y))\}$$

Definition 23
Let $$C_1$$ and $$C_2$$ be two clauses with no variables in common, such that $$L_1 \in C_1$$ and $$L_2 \in C_2$$ and $$L_1$$ and $$L_2$$ have a most general unifier $$\sigma$$. A binary resolvent of $$C_1$$ and $$C_2$$ is $$ (C_1\sigma - L_1\sigma) \cup (C_2 \sigma - L_2\sigma) $$ Example: Given $$C_1 = \{ p(x), q(x)\}$$ and $$C_2 = \{\lnot p(a),r(x)\}$$. After renaming $$C_2$$ into $$C_2 = \{\lnot p(a), r(y)\}$$ we get the resolvent $$\{q(a), r(y)\}$$ by using the most general unifier $$\{x/a\} $$.

We often depict resolvent graphically, e.g.

Definition 24
A resolvent of two clauses $$C_1$$ and $$C_2$$ is one of the following binary resolvents: Example: Given $$C_1 = \{ p(x), p(f(y)), r(g(y))\}$$ and $$C_2 = \{\lnot p(f(g(a))),q(b)\}$$.
 * a binary resolvent of $$C_1$$ and $$C_2$$
 * a binary resolvent of $$C_1$$ and a factor of $$C_2$$
 * a binary resolvent of a factor of $$C_1$$ and $$C_2$$
 * a binary resolvent of a factor of $$C_1$$ and a factor of $$C_2$$

A factor of $$C_1$$ is $$C_1\prime = \{p(f(y)), r(g(y))\}$$. A binary resolvent of $$C_1\prime$$ and $$C_2$$ and hence also of $$C_1$$ and $$C_2$$ is $$C_3 = \{ r(g(g(a))), q(b)\} $$. The following lemma is used in the completeness proof of resolution.

Lemma 5 (Lifting lemma)
If $$C'_1$$ and $$C'_2$$ are instances of $$C_1$$ and $$C_2$$, respectively, and $$C'$$ is a resolvent of $$C'_1$$ and $$C'_2$$, then there is a resolvent $$C$$ of $$C_1$$ and $$C_2$$ such that $$C'$$ is an instance of $$C$$. Figure 1

Theorem 8
A set $$S$$ of clauses is unsatisfiable iff the empty clause can be derived from $$S$$ by resolution. Proof: Assume that $$S$$ is unsatisfiable. Let $$A = \{ A_1,A_2, \ldots\}$$ be the ground atom set of $$S$$, hence the Herbrand basis. Let $$T$$ be a complete binary tree, as given in Figure 2. According to Herbrand's theorem (version1) there exists a closed finite semantic tree $$T'$$. There are two cases: I(N) & =& \{m_1, m_2, \ldots, m_n\} I(N_1) & =& \{m_1, m_2, \ldots, m_n, m_n, m_{n+1}\} I(N_2) & =&  \{m_1, m_2, \ldots, m_n, m_n, \lnot m_{n+1}\} \end{matrix}$$ Now, let $$C_1'$$ and $$C_2'$$ be ground instances of clauses $$C_1$$ and $$C_2$$, such that $$C_1'$$ is falsified by $$I(N_1)$$ and $$C_2'$$  by $$I(N_2)$$, such that both are not falsified by $$I(N)$$. Hence we have $$\lnot m_{n+1} \in C_1'$$ and $$ m_{n+1} \in C_2'$$ and we can construct the resolvent $$ C' = (C_1' - \{ \lnot m_{n+1}\} ) \cup (C_2' - \{ m_{n+1}\} ) $$ $$C'$$ must be false in $$I(N)$$, because both $$(C_1' - \lnot m_{n+1})$$ and $$(C_2' - m_{n+1})$$ are false in $$I(N)$$. According to the Lifting Lemma 5 there exists a resolvent $$C$$ of $$C_1$$ and  $$C_2$$, such that $$C'$$ is a ground instance of $$C$$. Let $$T \; '' $$ be the closed semantic tree for $$ S \cup \{ C\} $$, obtained from $$T'$$ by deleting all nodes below the first node which falsifies $$C'$$. Note, that $$S$$ is unsatisfiable if and only if $$S \cup \{ C\} $$ is unsatisfiable. Clearly, $$T \; ''$$ has less nodes than $$T'$$ and we now can iterate this process until only the root of the semantic tree is remaining. This, however is only possible if the empty clause $$\square$$ is derivable. For the opposite direction, assume that $$\square$$ is derivable by resolution from $$S$$ and let $$R_1, \ldots, R_k$$ the resolvents constructed during this process. Assume $$S$$ is satisfiable and $$M$$ to be a model for $$S$$. From the correctness lemma according to the propositional case we known, that if a model satisfies two clauses it also satisfies its resolvent. Therefore $$M$$ has to satisfy $$R1, \ldots, R_k$$; this, however, is impossible, because one of this resolvents is $$\square$$. Figure 2
 * If $$T'$$ consists only of one node (hence the root), The interpretation to be collected from the empty branch in this tree falsifies only the empty clause. Hence the empty clause must be in $$S$$.
 * Assume $$T'$$ consists of more than one node. Then there must be an inference node $$N$$ in $$T'$$, hence both its descendants  $$N_1$$ and $$N_2$$ are failure nodes. If such a node would not exist, every node would have at least one non-failure node, which would mean that there is at least an infinite path in $$T'$$, which   would violate, that fact that it is a finite closed semantic tree.   Let $$N, N_1, N_2$$ given as described above; and let $$\begin{matrix}

Problem 14 (Predicate)
Indicate in each case a derivation of the empty clause with predicate-logical resolution! $$\Box$$
 * 1) $$\{ \{p(x,0,x)\}, \{p(x,s(y),s(z)),\lnot p(x,y,z)\}, \{\lnot p(s(s(s(0))),s(s(0)),u)\}\}$$
 * 2) $$\{\{q(x),q(s(x))\},\{\lnot q(x),\lnot q(s(s(x)))\}\}$$ ($$\star$$)
 * 3) $$\{ \{\lnot r(x,f(x),y),\lnot r(x,g(y),z)\},\{r(c,u,i(v)),r(h(u),v,j(v))\} \}$$

Problem 15 (Predicate)
Show the following Lifting lemma by means of induction over the term- and formula construction: Is $$F$$ a predicate-logical formula, and $$\mathcal{I}$$ a fitting interpretation for $$F$$ and $$F[x/t]$$. Then $$ \mathcal{I}(F[x/t]) = \mathcal{I}_{[x/\mathcal{I}(t)]}(F), $$ is valid, if $$t$$ does not contain any variable that $$[x/t]$$ is laced by the substitution in $$F$$. $$\Box$$

Problem 16 (Predicate)
Compute - if possible - the most general unifier of following sets of clauses: $$\Box$$
 * 1) $$\{p(x,a),p(f(c),y)\}$$
 * 2) $$\{p(f(x),a,x),p(y,z,z)\}$$
 * 3) $$\{q(x,x),q(g(y),y)\}$$
 * 4) $$\{r(x,x),r(a,h(y))\}$$

Problem 17 (Predicate)
Determine all direct resolvents of the following pairs of clauses: $$\Box$$
 * 1) $$\{\lnot p(x), q(x,b)\}$$ and $$\{p(a), q(a,b)\}$$
 * 2) $$\{p(x), p(f(x))\}$$ and $$\{\lnot p(x), \lnot p(f(f(x)))\}$$
 * 3) $$\{\lnot q(c,g(c))\}$$ and $$\{\lnot p(x), q(x,x)\}$$
 * 4) $$\{\lnot p(x,y,z), \lnot p(y,u,v), \lnot p(x,v,w), p(z,u,w)\}$$ and $$\{p(g(x,y),x,y)\}$$

Problem 18 (Predicate)
Compute - if possible - the most general unifier of following sets of clauses: $$\Box$$
 * 1) $$\{o(x,x),o(a,f(y))\}$$
 * 2) $$\{p(x,a),p(f(c),y)\}$$
 * 3) $$\{q(g(x),a,x),q(y,z,z)\}$$
 * 4) $$\{r(x,x),r(h(y),y)\}$$

Problem 19 (Predicate)
Determine all direct resolvents of the following pairs of clauses: $$\Box$$
 * 1) $$\{\lnot p(x),\lnot p(b), q(x,b)\}$$ and $$\{p(a), q(a,b)\}$$
 * 2) $$\{r(x), r(f(x))\}$$ and $$\{\lnot r(x),\lnot r(f(f(x)))\}$$
 * 3) $$\{\lnot s(c,g(c))\}$$ and $$\{s(x,x), \lnot t(x)\}$$

Problem 20 (Predicate)
Give for the following set of clauses (a) a linear derivation, (b) a derivation with unit resolution, (c) a further (maximally short) derivation of the empty clause by means of predicate-logical resolution! $$ \{ \{\lnot e(x),o(s(x))\},\{\lnot e(x),\lnot o(s(x)),e(s(s(x)))\},\{e(a)\},\{\lnot o(s(s(s(s(s(a))))))\}\} $$ $$\Box$$

Problem 21 (Predicate)
Indicate in each case a derivation of the empty clause with predicate-logical resolution! $$\Box$$
 * 1) $$\{ \{p(x,0,x)\}, \{p(x,s(y),s(z)),\lnot p(x,y,z)\},\{\lnot p(s(s(s(0))),s(s(0)),u)\}\}$$
 * 2) $$\{\{q(x),q(s(x))\},\{\lnot q(x),\lnot q(s(s(x)))\}\}$$ ($$\star$$)
 * 3) $$\{ \{\lnot r(x,f(x),y),\lnot r(x,g(y),z)\},\{r(c,u,i(v)),r(h(u),v,j(v))\} \}$$


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AP Chemistry/Solutions

Molarity versus Molality

 * Molarity (M) - moles of solute per liter of solution.
 * Molality (m) - moles of solute per kilogram of solvent.

Solubility Rules
These will NOT be given to you on the test. You must memorize them.
 * 1) Compounds with Group 1 elements are soluble or the ammonium ion are soluble.
 * 2) Nitrates, acetates, chlorates, and perchlorates are soluble.
 * 3) Chlorides, bromides, and iodides are generally soluble, unless they contain copper, silver, lead, or mercury.
 * 4) Sulfates are soluble, unless they contain barium, lead, silver, strontium, or calcium.
 * 5) Most silver salts are insoluble unless listed in rule #2.
 * 6) Most hydroxide salts are insoluble unless stated in rule #1 or contain calcium, strontium, or barium.
 * 7) Most sulfides are insoluble unless stated in rule #1, or contain Group 2 elements.
 * 8) Carbonates and phosphates are insoluble unless listed in rule #1.

Forgot Your Polyatomic Ions?

 * Ammonium -
 * Nitrate -
 * Acetate -
 * Chlorate -
 * Perchlorate -
 * Sulfate -
 * Carbonate -
 * Phosphate -

Solubility

 * Solids are more soluble when they are warm, but gases are the opposite.
 * Supersaturated solutions will settle if disturbed.

Colligative Properties
Colligative properties are properties of solutions that depend on the amount of solute particles present rather than the identity of the particles.
 * Vapor pressure lowering
 * Freezing point depression and boiling point elevation (molality)
 * Osmotic pressure

Not Solutions

 * Colloids look "milky" when light is passed through them (Tyndall Effect)
 * Suspensions settle if left long enough, and also look milky.

title: AP Chemistry/Solutions


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