Computer algebra for x-ray spectral reconstruction between 6 and 25 MV

A previously presented algorithm for the reconstruction of bremsstrahlung spectra from transmission data has been implemented into MATHEMATICA. Spectra vectorial algebra has been used to solve the matrix system A * F = T. The new implementation has been tested by reconstructing photon spectra from transmission data acquired in narrow beam conditions, for nominal energies of 6, 15, and 25 MV. The results were in excellent agreement with the original calculations. Our implementation has the advantage to be based on a well-tested mathematical kernel. Furthermore it offers a comfortable user interface.

Accelerated partial breast irradiation with interstitial brachytherapy as second conservative treatment for ipsilateral breast tumour recurrence: multicentric study of the GEC-ESTRO Breast Cancer Working Group

PURPOSE To analyse the clinical outcome after salvage lumpectomy and multi-catheter brachytherapy (MCB) for ipsilateral breast tumour recurrence (IBTR). MATERIAL AND METHODS Between 09/00 and 09/10, 217 patients presenting an IBTR underwent lumpectomy and MCB (low, pulsed, or high-dose rate). Survival rates without second local recurrence (2nd LR), distant metastasis (DM), and overall survival (OS) were analysed as well as late effects and cosmetic results. Univariate and multivariate analyses (MVA) based on IBTR data were performed to find prognostic factors for 2nd LR, DM, and OS. RESULTS Median follow-up after the IBTR was 3.9 years [range: 1.1-10.3]. Five and 10-year actuarial 2nd LR rates were 5.6% [range: 1.5-9.5] and 7.2% [range: 2.1-12.1], respectively. Five and 10-year actuarial DM rates were 9.6% [range: 5.7-15.2] and 19.1% [range: 7.8-28.3], respectively. Five and 10-year actuarial OS rates were 88.7% [range: 83.1-94.8] and 76.4% [range: 66.9-87.3], respectively. In MVA, histological grade was prognostic factor for 2nd LR (p=0.008) and OS (p=0.02); while tumour size was prognostic factor for DM (p=0.03). G3-4 complication rate was 11%. Excellent/good cosmetic result was achieved in 85%. CONCLUSION This study suggests that in case of IBTR, lumpectomy plus MCB is feasible and effective in preventing 2nd LR with an OS rate at least equivalent to those achieved with salvage mastectomy.

A feasible theory of truth over combinatory algebra

We define an applicative theory of truth TPT which proves totality exactly for the polynomial time computable functions. TPT has natural and simple axioms since nearly all its truth axioms are standard for truth theories over an applicative framework. The only exception is the axiom dealing with the word predicate. The truth predicate can only reflect elementhood in the words for terms that have smaller length than a given word. This makes it possible to achieve the very low proof-theoretic strength. Truth induction can be allowed without any constraints. For these reasons the system TPT has the high expressive power one expects from truth theories. It allows embeddings of feasible systems of explicit mathematics and bounded arithmetic. The proof that the theory TPT is feasible is not easy. It is not possible to apply a standard realisation approach. For this reason we develop a new realisation approach whose realisation functions work on directed acyclic graphs. In this way, we can express and manipulate realisation information more efficiently.

Algebra of Classical Theoretical Term Reductions in the Sciences

An elementary algebra identifies conceptual and corresponding applicational limitations in John Kemeny and Paul Oppenheim’s (K-O) 1956 model of theoretical reduction in the sciences. The K-O model was once widely accepted, at least in spirit, but seems afterward to have been discredited, or in any event superceeded. Today, the K-O reduction model is seldom mentioned, except to clarify when a reduction in the Kemeny-Oppenheim sense is not intended. The present essay takes a fresh look at the basic mathematics of K-O comparative vocabulary theoretical term reductions, from historical and philosophical standpoints, as a contribution to the history of the philosophy of science. The K-O theoretical reduction model qualifies a theory replacement as a successful reduction when preconditions of explanatory adequacy and comparable systematicization are met, and there occur fewer numbers of theoretical terms identified as replicable syntax types in the most economical statement of a theory’s putative propositional truths, as compared with the theoretical term count for the theory it replaces. The challenge to the historical model developed here, to help explain its scope and limitations, involves the potential for equivocal theoretical meanings of multiple theoretical term tokens of the same syntactical type.

Recommendations from GEC ESTRO Breast Cancer Working Group (I): Target definition and target delineation for accelerated or boost Partial Breast Irradiation using multicatheter interstitial brachytherapy after breast conserving closed cavity surgery

OBJECTIVE The aim was to develop a delineation guideline for target definition for APBI or boost by consensus of the Breast Working Group of GEC-ESTRO. PROPOSED RECOMMENDATIONS Appropriate delineation of CTV (PTV) with low inter- and intra-observer variability in clinical practice is complex and needs various steps as: (1) Detailed knowledge of primary surgical procedure, of all details of pathology, as well as of preoperative imaging. (2) Definition of tumour localization before breast conserving surgery inside the breast and translation of this information in the postoperative CT imaging data set. (3) Calculation of the size of total safety margins. The size should be at least 2 cm. (4) Definition of the target. (5) Delineation of the target according to defined rules. CONCLUSION Providing guidelines based on the consensus of a group of experts should make it possible to achieve a reproducible and consistent definition of CTV (PTV) for Accelerated Partial Breast Irradiation (APBI) or boost irradiation after breast conserving closed cavity surgery, and helps to define it after selected cases of oncoplastic surgery.