Abstract:
Objectives. The “Sick Lobe” hypothesis states that breast cancers evolve from entire lobes or portions of lobes of the breast where initiation events have occurred early in development. The implication is that some cancers are isolated events and others are truly multi-focal but limited to single lobar-ductal units. Methods. This is a single surgeon retrospective review of early stage breast cancer lumpectomy patients treated from 1/2000 to 2/2005. Ductal endoscopy was used direct lumpectomy surgical margins by defining ductal anatomy and mapping proliferative changes within the sick lobe for complete excision. Results. Breast conservation surgery for stage 0–2 breast cancer with an attempt to perform endoscopy in association with therapeutic lumpectomy was performed in 554 patients (successful endoscopy in 465 cases). With an average followup of >5 years for the entire group, annual hazard rate for local failure in traditional lumpectomy without ductal mapping was 0.97%/yr. and for lumpectomy with ductal mapping and excision of entire sick lobe was 0.18%/yr. With endoscopy, 42% of patients were found to have extensive disease within their “sick lobe.” Conclusions. Targeting breast cancer lumpectomy using endoscopy and excision of regional associated proliferation seems associated with lower recurrence in this non-randomized series. 1. Introduction The “Sick Lobe” hypothesis was proposed by Tibor Tot in 2005 [1]. His work was really a culmination of collecting relevant clinical and pathologic observations of the last century and a half. His first observations and predictions were based upon DCIS. The breast is defined as a single organ made of multiple lobes. Each lobe is identified by a single orifice on the nipple papilla connecting to branching tree of ducts and hundreds to thousands of individual lobules in the periphery. He proposed that for many cases of DCIS (especially extensive ones) the initiating events of carcinogenesis occurred perhaps as early as in the womb. Then throughout life as the lobe both grew and contracted from hormonal and other influences progression would occur at varying rates in different regions of the ductal tree. This led to the situation of apparent multifocality within the ductal tree and pathologic “skips” between DCIS patches. With further whole mount examination, extensive dissection of extensive intraductal component small invasive cancer cases, and multifocal invasive cancers, the findings support this theory [2–7]. Further molecular studies would seem to indicate that serious adverse genetic events are present

Abstract:
This article argues that nagid indicates divinely sanctioned leader of Israel in 1 Samuel 9:1-10:16 and 11:1-11. The use of nagid is intricately interplayed with that of melek in the context of 1 Samuel 8-12. In the Saul tradition (1 Sm 9:1-10:16; 11:1-11) nagid signifies the leadership of Saul as a divinely sanctioned kingship, unlike in the context of the Deuteronomistic History (DH). The royal ideology of the ancient Near East (ANE) provides an ideological background of the kingship of Saul.

Abstract:
We construct a new cohomology functor from the a certain category of {\it quantum operator algebras} to the category of {\it Batalin-Vilkovisky algebras}. This {\it Moonshine cohomology} has, as a group of natural automorphisms, the Fischer-Griess Monster finite group. We prove a general vanishing theorem for this cohomology. For a certain commutative QOA attached to a rank two hyperbolic lattice, we show that the degree one cohomology is isomorphic to the so-called Lie algebra of physical states. In the case of a rank two unimodular lattice, the degree one cohomology gives a new construction of Borcherd's Monster Lie algebra. As applications, we compute the graded dimensions and signatures of this cohomology as a hermitean Lie algebra graded by a hyperbolic lattice. In the first half of this paper, we give as preparations an exposition of the theory of quantum operator algebras. Some of the results here were announced in lectures given by the first author at the Research Institute for Mathematical Sciences in Kyoto in September 94.

Abstract:
A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is not commutativity in any ordinary sense, but it is clearly the correct generalization to the quantum context. The main purpose of the current paper is to begin laying the foundations for a complete mathematical theory of {\it commutative quantum operator algebras.} We give proofs of most of the relevant results announced in \cite{LZ10}, and we carry out some calculations with sufficient detail to enable the interested reader to become proficient with the algebra of commuting quantum operators.

Abstract:
We discuss the notion of a Batalin-Vilkovisky (BV) algebra and give several classical examples from differential geometry and Lie theory. We introduce the notion of a quantum operator algebra (QOA) as a generalization of a classical operator algebra. In some examples, we view a QOA as a deformation of a commutative algebra. We then review the notion of a vertex operator algebra (VOA) and show that a vertex operator algebra is a QOA with some additional structures. Finally, we establish a connection between BV algebras and VOAs.

Abstract:
The BRST formalism has played a fundamental role in the construction of bosonic closed string backgrounds, ie. the stringy analogs of classical solutions to the field equations of general relativity. The concept of a string background has been extended to the notion of $W$-strings, where the BRST symmetry is still largely conjectural. More recently, the BRST formalism has entered the construction of two dimensional topological conformal quantum field theories, such as those that arise from Calabi-Yau varieties. In this lecture, we focus on common features of the BRST cohomology algebras of string backgrounds and topological field theories. In this context, we present some new evidence for a remarkable relationship that transports us from bosonic and $W$-string backgrounds to the B-model topological conformal field theories associated to certain noncompact Calabi-Yau varieties. This paper will appear in the proceedings of the {\it Symposium on BRS Symmetry} held at RIMS, September 18-22, 1995.

Abstract:
We give a brief introduction to the study of the algebraic structures -- and their geometrical interpretations -- which arise in the BRST construction of a conformal string background. Starting from the chiral algebra $\cA$ of a string background, we consider a number of elementary but universal operations on the chiral algebra. From these operations we deduce a certain fundamental odd Poisson structure, known as a Gerstenhaber algebra, on the BRST cohomology of $\cA$. For the 2D string background, the correponding G-algebra can be partially described in term of a geometrical G-algebra of the affine plane $\bC^2$. This paper will appear in the proceedings of {\it Strings 95}.

Abstract:
Motivated by the descent equation in string theory, we give a new interpretation for the action of the symmetry charges on the BRST cohomology in terms of what we call {\em the Gerstenhaber bracket}. This bracket is compatible with the graded commutative product in cohomology, and hence gives rise to a new class of examples of what mathematicians call a {\em Gerstenhaber algebra}. The latter structure was first discussed in the context of Hochschild cohomology theory \cite{Gers1}. Off-shell in the (chiral) BRST complex, all the identities of a Gerstenhaber algebra hold up to homotopy. Applying our theory to the c=1 model, we give a precise conceptual description of the BRST-Gerstenhaber algebra of this model. We are led to a direct connection between the bracket structure here and the anti-bracket formalism in BV theory \cite{W2}. We then discuss the bracket in string backgrounds with both the left and the right movers. We suggest that the homotopy Lie algebra arising from our Gerstenhaber bracket is closely related to the HLA recently constructed by Witten-Zwiebach. Finally, we show that our constructions generalize to any topological conformal field theory.

Abstract:
Model updating methodologies are invariably successful when used on noise-free simulated data, but tend to be unpredictable when presented with real experimental data that are unavoidably corrupted with uncorrelated noise content. In this paper, reanalysis using frequency response functions for correlating and updating dynamic systems is presented. A transformation matrix is obtained from the relationship between the complex and the normal frequency response functions of a structure. The transformation matrix is employed to calculate the modified damping matrix of the system. The modified mass and stiffness matrices are identified from the normal frequency response functions by using the least squares method. A numerical example is employed to illustrate the applicability of the proposed method. The result indicates that the present method is effective.

Abstract:
Simultaneous observations at multiple frequency bands have the potential to overcome the fundamental limitation imposed by the atmospheric propagation in mm-VLBI observations. The propagation effects place a severe limit in the sensitivity achievable in mm-VLBI, reducing the time over which the signals can be coherently combined, and preventing the use of phase referencing and astrometric measurements. We carried out simultaneous observations at 22, 43, 87 and 130 GHz of a group of five AGNs, the weakest of which is ca. 200 mJy at 130 GHz, with angular separations ranging from 3.6 to 11 degrees, using the KVN. We analysed this data using the Frequency Phase Transfer (FPT) and the Source Frequency Phase Referencing (SFPR) techniques, which use the observations at a lower frequency to correct those at a higher frequency. The results of the analysis provide an empirical demonstration of the increase in the coherence times at 130 GHz from a few tens of seconds to about twenty minutes, with FPT, and up to many hours with SFPR. Moreover the astrometric analysis provides high precision relative position measurements between two frequencies, including, for the first time, astrometry at 130 GHz. Finally we demonstrate a method for the generalised decomposition of the relative position measurements into absolute position shifts for bona fide astrometric registration of the maps of the individual sources at multiple frequencies, up to 130 GHz.