17O Nuclear Magnetic Resonance Chemical Shift in Oxyhaemoglobin

The 170 chemical shift of oxygen in oxyhaemoglobin is calculated for two models, one corresponding to the Griffith structure and the other to the Pauling structure. In both cases the oxygen resonance is predicted to be several thousand ppm to low field of the oxygen resonance in water. The shift between the oxygen nuclei in the Pauling structure is predicted to be at least one thousand ppm. This large deshielding arises from the local environment of the oxygen molecule and depends critically on the splitting of the degenerate it orbitals on complexing

17O Nuclear Magnetic Resonance Chemical Shift in Oxyhaemoglobin

The 170 chemical shift of oxygen in oxyhaemoglobin is calculated for two models, one corresponding to the Griffith structure and the other to the Pauling structure. In both cases the oxygen resonance is predicted to be several thousand ppm to low field of the oxygen resonance in water. The shift between the oxygen nuclei in the Pauling structure is predicted to be at least one thousand ppm. This large deshielding arises from the local environment of the oxygen molecule and depends critically on the splitting of the degenerate it orbitals on complexing

Entropy-driven phase transition in a polydisperse hard-rods lattice system

We study a system of rods on the 2d square lattice, with hard-core exclusion. Each rod has a length between 2 and N. We show that, when N is sufficiently large, and for suitable fugacity, there are several distinct Gibbs states, with orientational long-range order. This is in sharp contrast with the case N=2 (the monomer-dimer model), for which Heilmann and Lieb proved absence of phase transition at any fugacity. This is the first example of a pure hard-core system with phases displaying orientational order, but not translational order; this is a fundamental characteristic feature of liquid crystals

A Finite-Volume Version of Aizenman-Higuchi Theorem for the 2d Ising Model

In the late 1970s, in two celebrated papers, Aizenman and Higuchi independently established that all infinite-volume Gibbs measures of the two-dimensional ferromagnetic nearest-neighbor Ising model are convex combinations of the two pure phases. We present here a new approach to this result, with a number of advantages: (i) We obtain an optimal finite-volume, quantitative analogue (implying the classical claim); (ii) the scheme of our proof seems more natural and provides a better picture of the underlying phenomenon; (iii) this new approach might be applicable to systems for which the classical method fails.Comment: A couple of typos corrected. To appear in Probab. Theory Relat. Field

Rigorous Probabilistic Analysis of Equilibrium Crystal Shapes

The rigorous microscopic theory of equilibrium crystal shapes has made enormous progress during the last decade. We review here the main results which have been obtained, both in two and higher dimensions. In particular, we describe how the phenomenological Wulff and Winterbottom constructions can be derived from the microscopic description provided by the equilibrium statistical mechanics of lattice gases. We focus on the main conceptual issues and describe the central ideas of the existing approaches.Comment: To appear in the March 2000 special issue of Journal of Mathematical Physics on Probabilistic Methods in Statistical Physic

Neoadjuvant capecitabine, radiotherapy, and bevacizumab (CRAB) in locally advanced rectal cancer: results of an open-label phase II study

<p>Abstract</p> <p>Background</p> <p>Preoperative capecitabine-based chemoradiation is a standard treatment for locally advanced rectal cancer (LARC). Here, we explored the safety and efficacy of the addition of bevacizumab to capecitabine and concurrent radiotherapy for LARC.</p> <p>Methods</p> <p>Patients with MRI-confirmed stage II/III rectal cancer received bevacizumab 5 mg/kg i.v. 2 weeks prior to neoadjuvant chemoradiotherapy followed by bevacizumab 5 mg/kg on Days 1, 15 and 29, capecitabine 825 mg/m²twice daily on Days 1-38, and concurrent radiotherapy 50.4 Gy (1.8 Gy/day, 5 days/week for 5 weeks + three 1.8 Gy/day), starting on Day 1. Total mesorectal excision was scheduled 6-8 weeks after completion of chemoradiotherapy. Tumour regression grades (TRG) were evaluated on surgical specimens according to Dworak. The primary endpoint was pathological complete response (pCR).</p> <p>Results</p> <p>61 patients were enrolled (median age 60 years [range 31-80], 64% male). Twelve patients (19.7%) had T3N0 tumours, 1 patient T2N1, 19 patients (31.1%) T3N1, 2 patients (3.3%) T2N2, 22 patients (36.1%) T3N2 and 5 patients (8.2%) T4N2. Median tumour distance from the anal verge was 6 cm (range 0-11). Grade 3 adverse events included dermatitis (n = 6, 9.8%), proteinuria (n = 4, 6.5%) and leucocytopenia (n = 3, 4.9%). Radical resection was achieved in 57 patients (95%), and 42 patients (70%) underwent sphincter-preserving surgery. TRG 4 (pCR) was recorded in 8 patients (13.3%) and TRG 3 in 9 patients (15.0%). T-, N- and overall downstaging rates were 45.2%, 73.8%, and 73.8%, respectively.</p> <p>Conclusions</p> <p>This study demonstrates the feasibility of preoperative chemoradiotherapy with bevacizumab and capecitabine. The observed adverse events of neoadjuvant treatment are comparable with those previously reported, but the pCR rate was lower.</p

Optimal designs for rational function regression

We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The proposed method treats D-, E-, A-, and $\Phi_p$-optimal designs in a unified manner, and generates a polynomial whose zeros are the support points of the optimal approximate design, generalizing a number of previously known results of the same flavor. The method is based on a mathematical optimization model that can incorporate various criteria of optimality and can be solved efficiently by well established numerical optimization methods. In contrast to previous optimization-based methods proposed for similar design problems, it also has theoretical guarantee of its algorithmic efficiency; in fact, the running times of all numerical examples considered in the paper are negligible. The stability of the method is demonstrated in an example involving high degree polynomials. After discussing linear models, applications for finding locally optimal designs for nonlinear regression models involving rational functions are presented, then extensions to robust regression designs, and trigonometric regression are shown. As a corollary, an upper bound on the size of the support set of the minimally-supported optimal designs is also found. The method is of considerable practical importance, with the potential for instance to impact design software development. Further study of the optimality conditions of the main optimization model might also yield new theoretical insights.Comment: 25 pages. Previous version updated with more details in the theory and additional example

On the Gibbs states of the noncritical Potts model on Z^2

We prove that all Gibbs states of the q-state nearest neighbor Potts model on Z^2 below the critical temperature are convex combinations of the q pure phases; in particular, they are all translation invariant. To achieve this goal, we consider such models in large finite boxes with arbitrary boundary condition, and prove that the center of the box lies deeply inside a pure phase with high probability. Our estimate of the finite-volume error term is of essentially optimal order, which stems from the Brownian scaling of fluctuating interfaces. The results hold at any supercritical value of the inverse temperature.Comment: Minor typos corrected after proofreading. Final version, to appear in Probab. Theory Relat. Field

An exactly solvable model for the Fermi contact interaction

A model for the Fermi contact interaction is proposed in which the nuclear moment is represented as a magnetized spherical shell of radius r 0 . For a hydrogen-like system thus perturbed, the Schrödinger equation is solvable without perturbation theory by use of the Coulomb Green's function. Approximation formulas are derived in terms of a quantum defect in the Coulombic energy formula. It is shown that the usual Fermi potential cannot be applied beyond first-order perturbation theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46454/1/214_2004_Article_BF00548828.pd