Extended GCD and Hermite normal form algorithms via lattice basis reduction

Extended gcd calculation has a long history and plays an important role in computational number theory and linear algebra. Recent results have shown that finding optimal multipliers in extended gcd calculations is difficult. We present an algorithm which uses lattice basis reduction to produce small integer multipliers x(1), ..., x(m) for the equation s = gcd (s(1), ..., s(m)) = x(1)s(1) + ... + x(m)s(m), where s1, ... , s(m) are given integers. The method generalises to produce small unimodular transformation matrices for computing the Hermite normal form of an integer matrix.

Extended integrability regime for the supersymmetric U model

An extension of the supersymmetric U model for correlated electrons is given and integrability is established by demonstrating that the model can he constructed through the quantum inverse scattering method using an R-matrix without the difference property. Some general symmetry properties of the model are discussed and from the Bethe ansatz solution an expression for the energies is presented.

Integrable Kondo impurities in the one-dimensional supersymmetric extended Hubbard model

An integrable Kondo problem in the one-dimensional supersymmetric extended Hubbard model is studied by means of the boundary graded quantum inverse scattering method. The boundary K-matrices depending on the local moments of the impurities are presented as a non-trivial realization of the graded reflection equation algebras in a two-dimensional impurity Hilbert space. Further, the model is solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained.

Modeling of hepatic elimination and organ distribution kinetics with the extended convection-dispersion model

The conventional convection-dispersion (also called axial dispersion) model is widely used to interrelate hepatic availability (F) and clearance (Cl) with the morphology and physiology of the liver and to predict effects such as changes in liver blood flow on F and Cl. An extended form of the convection-dispersion model has been developed to adequately describe the outflow concentration-time profiles for vascular markers at both short and long times after bolus injections into perfused livers. The model, based on flux concentration and a convolution of catheters and large vessels, assumes that solute elimination in hepatocytes follows either fast distribution into or radial diffusion in hepatocytes. The model includes a secondary vascular compartment, postulated to be interconnecting sinusoids. Analysis of the mean hepatic transit time (MTT) and normalized variance (CV2) of solutes with extraction showed that the discrepancy between the predictions of MTT and CV2 for the extended and conventional models are essentially identical irrespective of the magnitude of rate constants representing permeability, volume, and clearance parameters, providing that there is significant hepatic extraction. In conclusion, the application of a newly developed extended convection-dispersion model has shown that the unweighted conventional convection-dispersion model can be used to describe the disposition of extracted solutes and, in particular, to estimate hepatic availability and clearance in booth experimental and clinical situations.

Integrable Kondo impurities in one-dimensional extended Hubbard models

Three kinds of integrable Kondo problems in one-dimensional extended Hubbard models are studied by means of the boundary graded quantum inverse scattering method. The boundary K matrices depending on the local moments of the impurities are presented as a nontrivial realization of the graded reflection equation algebras acting in a (2s alpha + 1)-dimensional impurity Hilbert space. Furthermore, these models are solved using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

Algebraic Bethe ansatz for integrable one-dimensional extended Hubbard models with open boundary conditions

Nine classes of integrable open boundary conditions, further extending the one-dimensional U-q (gl (212)) extended Hubbard model, have been constructed previously by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary systems are now solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained for all nine cases.

Fast-convergent iterative scheme for filtering velocity signals and finding Kolmogorov scales

The present fundamental knowledge of fluid turbulence has been established primarily from hot- and cold-wire measurements. Unfortunately, however, these measurements necessarily suffer from contamination by noise since no certain method has previously been available to optimally filter noise from the measured signals. This limitation has impeded our progress of understanding turbulence profoundly. We address this limitation by presenting a simple, fast-convergent iterative scheme to digitally filter signals optimally and find Kolmogorov scales definitely. The great efficacy of the scheme is demonstrated by its application to the instantaneous velocity measured in a turbulent jet.

A new algorithm and refined bounds for extended gcd computation

Extended gcd computation is interesting itself. It also plays a fundamental role in other calculations. We present a new algorithm for solving the extended gcd problem. This algorithm has a particularly simple description and is practical. It also provides refined bounds on the size of the multipliers obtained.

Immediate Locally Advanced Breast Cancer and Chest Wall Reconstruction: Surgical Planning and Reconstruction Strategies with Extended V-Y Latissimus Dorsi Myocutaneous Flap

Background: Surgical resection in locally advanced breast cancer produces large defects that may not be suitable for primary closure. Immediate reconstruction is controversial and presents a complicated scenario for breast surgeons and plastic surgeons. Methods: In this study, a different design was planned for the latissimus dorsi musculocutaneous flap with primary closure in V-Y for the correction of major lesions in the anterior chest wall. Twenty-five patients underwent immediate locally advanced breast cancer reconstruction with a V-Y latissimus dorsi musculocutaneous flap. This flap was raised from adjacent tissue located on the lateral and posterior thoracic region and presented a triangular shape whose base was the lateral aspect of the mastectomy wound. The technique was indicated in patients with large thoracic wounds. Results: Mean follow-up time was 16 months. Closure was obtained in the donor and recipient sites without the use of skin grafts or other more major procedures. Complications occurred in nine patients (36 percent), including dorsal wound dehiscence in five patients and seroma in three. All cases except one were treated by a conservative approach with a good result. No total flap loss was reported. All patients achieved a satisfactory thoracic reconstruction and adequate wound care. Conclusions: The V-Y latissimus dorsi musculocutaneous flap is a reliable technique for immediate locally advanced breast cancer reconstruction. The technique is advantageous because the V-Y design allows primary closure of the chest wound and donor defect. Success depends on patient selection, coordinated planning with the breast cancer surgeon, and careful intraoperative management. (Plast. Reconstr. Surg. 127: 2186, 2011.)

Laparoscopic extended cardiomyotomy in children: an effective procedure for the treatment of esophageal achalasia

Purpose: Achalasia of the esophagus is characterized by aperistalsis and incomplete relaxation of the lower esophageal sphincter in response to swallowing. The objective of the present study is to present the experience of a modified Heller myotomy via a laparoscopic approach for the treatment of children who had this condition. Methods: A retrospective review of medical records of all patients who underwent this procedure from 2000 to 2009 was performed. The procedure consisted of an extended esophagomyotomy beginning on the lower part of the lower esophageal sphincter and continuing 5 to 6 cm above on the lower third of the esophagus, and then extended 3 to 4 cm below to the stomach, associated with an anterior 180-degree hemi-fundoplication according to Dor`s technique. Results: Fifteen patients were included in the study. There were 8 female and 7 male patients. Mean operating time was 190 minutes with no intraoperative complications and 1 conversion to open surgery because of difficulty in dissecting an inflamed distal esophagus. In a mean follow-up period of 32.3 months, 2 patients had recurrence of mild dysphagia that disappeared spontaneously, and 1 required a single botulinum toxin injection with complete resolution of symptoms. Conclusion: We conclude that the laparoscopic extended Heller myotomy with Dor fundoplication is a safe and effective method for the treatment for achalasia in the pediatric population even in advanced cases. (C) 2010 Elsevier Inc. All rights reserved.

UPGRADING THE GLEASON SCORE IN EXTENDED PROSTATE BIOPSY: IMPLICATIONS FOR TREATMENT CHOICE

Purpose: To determine the incidence of overestimation of Gleason score (GS) in extended prostate biopsy, and consequently circumventing unnecessary aggressive treatment. Methods and Materials: This is a retrospective study of 464 patients who underwent prostate biopsy and radical prostatectomy between January 2001 and November 2007. The GS from biopsy and radical prostatectomy were compared. The incidence of overestimation of GS in biopsies and tumor volume were studied. Multivariate analysis was applied to find parameters that predict upgrading the GS in prostate biopsy. Results: The exact agreement of GS between prostate biopsy and radical prostatectomy occurred in 56.9% of cases. In 29.1% cases it was underestimated, and it was overestimated in 14%. One hundred and six (22.8%) patients received a diagnosis of high GS (8, 9, or 10) in a prostate biopsy. In 29.2% of cases, the definitive Gleason Score was 7 or lower. In cases in which GS was overestimated in the biopsy, tumors were significantly smaller. In multivariate analysis, the total percentage of tumor was the only independent factor in overestimation of GS. Tumors occupying less than 33% of cores had a 5.6-fold greater chance of being overestimated. Conclusion: In the extended biopsy era and after the International Society of Urological Pathology consensus on G, almost one third of tumors considered to have high GS at the biopsy may be intermediate-risk cancers. In that condition, tumors are smaller in biopsy. This should be remembered by professionals involved with prostate cancer to avoid overtreatment and undesirable side effects. (c) 2009 Elsevier Inc.