Quasistationarity of continuous-time Markov chains with positive drift

We shall study continuous-time Markov chains on the nonnegative integers which are both irreducible and transient, and which exhibit discernible stationarity before drift to infinity sets in. We will show how this 'quasi' stationary behaviour can be modelled using a limiting conditional distribution: specifically, the limiting state probabilities conditional on not having left 0 for the last time. By way of a dual chain, obtained by killing the original process on last exit from 0, we invoke the theory of quasistationarity for absorbing Markov chains. We prove that the conditioned state probabilities of the original chain are equal to the state probabilities of its dual conditioned on non-absorption, thus allowing us to establish the simultaneous existence and then equivalence, of their limiting conditional distributions. Although a limiting conditional distribution for the dual chain is always a quasistationary distribution in the usual sense, a similar statement is not possible for the original chain.

Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains

This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on mu-invariant and mu-subinvariant measures where absorption occurs with probability less than one. In particular, the well-known premise that the mu-invariant measure, m, for the transition rates be finite is replaced by the more natural premise that m be finite with respect to the absorption probabilities. The relationship between mu-invariant measures and quasi-stationary distributions is discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.

New methods for determining quasi-stationary distributions for Markov chains

We shall be concerned with the problem of determining quasi-stationary distributions for Markovian models directly from their transition rates Q. We shall present simple conditions for a mu-invariant measure m for Q to be mu-invariant for the transition function, so that if m is finite, it can be normalized to produce a quasi-stationary distribution. (C) 2000 Elsevier Science Ltd. All rights reserved.

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.

Jordan-Wigner fermionization of the one-dimensional Bariev model of three coupled XY chains

The Jordan-Wigner fermionization for the one-dimensional Bariev model of three coupled XY chains is formulated. The L-matrix in terms of fermion operators and the R-matrix are presented explicitly. Furthermore, the graded reflection equations and their solutions are discussed.

Characterization of the rat exploratory behavior in the elevated plus-maze with Markov chains

The elevated plus-maze is an animal model of anxiety used to study the effect of different drugs on the behavior of the animal It consists of a plus-shaped maze with two open and two closed arms elevated 50 cm from the floor The standard measures used to characterize exploratory behavior in the elevated plus-maze are the time spent and the number of entries in the open arms In this work we use Markov chains to characterize the exploratory behavior of the rat in the elevated plus-maze under three different conditions normal and under the effects of anxiogenic and anxiolytic drugs The spatial structure of the elevated plus-maze is divided into squares which are associated with states of a Markov chain By counting the frequencies of transitions between states during 5-min sessions in the elevated plus-maze we constructed stochastic matrices for the three conditions studied The stochastic matrices show specific patterns which correspond to the observed behaviors of the rat under the three different conditions For the control group the stochastic matrix shows a clear preference for places in the closed arms This preference is enhanced for the anxiogenic group For the anxiolytic group the stochastic matrix shows a pattern similar to a random walk Our results suggest that Markov chains can be used together with the standard measures to characterize the rat behavior in the elevated plus-maze (C) 2010 Elsevier B V All rights reserved

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.

On the construction of integrable closed chains with quantum supersymmetry

We present a general prescription for the construction of integrable one-dimensional systems with closed boundary conditions and quantum supersymmetry.

Glycosaminoglycan chains from alpha(5)beta(1) integrin are involved in fibronectin-dependent cell migration

alpha(5)beta(1) integrin from both wild-type CHO cells (CHO-K1) and deficient in proteoglycan biosynthesis (CHO-745) is post-translationally modified by glycosaminoglycan chains. We demonstrated this using [(35)S]sulfate metabolic labeling of the cells, enzymatic degradation, immunoprecipitation reaction with monoclonal antibody, fluorescence microscopy, and flow cytometry. The alpha(5)beta(1) integrin heterodimer is a hybrid proteoglycan containing both chondroitin and heparan sulfate chains. Xyloside inhibition of sulfate incorporation into alpha(5)beta(1) integrin also supports that integrin is a proteoglycan. Also. cells grown with xyloside adhered on fibronectin with no alteration in alpha(5)beta(1) integrin expression. However, haptotactic motility on fibronectin declined in cells grown with xyloside or chlorate as compared with controls. Thus, alpha(5)beta(1) integrin is a proteoglycan and the glycosaminoglycan chains of the integrin influence cell motility on fibronectin. Similar glycosylation of alpha(5)beta(1) integrin was observed in other normal and malignant cells, suggesting that this modification is conserved and important in the function of this integrin. Therefore, these glycosaminoglycan chains of alpha(5)beta(1) integrin are involved in cellular migration on fibronectin.

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.