Computing the kk-binomial complexity of the Thue--Morse word

Two words are $k$-binomially equivalent whenever they share the same subwords, i.e., subsequences, of length at most $k$ with the same multiplicities. This is a refinement of both abelian equivalence and the Simon congruence. The $k$-binomial complexity of an infinite word $\mathbf{x}$ maps the integer $n$ to the number of classes in the quotient, by this $k$-binomial equivalence relation, of the set of factors of length $n$ occurring in $\mathbf{x}$. This complexity measure has not been investigated very much. In this paper, we characterize the $k$-binomial complexity of the Thue--Morse word. The result is striking, compared to more familiar complexity functions. Although the Thue--Morse word is aperiodic, its $k$-binomial complexity eventually takes only two values. In this paper, we first obtain general results about the number of occurrences of subwords appearing in iterates of the form $\Psi^\ell(w)$ for an arbitrary morphism $\Psi$. We also thoroughly describe the factors of the Thue--Morse word by introducing a relevant new equivalence relation

Pleurotomy with subxyphoid pleural drain affords similar effects to pleural integrity in pulmonary function after off-pump coronary artery bypass graft

Background: Exacerbation of pulmonary dysfunction has been reported in patients receiving a pleural drain inserted through the intercostal space in comparison to patients with an intact pleura undergoing coronary artery bypass grafting (CABG). Evidence suggests that shifting the site of pleural drain insertion to the subxyphoid position minimizes chest wall trauma and preserves respiratory function in the early postoperative period. the aim of this study was to compare the pulmonary function parameters, clinical outcomes, and pain score between patients undergoing pleurotomy with pleural drain placed in the subxyphoid position and patients with intact pleural cavity after off-pump CABG (OPCAB) using left internal thoracic artery (LITA).Methods: Seventy-one patients were allocated into two groups: I (n = 38 open left pleural cavity and pleural drain inserted in the subxyphoid position); II (n = 33 intact pleural cavity). Pulmonary function tests and clinical parameters were recorded preoperatively and on postoperative days (POD) 1, 3 and 5. Arterial blood gas analysis and shunt fraction were evaluated preoperatively and in POD1. Pain score was assessed on POD1. To monitor pleural effusion and atelectasis chest radiography was performed routinely 1 day before operation and until POD5.Results: in both groups a significant impairment was found in lung function parameters until on POD5. However, no significant difference in forced vital capacity and forced expiratory volume in 1 second were seen between groups. A significant decrease in partial pressure of arterial oxygen and an increase in shunt fraction values were observed on POD1 in both groups, but no statistical difference was found when the groups were compared. Pleural effusion and atelectasis until on POD5 were similar in both groups. There were no statistical differences in pain score, duration of mechanical ventilation and postoperative hospital stay between groups.Conclusion: Subxyphoid insertion of pleural drain provides similar effects to preserved pleural integrity in pulmonary function, clinical outcomes, and thoracic pain after OPCAB. Therefore, our results support the hypothesis that once pleural cavities are incidentally or purposely opened during LITA dissection, subxyphoid placement of the pleural drain is recommended.Universidade Federal de São Paulo, Escola Paulista Med, Pirajussara Hosp, Dept Med,Cardiol Discipline, BR-04024002 São Paulo, BrazilUniversidade Federal de São Paulo, Escola Paulista Med, São Paulo Hosp, Dept Med,Cardiol Discipline, BR-04024002 São Paulo, BrazilUniversidade Federal de São Paulo, Physiotherapy Sch, Dept Human Movement Sci, BR-11060001 Santos, BrazilUniversidade Federal de São Paulo, Escola Paulista Med, São Paulo Hosp, Dept Med,Pneumol Discipline, BR-04039002 São Paulo, BrazilUniversidade Federal de São Paulo, Escola Paulista Med, Pirajussara Hosp, Dept Med,Cardiovasc Surg Discipline, BR-04024002 São Paulo, BrazilUniversidade Federal de São Paulo, Escola Paulista Med, São Paulo Hosp, Dept Med,Cardiovasc Surg Discipline, BR-04024002 São Paulo, BrazilUniversidade Federal de São Paulo, Escola Paulista Med, Pirajussara Hosp, Dept Med,Cardiol Discipline, BR-04024002 São Paulo, BrazilUniversidade Federal de São Paulo, Escola Paulista Med, São Paulo Hosp, Dept Med,Cardiol Discipline, BR-04024002 São Paulo, BrazilUniversidade Federal de São Paulo, Physiotherapy Sch, Dept Human Movement Sci, BR-11060001 Santos, BrazilUniversidade Federal de São Paulo, Escola Paulista Med, São Paulo Hosp, Dept Med,Pneumol Discipline, BR-04039002 São Paulo, BrazilUniversidade Federal de São Paulo, Escola Paulista Med, Pirajussara Hosp, Dept Med,Cardiovasc Surg Discipline, BR-04024002 São Paulo, BrazilUniversidade Federal de São Paulo, Escola Paulista Med, São Paulo Hosp, Dept Med,Cardiovasc Surg Discipline, BR-04024002 São Paulo, BrazilWeb of Scienc

Strategies to prevent intraoperative lung injury during cardiopulmonary bypass

During open heart surgery the influence of a series of factors such as cardiopulmonary bypass (CPB), hypothermia, operation and anaesthesia, as well as medication and transfusion can cause a diffuse trauma in the lungs. This injury leads mostly to a postoperative interstitial pulmonary oedema and abnormal gas exchange. Substantial improvements in all of the above mentioned factors may lead to a better lung function postoperatively. By avoiding CPB, reducing its time, or by minimizing the extracorporeal surface area with the use of miniaturized circuits of CPB, beneficial effects on lung function are reported. In addition, replacement of circuit surface with biocompatible surfaces like heparin-coated, and material-independent sources of blood activation, a better postoperative lung function is observed. Meticulous myocardial protection by using hypothermia and cardioplegia methods during ischemia and reperfusion remain one of the cornerstones of postoperative lung function. The partial restoration of pulmonary artery perfusion during CPB possibly contributes to prevent pulmonary ischemia and lung dysfunction. Using medication such as corticosteroids and aprotinin, which protect the lungs during CPB, and leukocyte depletion filters for operations expected to exceed 90 minutes in CPB-time appear to be protective against the toxic impact of CPB in the lungs. The newer methods of ultrafiltration used to scavenge pro-inflammatory factors seem to be protective for the lung function. In a similar way, reducing the use of cardiotomy suction device, as well as the contact-time between free blood and pericardium, it is expected that the postoperative lung function will be improved

Computing the k-binomial complexity of the Thue–Morse word

Two words are k-binomially equivalent whenever they share the same subwords, i.e., subsequences, of length at most k with the same multiplicities. This is a refinement of both the abelian equivalence and the Simon congruence. The k-binomial complexity of an infinite word x maps the integer n to the number of classes in the quotient, by this k-binomial equivalence relation, of the set of factors of length n occurring in x. This complexity measure has not been investigation very much. In this paper, we characterize the k-binomial complexity of the Thue–Morse word. The result is striking, compared to more familiar complexity functions. Although the Thue–Morse word is aperiodic, its k-binomial complexity eventually takes only two values. In this paper, we first express the number of occurrences of subwords appearing in iterates of the form Ψ^l(w) for an arbitrary morphism Ψ. We also thoroughly describe the factors of the Thue–Morse word by introducing a relevant new equivalence relation