On the characterization of totally nonpositive matrices

The final publication is available at Springer via http://dx.doi.org/10.1007/s40324-016-0073-1[EN] A nonpositive real matrix $A= (a_{ij})_{1 \leq i, j \leq n}$ is said to be totally nonpositive (negative) if all its minors are nonpositive (negative) and it is abbreviated as t.n.p. (t.n.). In this work a bidiagonal factorization of a nonsingular t.n.p. matrix $A$ is computed and it is stored in an matrix represented by $\mathcal{BD}_{(t.n.p.)}(A)$ when $a_{11}< 0$ (or $\mathcal{BD}_{(zero)}(A)$ when $a_{11}= 0$). As a converse result, an efficient algorithm to know if an matrix $\mathcal{BD}_{(t.n.p.)}(A)$ ($\mathcal{BD}_{(zero)}(A)$) is the bidiagonal factorization of a t.n.p. matrix with $a_{11}<0$ ($a_{11}= 0$) is given. Similar results are obtained for t.n. matrices using the matrix $\mathcal{BD}_{(t.n.)}(A)$, and these characterizations are extended to rectangular t.n.p. (t.n.) matrices. Finally, the bidiagonal factorization of the inverse of a nonsingular t.n.p. (t.n.) matrix $A$ is directly obtained from $\mathcal{BD}_{(t.n.p.)}(A)$ ($\mathcal{BD}_{(t.n.)}(A)$).This research was supported by the Spanish DGI grant MTM2013-43678-P and by the Chilean program FONDECYT 1100029Cantó Colomina, R.; Pelaez, MJ.; Urbano Salvador, AM. (2016). On the characterization of totally nonpositive matrices. SeMA Journal. 73(4):347-368. doi:10.1007/s40324-016-0073-1S347368734Ando, T.: Totally positive matrices. Linear Algebra Appl. 90, 165–219 (1987)Alonso, P., Peña, J.M., Serrano, M.L.: Almost strictly totally negative matrices: an algorithmic characterization. J. Comput. Appl. Math. 275, 238–246 (2015)Bapat, R.B., Raghavan, T.E.S.: Nonnegative Matrices and Applications. Cambridge University Press, New York (1997)Cantó, R., Koev, P., Ricarte, B., Urbano, A.M.: $$LDU$$ L D U -factorization of nonsingular totally nonpositive matrices. SIAM J. Matrix Anal. Appl. 30(2), 777–782 (2008)Cantó, R., Ricarte, B., Urbano, A.M.: Full rank factorization in echelon form of totally nonpositive (negative) rectangular matrices. Linear Algebra Appl. 431, 2213–2227 (2009)Cantó, R., Ricarte, B., Urbano, A.M.: Characterizations of rectangular totally and strictly totally positive matrices. Linear Algebra Appl. 432, 2623–2633 (2010)Cantó, R., Ricarte, B., Urbano, A.M.: Quasi- $$LDU$$ L D U factorization of nonsingular totally nonpositive matrices. Linear Algebra Appl. 439, 836–851 (2013)Cantó, R., Ricarte, B., Urbano, A.M.: Full rank factorization in quasi- $$LDU$$ L D U form of totally nonpositive rectangular matrices. Linear Algebra Appl. 440, 61–82 (2014)Fallat, S.M., Van Den Driessche, P.: On matrices with all minors negative. Electron. J. Linear Algebra 7, 92–99 (2000)Fallat, S.M.: Bidiagonal factorizations of totally nonnegative matrices. Am. Math. Mon. 108(8), 697–712 (2001)Fallat, S.M., Johnson, C.R.: Totally Nonnegative Matrices. Princeton University Press, New Jersey (2011)Gasca, M., Micchelli, C.A.: Total positivity and applications. Math. Appl. 359, Kluwer Academic Publishers, Dordrecht (1996)Gasca, M., Peña, J.M.: Total positivity, $$QR$$ Q R factorization and Neville elimination. SIAM J. Matrix Anal. Appl. 4, 1132–1140 (1993)Gasca, M., Peña, J.M.: A test for strict sign-regularity. Linear Algebra Appl. 197(198), 133–142 (1994)Gasca, M., Peña, J.M.: A matricial description of Neville elimination with applications to total positivity. Linear Algebra Appl. 202, 33–53 (1994)Gassó, M., Torregrosa, J.R.: A totally positive factorization of rectangular matrices by the Neville elimination. SIAM J. Matrix Anal. Appl. 25, 86–994 (2004)Huang, R., Chu, D.: Total nonpositivity of nonsingular matrices. Linear Algebra Appl. 432, 2931–2941 (2010)Huang, R., Chu, D.: Relative perturbation analysis for eigenvalues and singular values of totally nonpositive matrices. SIAM J. Matrix Anal. Appl. 36(2), 476–495 (2015)Karlin, S.: Total Nonpositivity. Stanford University Press, Stanford (1968)Koev, P.: Accurate eigenvalues and SVDs of totally nonnegative matrices. SIAM J. Matrix Anal. Appl. 27(1), 1–23 (2005)Koev, P.: Accurate computations with totally nonnegative matrices. SIAM J. Matrix Anal. Appl. 29(3), 731–751 (2007)Parthasarathy, T.: $$N$$ N -matrices. Linear Algebra Appl. 139, 89–102 (1990)Peña, J.M.: Test for recognition of total positivity. SeMA J. 62(1), 61–73 (2013)Pinkus, A.: Totally Positive Matrices. Cambridge Tracts in Mathematics, vol. 181. Cambridge University Press (2009)Saigal, R.: On the class of complementary cones and Lemke’s algorithm. SIAM J. Appl. Math. 23, 46–60 (1972

Transfusión según cifras de hemoglobina o de acuerdo con objetivos terapéuticos

La transfusión de sangre alogénica y la anemia se han relacionado con peores resultados clínicos en diferentes poblaciones de pacientes quirúrgicos. En la actualidad, esta afirmación sigue siendo un tema de debate porque está por afirmar si la anemia es un factor de riesgo independiente de peor pronóstico..

Full rank Cholesky factorization for rank deficient matrices

[EN] Let A be a rank deficient square matrix. We characterize the unique full rank Cholesky factorization LL^T of A where the factor L is a lower echelon matrix with positive leading entries. We compute an extended decomposition for the normal matrix B^TB where B is a rectangular rank deficient matrix. This decomposition is obtained without interchange of rows and without computing all entries of the normal matrix. Algorithms to compute both factorizations are given.This research was supported by the Spanish DGI grant MTM2010-18228 and by the Chilean program FONDECYT 1100029.Cantó Colomina, R.; Peláez, MJ.; Urbano Salvador, AM. (2015). Full rank Cholesky factorization for rank deficient matrices. Applied Mathematics Letters. 40:17-22. https://doi.org/10.1016/j.aml.2014.09.001S17224

Peri-operative treatment of anaemia in major orthopaedic surgery: a practical approach from Spain

In patients undergoing major orthopaedic surgery, pre-operative anaemia, peri-operative bleeding and a liberal transfusion policy are the main risk factors for requiring red blood cell transfusion (RBCT). The clinical and economic disadvantages of RBCT have led to the development and implementation of multidisciplinary, multimodal, individualised strategies, collectively termed patient blood management, which aim to reduce RBCT and improve patients' clinical outcome and safety. Within a patient blood management programme, low pre-operative haemoglobin is one of the few modifiable risk factors for RBCT. However, a survey among Anaesthesia Departments in Spain revealed that, although pre-operative assessment was performed in the vast majority of hospitals, optimisation of haemoglobin concentration was attempted in <40% of patients who may have benefitted from it, despite there being enough time prior to surgery. This indicates that haemoglobin optimisation takes planning and forethought to be implemented in an effective manner. This review, based on available clinical evidence and our experience, is intended to provide clinicians with a practical tool to optimise pre-operative haemoglobin levels, in order to minimise the risk of patients requiring RBCT. To this purpose, after reviewing the diagnostic value and limitations of available laboratory parameters, we developed an algorithm for the detection, classification and treatment of pre-operative anaemia, with a patient-tailored approach that facilitates decision-making in the pre-operative assessment. We also reviewed the efficacy of the different pharmacological options for pre-operative and post-operative management of anaemia. We consider that such an institutional pathway for anaemia management could be a viable, cost-effective strategy that is beneficial to both patients and healthcare systems

Transcranial Doppler monitoring during laparoscopic anterior lumbar interbody fusion

We studied the consequences on cerebral hemodynamics of lengthy laparoscopic procedures requiring pneumoperitoneum and head-down positioning. From October 1995 to April 1999, 17 ASA status I or II patients (16 women and 1 man; mean age, 38 yr) were treated with laparoscopic anterior lumbar fusion. Besides standard perioperative monitoring for laparoscopic surgery, the mean blood-flow velocity of both middle cerebral arteries and the pulsatility index were determined by transcranial Doppler ultrasound. Adequate acoustic windows were encountered in 11 of the 17 patients, and the remaining 6 were excluded from the analysis. PaCO(2) and end-tidal CO(2) were maintained within normal limits (<40 mm Hg); ventilation was optimized in all cases. There was a significant increase (P < 0.05) in heart rate and central venous pressure with the change from supine to head-down position in all patients. Transcranial Doppler results for mean middle cerebral artery blood-flow velocity and pulsatility index showed no significant variations at any of the four time points studied during the procedure. There were no technique-related complications, except for moderate postoperative headache in eight patients that resolved with rest and oxygen therapy. We conclude that lengthy laparoscopic procedures in the head-down position performed in otherwise healthy patients do not significantly affect intracranial circulation

Coagulation abnormalities following nexoBrid use: a case report

Patients with major burn injury undergo a series of pathophysiologic changes that begin with a systemic inflammatory response and coagulation abnormalities, similar to those experienced by patients with sepsis or severe trauma. Coagulation changes in patients with burns are generally characterized by procoagulant abnormalities, but alterations in fibrinolysis and anticoagulation factors have also been observed. Around 40% of patients with major burn show changes on standard coagulation tests, and these have been related to the severity of the lesions, smoke inhalation, and administration of intensive fluid resuscitation therapy. Current surgical techniques for debridement of burn lesions are aggressive and associated with considerable blood loss. A fast-acting selective enzymatic debriding agent based on bromelain has been recently developed. NexoBrid is indicated for removing eschar in adults with deep partial- and full-thickness thermal burns. A potential effect of oral bromelain on hemostasis has been described, but it is uncertain whether NexoBrid application has a clinically relevant impact in this regard. We present the clinical case of a patient with burns who showed a coagulation abnormality shortly after NexoBrid use

Cardiac tamponade associated with a peripheral vein central venous catheter

We present a case of cardiac tamponade associated with placement of a central venous catheter (CVC) via a peripheral vein in a 14-year-old girl with idiopathic scoliosis undergoing corrective surgery. A number of complications have been described in association with CVC misplacement. Sporadic cases of cardiac tamponade from this have been reported, but the actual incidence is unknown. Death from cardiac tamponade attributed to CVCs ranges from 65 to 100%. In our patient, cannulation of the pericardiophrenic vein was probably the cause of cardiac tamponade, based on radiological evidence that the initial location of the catheter was near the right atrium and possibly at the outlet of the pericardiophrenic vein. The catheter could have advanced into the vein and then to the pericardial sac with postural changes. The acute clinical course of cardiac tamponade in our patient had potentially lethal hemodynamic repercussions. The main diagnostic test for this condition is echocardiography and the only effective treatment is drainage of the pericardial effusion. Echocardiography should be performed before pericardiocentesis except in life-threatening situations or high clinical suspicion. Although they are rare, it is important to be aware of the potential for CVC complications

Epidemiology and mortality in patients hospitalized for burns in Catalonia, Spain

Burn injuries are one of the leading causes of morbidity worldwide. Although the overall incidence of burns and burn-related mortality is declining, these factors have not been analysed in our population for 25 years. The aim of this study has been to determine whether the epidemiological profile of patients hospitalized for burns has changed over the past 25 years. We performed a retrospective cohort study of patients hospitalised between 1 January 2011 and 31 December 2018 with a primary diagnosis of burns. The incidence of burns in our setting was 3.68/105 population. Most patients admitted for burns were men (61%), aged between 35 and 45 years (16.8%), followed by children aged between 0 and 4 years (12.4%). Scalding was the most prevalent mechanism of injury, and the region most frequently affected was the hands. The mean burned total body surface (TBSA) area was 8.3%, and the proportion of severely burned patients was 9.7%. Obesity was the most prevalent comorbidity (39.5%). The median length of stay was 1.8 days. The most frequent in-hospital complications were sepsis (16.6%), acute kidney injury (7.9%), and cardiovascular complications (5.9%). Risk factors for mortality were advanced age, high abbreviated burn severity index score, smoke inhalation, existing cardiovascular disease full-thickness burn, and high percentage of burned TBSA. Overall mortality was 4.3%. Multi-organ failure was the most frequent cause of death, with an incidence of 49.5%. The population has aged over the 25 years since the previous study, and the number of comorbidities has increased. The incidence and severity of burns, and the percentage of burned TBSA have all decreased, with scalding being the most prevalent mechanism of injury. The clinical presentation and evolution of burns differs between children and adults. Risk factors for mortality were advanced age, smoke inhalation, existing cardiovascular disease, full-thickness burn, and high percentage of burned TBSA

Perioperative use of prothrombin complex concentrates

Prothrombin complex concentrates (PCCs) are purified drug products with hemostatic activity derived from a plasma pool. Today, PCCs contain a given and proportional amount of four non-activated vitamin K-dependent coagulation factors (II, VII, IX, and X), a variable amount of anticoagulant proteins (proteins C and S, and in some antithrombin) and low-dose heparin. In some countries PCC products contained only three clotting factors, II, IX, and X. Dosage recommendations are based on IU of F-IX, so that one IU of F-IX represents the activity of F-IX in 1 mL of plasma. Reversion of the anticoagulant effect of vitamin K antagonists (VKAs) in cases of symptomatic overdose, active bleeding episodes, or need for emergency surgery is the most important indication for PCCs and this effect of PCCs appears to be more complete and rapid than that caused by administration of fresh frozen plasma. They may be considered as safe preparations if they are used for their approved indications at the recommended dosage with adequate precautions for administration, and have been shown to be effective for reversing the effect of VKAs. Their adequate use based on decision algorithms in the perioperative setting allows a rapid normalization of International Normalized Ratio (INR) for performing emergency surgery, minimizing bleeding risk. This review aims to propose two algorithms for the use of PCCs in the perioperative setting, one to calculate the PCCs dose to be administered in a bleeding patient and/or immediately before urgent surgery, based on patient's clinical status, prior INR and INR target and another for reversing the action of oral anticoagulants depending on urgency of surgery

Perioperative management of face transplantation: A survey

Background: Since the first facial allograft transplantation was reported in France in 2005, 18 cases have been performed in 4 countries and the rate is increasing. Methods: We have devised a survey to assess anesthesia-related management and rationale of facial allograft transplantation. It was sent to the lead anesthesiologists of the first 14 face transplants performed worldwide. Results: Responses were received corresponding to 13 face transplants. The median duration of surgery and anesthesia was 19 hours (95% confidence interval 15-23 hours). The surgical preparation and dissection of multiple small anatomical structures of the recipient was time-consuming for 11 cases. Blood loss was considerable. All patients received packed red blood cells (median 20 U, 95% confidence interval 5-28 U). A median of 13 L of crystalloid was administered (95% confidence interval 10-18 L). Conclusions: During facial allograft transplantation, the anesthesiologist must be prepared for a long anesthetic with rapid blood loss after reperfusion of the graft. Comment in Out on a limb with composite tissue allografts: expanding the immunology toolbox. [Anesth Analg. 2012