Integral representations of shallow neural network with rectified power unit activation function.

In this paper we characterize the set of functions that can be represented by infinite width neural networks with RePU activation function max(0,x)p, when the network coefficients are regularized by an ℓ2/p (quasi)norm. Compared to the more well-known ReLU activation function (which corresponds to p=1), the RePU activation functions exhibit a greater degree of smoothness which makes them preferable in several applications. Our main result shows that such representations are possible for a given function if and only if the function is κ-order Lipschitz and its R-norm is finite. This extends earlier work on this topic that has been restricted to the case of the ReLU activation function and coefficient bounds with respect to the ℓ2 norm. Since for q<2, ℓq regularizations are known to promote sparsity, our results also shed light on the ability to obtain sparse neural network representations.

Does an Early Implantation of Extracorporeal Membrane Oxygenator in High-Risk Emergency Open Heart Surgery Patients Improve the Outcome in Comparison with Elective Patients? A Prospective Cohort Comparative Study.

BACKGROUND: Extracorporeal membrane oxygenator (ECMO) has been implemented in refractory postcardiotomy cardiogenic shock (PCCS) patients to maintain excellent oxygenation and hemodynamic support. The aim of this study is to compare the results of early ECMO implantation to treat refractory PCCS in emergency versus elective patients who developed univentricular or biventricular pump failure. PATIENTS AND METHODS: Between January 2019 and June 2021, 35 patients received ECMO after refractory PCCS. Patients have been categorized into two groups: Group A contains 18 patients who were urgently operated on and Group B, which includes 17 patients who were electively operated on. ECMO was implanted through central cannulation (right atrium and ascending aorta), or through peripheral cannulation (femoral vessels or through axillary artery). RESULTS: There was no statistically significant difference between the two ECMO groups in the preoperative patient's characteristics, complication rate, duration of mechanical ventilation, post-ECMO weaning hospital stay, duration of ICU stay, in-hospital mortality, and number of patients discharged from the hospital or in 1-year survival on follow up. CONCLUSION: Early use of ECMO in high-risk emergency cardiac surgery should be taken into consideration when possible, without hesitance. Emergency and elective patients benefit equally from ECMO implantation and show comparable complication rates.

A Comparative Study Between Different Surgical Techniques For Left Atrial Exclusion in Patients Undergoing Concomitant Cardiac Surgery.

OBJECTIVES: To find out the most successful surgical technique to obliterate left atrial appendage (LAA) in atrial fibrillation (AF) patients who had undergone concomitant cardiac surgery. BACKGROUND: About 10%-65% of patients develop AF following cardiac surgery [Rho 2009; Mathew 2004; Maesen 2012]. Cerebral cardio-embolic stroke remains the most serious complication in AF patients. LAA is the main anatomical source for thromboembolic events. The use of oral anticoagulants (OAG) is considered to be an effective method for reduction of thromboembolic complications [Johnson 2000]. The use of oral anticoagulants is faced by two important facts which are the therapy duration is still unknown [Kirchhof 2017] and importantly that between 30-50% of patients are not candidates for oral anticoagulants due to the high bleeding risk or other contraindications [Johnson 2000; Kirchhof 2017; Kirchhof 2014]. In such patients, LAA obliteration would be an optimal alternative technique as it will reduce the stroke risk by 50% [Go 2014]. Several surgical techniques with variable degrees of success rates have been used.  It still is unclear which surgical technique is optimum to achieve a successful obliteration of the LAA and a considerable reduction of the postoperative stroke events in AF patients. PATIENTS AND METHODS: A total of 100 patients have been subjected to surgical LAA exclusion from April 2017 to April 2019 in two different centers. All patients had postoperative transesophageal echo (TEE) examination to confirm the success of LAA occlusion. All patients included in our study suffered from AF at the time of surgery or in past history, which was confirmed by ECG examination in their previous medical files. A variety of surgical techniques to close the LAA have been utilized, including surgical excision by means of scissors, patch exclusion by means of an endocardial patch, suture exclusion and finally stapler exclusion. TEE examination 16 months postoperatively divided our patients into four groups as follows: successful LAA occlusion, Patent LAA, excluded LAA with persistent flow into LAA, and remnant LAA with a stump connection with LAA more than 1 cm. RESULTS: Out of 100 patients, 30 patients (30%) underwent surgical LAA excision, 24 patients (24%) underwent surgical epicardial suture ligation, eight patients (8%) underwent patch exclusion using autologous pericardial patch, 33 patients (33%) underwent LAA internal orifice purse string suture obliteration, and five patients (5%) underwent stapler exclusion. Forty-two patients out of 100 (42%) showed successful LAA closure. The successful LAA occlusion occurred mostly in LAA excision patients 87%, 24% in LAA internal orifice purse string suture obliteration patients, 21% in epicardial suture ligation patients, and 37.5% in patch exclusion patients. The stapler exclusion was very disappointing as we did not record a single case out of the five patients who showed a successful LAA occlusion. Stroke events were recorded in all surgical techniques except the LAA excision technique. The stroke rate after two years follow up was zero in the surgical excision group, 49% in the suture exclusion group, 20% in the patch exclusion group, and 40% in stapler exclusion group. CONCLUSION: Surgical LAA excision is the most successful technique for LAA occlusion and represents a promising technique for the reduction of thromboembolic events in AF patients who undergo a concomitant cardiac surgery.

Leg Wound Complications: A Comparison Between Endoscopic and Open Saphenous Vein Harvesting Techniques.

BACKGROUND: The most common conduit for coronary artery bypass graft (CABG) surgery is saphenous vein graft (SVG). There are two techniques for SVG harvesting: open and endoscopic. Our aim is to evaluate clinical results of endoscopic versus open SVG harvesting. Nowadays, endoscopic vein harvesting (EVH) has become prevalent because of reduced complications with more patient satisfaction. OBJECTIVE: We designed and performed a prospective randomized cohort study of patients undergoing CABG to compare the results of open versus endoscopic harvesting technique. METHODS: Patients who underwent elective CABG at our hospitals were divided into two groups, during the period of January 2019 to March 2021. The EVH group (50 patients) underwent endoscopic technique compared with the open vein harvesting (OVH) group (50 patients) that was underwent open surgical incision for great saphenous vein (GSV) harvesting. The two groups demographically were similar and received identical management. Leg wound was evaluated at discharge, two weeks, and four weeks for evidence of any complications. Early outcomes were recorded, including infection, gaped wound and surgical re-suture, degree of pain, level of cosmetic satisfaction, and early mobilization. RESULTS: In the EVH group, harvesting time increased, and incision closure time decreased in comparison with OVH. The hospital stay was 5.5 ± 2.4 days in the EVH group versus 9.5 ± 2.7 days in the OVH group. Leg wound complications were significantly reduced in the EVH group in comparison with the OVH group. CONCLUSIONS: Endoscopic vein harvesting technique reduced leg wound complications. Conveniently, patients also were cosmetically satisfied.