Machine Learning Regularization for the Minimum Volume Formula of Toric Calabi-Yau 3-folds

We present a collection of explicit formulas for the minimum volume of Sasaki-Einstein 5-manifolds. The cone over these 5-manifolds is a toric Calabi-Yau 3-fold. These toric Calabi-Yau 3-folds are associated with an infinite class of 4d N=1 supersymmetric gauge theories, which are realized as worldvolume theories of D3-branes probing the toric Calabi-Yau 3-folds. Under the AdS/CFT correspondence, the minimum volume of the Sasaki-Einstein base is inversely proportional to the central charge of the corresponding 4d N=1 superconformal field theories. The presented formulas for the minimum volume are in terms of geometric invariants of the toric Calabi-Yau 3-folds. These explicit results are derived by implementing machine learning regularization techniques that advance beyond previous applications of machine learning for determining the minimum volume. Moreover, the use of machine learning regularization allows us to present interpretable and explainable formulas for the minimum volume. Our work confirms that, even for extensive sets of toric Calabi-Yau 3-folds, the proposed formulas approximate the minimum volume with remarkable accuracy.Comment: 15 pages, 9 figures, 4 table

Prognostic Factors of Response to Laparoscopic Splenectomy in Patients with Idiopathic Thrombocytopenic Purpura

Laparoscopic splenectomy (LS) has become the treatment of choice for patients with idiopathic thrombocytopenic purpura (ITP) who do not respond to medical treatment. The aim of this study was to identify factors predictive of outcome after LS for ITP. From May 1997 to December 2002, we performed 30 LS on patients with ITP. A positive response was defined as a postoperative platelet count greater than 50,000/µL and no requirement for maintenance therapy. Chi-square testing was performed to determine the predictive effects of the following variables: age, sex, preoperative response to steroids or immunoglobulin, duration of disease, antiplatelet antibody, platelet associated antibody, and antinuclear antibody. LS was successfully performed in all patients. For a mean follow-up interval of 24.3 months, response to LS was 73.3%. Splenectomy for steroid nonresponders resulted in an inferior complete response rate (10 of 18, 55.6%) as compared with those that experienced relapse after steroid treatment (11 of 12, 91.7%) (p=0.042). The other significant predictor of outcome by univariate analysis was the time between diagnosis and surgery (p=0.049). The other variables showed no significant correlation with successful splenectomy. We conclude that LS can be performed safely with a satisfactory remission rate in patients with ITP who do not respond to medical treatment, and that the factors most frequently associated with surgical success are a response to steroid and disease duration

Usefulness of Anticoagulant Therapy in the Prevention of Embolic Complications in Patients with Acute Infective Endocarditis

Background. The use of anticoagulant therapy (ACT) in patients with acute infective endocarditis (IE) remains a controversial issue. Our study attempts to estimate the impact of ACT on the occurrence of embolic complications and the usefulness of ACT in the prevention of embolism in IE patients. Methods. The present authors analyzed 150 patients with left-sided IE. Embolisms including cerebrovascular events (CVE) and the use of ACT were checked at the time of admission and during hospitalization. Results. 57 patients (38.0%) experienced an embolic event. There was no significant difference in the incidence of CVE and in-hospital mortality between patients with and without warfarin use at admission, although warfarin-naïve patients were significantly more likely to have large (>1 cm) and mobile vegetation. In addition, there was no significant difference in the incidence of postadmission embolism and in-hospital death between patients with and without in-hospital ACT. On multivariate logistic regression analysis, ACT at admission was not significantly associated with a lower risk of embolism in patients with IE. Conclusions. The role of ACT in the prevention of embolism was limited in IE patients undergoing antibiotic therapy, although it seems to reduce the embolic potential of septic vegetation before treatment