Competing Pairing Symmetries in a Generalized Two-Orbital Model for the Pnictides

We introduce and study an extended "t-U-J" two-orbital model for the pnictides that includes Heisenberg terms deduced from the strong coupling expansion. Including these J terms explicitly allows us to enhance the strength of the (pi, 0)-(0, pi) spin order which favors the presence of tightly bound pairing states even in the small clusters that are here exactly diagonalized. The A1g and B2g pairing symmetries are found to compete in the realistic spin-ordered and metallic regime. The dynamical pairing susceptibility additionally unveils low-lying B1g states, suggesting that small changes in parameters may render any of the three channels stable.Comment: submitted PRL 10/5/1

Outcomes of surgery for patients with Behcet’s disease causing aortic pseudoaneurysm: a shift from open surgery to endovascular repair

OBJECTIVES: Behcet’s disease is a form of systematic vasculitis that affects vessels of various sizes. Aortic pseudoaneurysm is one of the most important causes of death among patients with Behcet’s disease due to its high risk of rupture and associated mortality. Our study aimed to investigate the outcomes of Behcet’s disease patients with aortic pseudoaneurysms undergoing open surgery and endovascular aortic repair. METHODS: From January 2003 to September 2014, ten consecutive patients undergoing surgery for aortic pseudoaneurysm met the diagnostic criteria for Behcet’s disease. Endovascular repair was the preferred modality and open surgery was performed as an alternative. Systemic immunosuppressive medication was administered after Behcet’s disease was definitively diagnosed. RESULTS: Eight patients initially underwent endovascular repair and two patients initially underwent open surgery. The overall success rate was 90% and the only failed case involved the use of the chimney technique to reach a suprarenal location. The median follow-up duration was 23 months. There were 7 recurrences in 5 patients. The median interval between operation and recurrence was 13 months. No significant risk factors for recurrence were identified, but a difference in recurrence between treatment and non-treatment with preoperative immunosuppressive medication preoperatively was notable. Four aneurysm-related deaths occurred within the follow-up period. The overall 1-year, 3-year and 5-year survival rates were 80%, 64% and 48%, respectively. CONCLUSIONS: Both open surgery and endovascular repair are safe and effective for treating aortic pseudoaneurysm in Behcet’s disease patients. The results from our retrospective study indicated that immunosuppressive medication was essential to defer the occurrence and development of recurrent aneurysms

Optimal Rate of Kernel Regression in Large Dimensions

We perform a study on kernel regression for large-dimensional data (where the sample size $n$ is polynomially depending on the dimension $d$ of the samples, i.e., $n\asymp d^{\gamma}$ for some $\gamma >0$ ). We first build a general tool to characterize the upper bound and the minimax lower bound of kernel regression for large dimensional data through the Mendelson complexity $\varepsilon_{n}^{2}$ and the metric entropy $\bar{\varepsilon}_{n}^{2}$ respectively. When the target function falls into the RKHS associated with a (general) inner product model defined on $\mathbb{S}^{d}$, we utilize the new tool to show that the minimax rate of the excess risk of kernel regression is $n^{-1/2}$ when $n\asymp d^{\gamma}$ for $\gamma =2, 4, 6, 8, \cdots$. We then further determine the optimal rate of the excess risk of kernel regression for all the $\gamma>0$ and find that the curve of optimal rate varying along $\gamma$ exhibits several new phenomena including the {\it multiple descent behavior} and the {\it periodic plateau behavior}. As an application, For the neural tangent kernel (NTK), we also provide a similar explicit description of the curve of optimal rate. As a direct corollary, we know these claims hold for wide neural networks as well