Fourier transform for quantum DD-modules via the punctured torus mapping class group

We construct a certain cross product of two copies of the braided dual $\tilde H$ of a quasitriangular Hopf algebra $H$, which we call the elliptic double $E_H$, and which we use to construct representations of the punctured elliptic braid group extending the well-known representations of the planar braid group attached to $H$. We show that the elliptic double is the universal source of such representations. We recover the representations of the punctured torus braid group obtained in arXiv:0805.2766, and hence construct a homomorphism to the Heisenberg double $D_H$, which is an isomorphism if $H$ is factorizable. The universal property of $E_H$ endows it with an action by algebra automorphisms of the mapping class group $\widetilde{SL_2(\mathbb{Z})}$ of the punctured torus. One such automorphism we call the quantum Fourier transform; we show that when $H=U_q(\mathfrak{g})$, the quantum Fourier transform degenerates to the classical Fourier transform on $D(\mathfrak{g})$ as $q\to 1$.Comment: 12 pages, 1 figure. Final version, to appear in Quantum Topolog

The international normalized ratio overestimates coagulopathy in patients after major hepatectomy

Abstract BACKGROUND: The International Normalized Ratio (INR) is commonly used to guide therapy after hepatectomy. We hypothesized that the use of thrombelastography (TEG) would demonstrate a decreased incidence of hypocoagulability in this patient population. METHODS: Seventy-eight patients were prospectively enrolled before undergoing hepatectomy. INR, TEG, and coagulation factors were drawn before incision, postoperatively, and on postoperative days 1, 3, and 5. RESULTS: Patients demonstrated an elevated INR at all postoperative time points. However, TEG demonstrated a decreased R value postoperatively, with subsequent normalization. Other TEG measurements were equivalent to preoperative values. All procoagulant factors save factor VIII decreased postoperatively, with a simultaneous decrease in protein C. CONCLUSIONS: TEG demonstrated a brief hypercoagulable state after major hepatectomy, with coagulation subsequently normalizing. The INR significantly overestimates hypocoagulability after hepatectomy and these data call into question current practices using the INR to guide therapy in this patient population. Ó 2014 Elsevier Inc. All rights reserved. Partial hepatectomy remains the treatment of choice for a wide range of both benign and malignant diseases of the liver. Following major hepatectomy, derangement of hepatic synthetic function has been well characterized, including impaired synthesis of serum clotting factors and regulatory proteins