Anchored burning bijections on finite and infinite graphs

Let $G$ be an infinite graph such that each tree in the wired uniform spanning forest on $G$ has one end almost surely. On such graphs $G$, we give a family of continuous, measure preserving, almost one-to-one mappings from the wired spanning forest on $G$ to recurrent sandpiles on $G$, that we call anchored burning bijections. In the special case of $\mathbb{Z}^d$, $d \ge 2$, we show how the anchored bijection, combined with Wilson's stacks of arrows construction, as well as other known results on spanning trees, yields a power law upper bound on the rate of convergence to the sandpile measure along any exhaustion of $\mathbb{Z}^d$. We discuss some open problems related to these findings.Comment: 26 pages; 1 EPS figure. Minor alterations made after comments from refere

Squeezing as an irreducible resource

We show that squeezing is an irreducible resource which remains invariant under transformations by linear optical elements. In particular, we give a decomposition of any optical circuit with linear input-output relations into a linear multiport interferometer followed by a unique set of single mode squeezers and then another multiport interferometer. Using this decomposition we derive a no-go theorem for superpositions of macroscopically distinct states from single-photon detection. Further, we demonstrate the equivalence between several schemes for randomly creating polarization-entangled states. Finally, we derive minimal quantum optical circuits for ideal quantum non-demolition coupling of quadrature-phase amplitudes.Comment: 4 pages, 3 figures, new title, removed the fat

Tensor Generalizations of Affine Symmetry Vectors

A definition is suggested for affine symmetry tensors, which generalize the notion of affine vectors in the same way that (conformal) Killing tensors generalize (conformal) Killing vectors. An identity for these tensors is proved, which gives the second derivative of the tensor in terms of the curvature tensor, generalizing a well-known identity for affine vectors. Additionally, the definition leads to a good definition of homothetic tensors. The inclusion relations between these types of tensors are exhibited. The relationship between affine symmetry tensors and solutions to the equation of geodesic deviation is clarified, again extending known results about Killing tensors.Comment: 11 page

Bowel Perforation in the Emergency Department Related to Bevacizumab Therapy and Recurrent Ovarian Cancer

Case Presentation: We describe the presentation to the emergency department of a patient with recurrent ovarian cancer treated with bevacizumab with the complication of bowel perforation. Discussion: We review the frequency and outcomes of bevacizumab-related bowel perforation. We also report the patient’s imaging findings, including the radiologic presentation of free intraperitoneal air and portal venous gas, both indicative of bowel perforation and the need for emergent surgical evaluation. Our case also illustrates the potentially catastrophic side effects of bevacizumab and other targeted oncologic therapies of which emergecny physicians may not be aware

A quantum analog of Huffman coding

We analyze a generalization of Huffman coding to the quantum case. In particular, we notice various difficulties in using instantaneous codes for quantum communication. Nevertheless, for the storage of quantum information, we have succeeded in constructing a Huffman-coding inspired quantum scheme. The number of computational steps in the encoding and decoding processes of N quantum signals can be made to be of polylogarithmic depth by a massively parallel implementation of a quantum gate array. This is to be compared with the O (N^3) computational steps required in the sequential implementation by Cleve and DiVincenzo of the well-known quantum noiseless block coding scheme of Schumacher. We also show that O(N^2(log N)^a) computational steps are needed for the communication of quantum information using another Huffman-coding inspired scheme where the sender must disentangle her encoding device before the receiver can perform any measurements on his signals.Comment: Revised version, 7 pages, two-column, RevTex. Presented at 1998 IEEE International Symposium on Information Theor