Quantum walks as a probe of structural anomalies in graphs

We study how quantum walks can be used to find structural anomalies in graphs via several examples. Two of our examples are based on star graphs, graphs with a single central vertex to which the other vertices, which we call external vertices, are connected by edges. In the basic star graph, these are the only edges. If we now connect a subset of the external vertices to form a complete subgraph, a quantum walk can be used to find these vertices with a quantum speedup. Thus, under some circumstances, a quantum walk can be used to locate where the connectivity of a network changes. We also look at the case of two stars connected at one of their external vertices. A quantum walk can find the vertex shared by both graphs, again with a quantum speedup. This provides an example of using a quantum walk in order to find where two networks are connected. Finally, we use a quantum walk on a complete bipartite graph to find an extra edge that destroys the bipartite nature of the graph.Comment: 10 pages, 2 figure

Approximating incompatible von Neumann measurements simultaneously

We study the problem of performing orthogonal qubit measurements simultaneously. Since these measurements are incompatible, one has to accept additional imprecision. An optimal joint measurement is the one with the least possible imprecision. All earlier considerations of this problem have concerned only joint measurability of observables, while in this work we also take into account conditional state transformations (i.e., instruments). We characterize the optimal joint instrument for two orthogonal von Neumann instruments as being the Luders instrument of the optimal joint observable.Comment: 9 pages, 4 figures; v2 has a more extensive introduction + other minor correction

The central limit problem for random vectors with symmetries

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein's method of exchangeable pairs; as far as we know, this approach has not previously been used in convex geometry and we give a brief introduction to the classical method. The spherically symmetric case is treated by a variation of Stein's method which is adapted for continuous symmetries.Comment: AMS-LaTeX, uses xy-pic, 23 pages; v3: added new corollary to Theorem

Observing Nucleon Decay in Lead Perchlorate

Lead perchlorate, part of the OMNIS supernova neutrino detector, contains two nuclei, 208Pb and 35Cl, that might be used to study nucleon decay. Both would produce signatures that will make them especially useful for studying less-well-studied neutron decay modes, e.g., those in which only neutrinos are emitted.Comment: 6 pages, 2 figure

Cytotoxic T-cells mediate exercise-induced reductions in tumor growth

Funder: Vetenskapsrådet; FundRef: http://dx.doi.org/10.13039/501100004359Funder: Cancerfonden; FundRef: http://dx.doi.org/10.13039/501100002794Funder: Barncancerfonden; FundRef: http://dx.doi.org/10.13039/501100006313Funder: Svenska Läkaresällskapet; FundRef: http://dx.doi.org/10.13039/501100007687Funder: Cancer Research UK; FundRef: http://dx.doi.org/10.13039/501100000289Funder: Medical Research Council; FundRef: http://dx.doi.org/10.13039/501100000265Exercise has a wide range of systemic effects. In animal models, repeated exertion reduces malignant tumor progression, and clinically, exercise can improve outcome for cancer patients. The etiology of the effects of exercise on tumor progression are unclear, as are the cellular actors involved. We show here that in mice, exercise-induced reduction in tumor growth is dependent on CD8+ T cells, and that metabolites produced in skeletal muscle and excreted into plasma at high levels during exertion in both mice and humans enhance the effector profile of CD8+ T-cells. We found that activated murine CD8+ T cells alter their central carbon metabolism in response to exertion in vivo, and that immune cells from trained mice are more potent antitumor effector cells when transferred into tumor-bearing untrained animals. These data demonstrate that CD8+ T cells are metabolically altered by exercise in a manner that acts to improve their antitumoral efficacy