Existence of the Wigner function with correct marginal distributions along tilted lines on a lattice

In order to determine the Wigner function uniquely, we introduce a new condition which ensures that the Wigner function has correct marginal distributions along tilted lines. For a system in $N$ dimensional Hilbert space, whose "phase space" is a lattice with $N^2$ sites, we get different results depending on whether $N$ is odd or even. Under the new condition, the Wigner function is determined if $N$ is an odd number, but it does not exist if $N$ is even.Comment: 18 page

Wigner Functions on a Lattice

The Wigner functions on the one dimensional lattice are studied. Contrary to the previous claim in literature, Wigner functions exist on the lattice with any number of sites, whether it is even or odd. There are infinitely many solutions satisfying the conditions which reasonable Wigner functions should respect. After presenting a heuristic method to obtain Wigner functions, we give the general form of the solutions. Quantum mechanical expectation values in terms of Wigner functions are also discussed.Comment: 11 pages, no figures, REVTE

Multiple early gastric cancer with duodenal invasion

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The Ndc80 Loop Region Facilitates Formation of Kinetochore Attachment to the Dynamic Microtubule Plus End

Proper chromosome segregation in mitosis relies on correct kinetochore-microtubule (KT-MT) interactions. The KT initially interacts with the lateral surface of a single MT (lateral attachment) extending from a spindle pole and is subsequently anchored at the plus end of the MT (end-on attachment) [1]. The conversion from lateral to end-on attachment is crucial because end-on attachment is more robust [2–4] and thought to be necessary to sustain KT-MT attachment when tension is applied across sister KTs upon their biorientation [1]. The mechanism for this conversion is still elusive. The Ndc80 complex is an essential component of the KT-MT interface [1, 5], and here we studied a role of the Ndc80 loop region, a distinct motif looping out from the coiled-coil shaft of the complex [6], in Saccharomyces cerevisiae. With deletions or mutations of the loop region, the lateral KT-MT attachment occurred normally; however, subsequent conversion to end-on attachment was defective, leading to failure in sister KT biorientation. The Ndc80 loop region was required for Ndc80-Dam1 interaction and KT loading of the Dam1 complex, which in turn supported KT tethering to the dynamic MT plus end [3, 7]. The Ndc80 loop region, therefore, has an important role in the conversion from lateral to end-on attachment, a crucial maturation step of KT-MT interaction