A Combinatorial Model for Exceptional Sequences in Type A

Exceptional sequences are certain ordered sequences of quiver representations. We use noncrossing edge-labeled trees in a disk with boundary vertices (expanding on T. Araya's work) to classify exceptional sequences of representations of Q, the linearly-ordered quiver with n vertices. We also show how to use variations of this model to classify c-matrices of Q, to interpret exceptional sequences as linear extensions, and to give a simple bijection between exceptional sequences and certain chains in the lattice of noncrossing partitions. In the case of c-matrices, we also give an interpretation of c-matrix mutation in terms of our noncrossing trees with directed edges.Comment: 18 page

Escaping the Shadow of Malpractice Law

Abinovich-Einy addresses several constituencies operating at the meeting point of alternative dispute resolution (ADR), communication theory, healthcare policy, and medical-malpractice doctrine. From an ADR perspective, the need for, and barriers to, addressing non-litigable disputes, for which the alternative route is the only one, is explored. It is shown that ADR mechanisms may not take root when introduced into an environment that is resistant to collaborative and open discourse without additional incentives and measures being adopted

Court Reform in England

In this report, the Direct Weight Optimization (DWO) approach to function estimation is studied for two special function classes: The classes of approximately constant and approximately linear functions. These classes consist of functions whose deviation from a constant/affine function is bounded by a known constant. Upper and lower bounds for the asymptotic maximum MSE are given, some of whic halso hold in the non-asymptotic case

Self-Sufficiency Under the Education for All Handicapped Children Act: A Suggested Judicial Approach

The Direct Weight Optimization (DWO) approach to statistical estimation and the application to nonlinear system identification has been proposed and developed during the last few years. Computationally, the approachis typically reduced to a convex (e.g., quadratic or conic) program, whichcan be solved efficiently. The optimality or sub-optimality of the obtained estimates, in a minimax sense w.r.t. the estimation error criterion, can be analyzed under weak a priori conditions. The main ideas of the approach are discussed here and an overview of the obtained results is presented

Tunability of Andreev levels via spin-orbit coupling in Zeeman-split Josephson junctions

We study Andreev reflection and Andreev levels $\varepsilon$ in Zeeman-split superconductor/Rashba wire/Zeeman-split superconductor junctions by solving the Bogoliubov de-Gennes equation. We theoretically demonstrate that the Andreev levels $\varepsilon$ can be controlled by tuning either the strength of Rashba spin-orbit interaction or the relative direction of the Rashba spin-orbit interaction and the Zeeman field. In particular, it is found that the magnitude of the band splitting is tunable by the strength of the Rashba spin-orbit interaction and the rength of the wire, which can be interpreted by a spin precession in the Rashba wire. We also find that if the Zeeman field in the superconductor has the component parallel to the direction of the junction, the $\varepsilon$-$\phi$ curve becomes asymmetric with respect to the superconducting phase difference $\phi$. Whereas the Andreev reflection processes associated with each pseudospin band are sensitive to the relative orientation of the spin-orbit field and the exchange field, the total electric conductance interestingly remains invariant.Comment: 10 pages, 8 figure