Quantum Computing and Hidden Variables I: Mapping Unitary to Stochastic Matrices

This paper initiates the study of hidden variables from the discrete, abstract perspective of quantum computing. For us, a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another, into a stochastic matrix that maps the initial probability distribution to the final one in some fixed basis. We list seven axioms that we might want such a theory to satisfy, and then investigate which of the axioms can be satisfied simultaneously. Toward this end, we construct a new hidden-variable theory that is both robust to small perturbations and indifferent to the identity operation, by exploiting an unexpected connection between unitary matrices and network flows. We also analyze previous hidden-variable theories of Dieks and Schrodinger in terms of our axioms. In a companion paper, we will show that actually sampling the history of a hidden variable under reasonable axioms is at least as hard as solving the Graph Isomorphism problem; and indeed is probably intractable even for quantum computers.Comment: 19 pages, 1 figure. Together with a companion paper to appear, subsumes the earlier paper "Quantum Computing and Dynamical Quantum Models" (quant-ph/0205059

Functional rescue of dystrophin deficiency in mice caused by frameshift mutations using Campylobacter jejuni Cas9

Duchenne muscular dystrophy (DMD) is a fatal, X-linked muscle wasting disease caused by mutations in the DMD gene. In 51% of DMD cases, a reading frame is disrupted because of deletion of several exons. Here, we show that CjCas9 derived from Campylobacter jejuni can be used as a gene editing tool to correct an out-of-frame Dmd exon in Dmd knockout mice. Herein, we used Cas9 derived from S. pyogenes to generate Dmd knockout (KO) mice with a frameshift mutation in Dmd gene. Then, we expressed CjCas9, its single-guide RNA, and the eGFP gene in the tibialis anterior muscle of the Dmd KO mice using an all-in-one adeno-associated virus (AAV) vector. CjCas9 cleaved the target site in the Dmd gene efficiently in vivo and induced small insertions or deletions at the target site. This treatment resulted in conversion of the disrupted Dmd reading frame from out-of-frame to in-frame, leading to the expression of dystrophin in the sarcolemma. Importantly, muscle strength was enhanced in the CjCas9-treated muscles, without off-target mutations, indicating high efficiency and specificity of CjCas9. This work suggests that in vivo DMD frame correction, mediated by CjCas9 has great potential for the treatment of DMD and other neuromuscular diseases

An iterative and targeted sampling design informed by habitat suitability models for detecting focal plant species over extensive areas

Prioritizing areas for management of non-native invasive plants is critical, as invasive plants can negatively impact plant community structure. Extensive and multi-jurisdictional inventories are essential to prioritize actions aimed at mitigating the impact of invasions and changes in disturbance regimes. However, previous work devoted little effort to devising sampling methods sufficient to assess the scope of multi-jurisdictional invasion over extensive areas. Here we describe a large-scale sampling design that used species occurrence data, habitat suitability models, and iterative and targeted sampling efforts to sample five species and satisfy two key management objectives: 1) detecting non-native invasive plants across previously unsampled gradients, and 2) characterizing the distribution of non-native invasive plants at landscape to regional scales. Habitat suitability models of five species were based on occurrence records and predictor variables derived from topography, precipitation, and remotely sensed data. We stratified and established field sampling locations according to predicted habitat suitability and phenological, substrate, and logistical constraints. Across previously unvisited areas, we detected at least one of our focal species on 77% of plots. In turn, we used detections from 2011 to improve habitat suitability models and sampling efforts in 2012, as well as additional spatial constraints to increase detections. These modifications resulted in a 96% detection rate at plots. The range of habitat suitability values that identified highly and less suitable habitats and their environmental conditions corresponded to field detections with mixed levels of agreement. Our study demonstrated that an iterative and targeted sampling framework can address sampling bias, reduce time costs, and increase detections. Other studies can extend the sampling framework to develop methods in other ecosystems to provide detection data. The sampling methods implemented here provide a meaningful tool when understanding the potential distribution and habitat of species over multi-jurisdictional and extensive areas is needed for achieving management objectives

Analysis of small-diameter wood supply in northern Arizona - Final report

Forest management to restore fire-adapted ponderosa pine ecosystems is a central priority of the Southwestern Region of the USDA Forest Service. Appropriately-scaled businesses are apt to play a key role in achieving this goal by harvesting, processing and selling wood products, thereby reducing treatment costs and providing economic opportunities. The manner in which treatments occur across northern Arizona, with its multiple jurisdictions and land management areas, is of vital concern to a diversity of stakeholder groups. To identify a level of forest thinning treatments and potential wood supply from restoration byproducts, a 20-member working group representing environmental non-governmental organizations (NGOs), private forest industries, local government, the Ecological Restoration Institute at Northern Arizona University (NAU), and state and federal land and resource management agencies was assembled. A series of seven workshops supported by Forest Ecosystem Restoration Analysis (ForestERA; NAU) staff were designed to consolidate geographic data and other spatial information and to synthesize potential treatment scenarios for a 2.4 million acre analysis area south of the Grand Canyon and across the Mogollon Plateau. A total of 94% of the analysis area is on National Forest lands. ForestERA developed up-to-date remote sensing-based forest structure data layers to inform the development of treatment scenarios, and to estimate wood volume in three tree diameter classes of 16" diameter at breast height (dbh, 4.5' above base). For the purposes of this report, the group selected a 16" dbh threshold due to its common use within the analysis landscape as a break point differentiating "small" and "large" diameter trees in the ponderosa pine forest type. The focus of this study was on small-diameter trees, although wood supply estimates include some trees >16" dbh where their removal was required to meet desired post-treatment conditions.4 There was no concurrence within the group that trees over 16" dbh should be cut and removed from areas outside community protection management areas (CPMAs)..

Separable Dual Space Gaussian Pseudo-potentials

We present pseudo-potential coefficients for the first two rows of the periodic table. The pseudo potential is of a novel analytic form, that gives optimal efficiency in numerical calculations using plane waves as basis set. At most 7 coefficients are necessary to specify its analytic form. It is separable and has optimal decay properties in both real and Fourier space. Because of this property, the application of the nonlocal part of the pseudo-potential to a wave-function can be done in an efficient way on a grid in real space. Real space integration is much faster for large systems than ordinary multiplication in Fourier space since it shows only quadratic scaling with respect to the size of the system. We systematically verify the high accuracy of these pseudo-potentials by extensive atomic and molecular test calculations.Comment: 16 pages, 4 postscript figure

Elliptic Solitons and Groebner Bases

We consider the solution of spectral problems with elliptic coefficients in the framework of the Hermite ansatz. We show that the search for exactly solvable potentials and their spectral characteristics is reduced to a system of polynomial equations solvable by the Gr\"obner bases method and others. New integrable potentials and corresponding solutions of the Sawada-Kotera, Kaup-Kupershmidt, Boussinesq equations and others are found.Comment: 18 pages, no figures, LaTeX'2

The Jet of 3C 17 and the Use of Jet Curvature as a Diagnostic of the X-ray Emission Process

We report on the X-ray emission from the radio jet of 3C 17 from Chandra observations and compare the X-ray emission with radio maps from the VLA archive and with the optical-IR archival images from the Hubble Space Telescope. X-ray detections of two knots in the 3C 17 jet are found and both of these features have optical counterparts. We derive the spectral energy distribution for the knots in the jet and give source parameters required for the various X-ray emission models, finding that both IC/CMB and synchrotron are viable to explain the high energy emission. A curious optical feature (with no radio or X-ray counterparts) possibly associated with the 3C 17 jet is described. We also discuss the use of curved jets for the problem of identifying inverse Compton X-ray emission via scattering on CMB photons.Comment: 6 pages, 6 figure (3 in color), 4 tables, ApJ accepte

A Census Of Highly Symmetric Combinatorial Designs

As a consequence of the classification of the finite simple groups, it has been possible in recent years to characterize Steiner t-designs, that is t-(v,k,1) designs, mainly for t = 2, admitting groups of automorphisms with sufficiently strong symmetry properties. However, despite the finite simple group classification, for Steiner t-designs with t > 2 most of these characterizations have remained longstanding challenging problems. Especially, the determination of all flag-transitive Steiner t-designs with 2 < t < 7 is of particular interest and has been open for about 40 years (cf. [11, p. 147] and [12, p. 273], but presumably dating back to 1965). The present paper continues the author's work [20, 21, 22] of classifying all flag-transitive Steiner 3-designs and 4-designs. We give a complete classification of all flag-transitive Steiner 5-designs and prove furthermore that there are no non-trivial flag-transitive Steiner 6-designs. Both results rely on the classification of the finite 3-homogeneous permutation groups. Moreover, we survey some of the most general results on highly symmetric Steiner t-designs.Comment: 26 pages; to appear in: "Journal of Algebraic Combinatorics

Perverse coherent t-structures through torsion theories

Bezrukavnikov (later together with Arinkin) recovered the work of Deligne defining perverse $t$-structures for the derived category of coherent sheaves on a projective variety. In this text we prove that these $t$-structures can be obtained through tilting torsion theories as in the work of Happel, Reiten and Smal\o. This approach proves to be slightly more general as it allows us to define, in the quasi-coherent setting, similar perverse $t$-structures for certain noncommutative projective planes.Comment: New revised version with important correction