Ngā mahi: Kaupapa Māori outcomes and indicators kete

As part of the Planning Under Cooperative Mandates research (PUCM) we developed a kaupapa Māori outcomes and indicators framework. This framework reflects tikanga Māori and Māori values. It also considers issues (including environmental issues) according to those tikanga that particular issues invoke. For example, tikanga brought into play in relation to council treatment and disposal of sewerage include tapu (sacred), and might also impact on the mauri (life-force) of water if treated effluent were to enter waterways. The intention of our research has been to clarify and define key Māori environmental concepts so that stakeholders (including council staff) will have a terms of reference against which they can compare desired environmental outcomes from different perspectives and be better placed to integrate Māori environmental outcomes into planning processes. The end-point is this Nga Mahi kete report containing tikanga-based worksheets and the guidelines for using them

First-order definable string transformations

The connection between languages defined by computational models and logic for languages is well-studied. Monadic second-order logic and finite automata are shown to closely correspond to each-other for the languages of strings, trees, and partial-orders. Similar connections are shown for first-order logic and finite automata with certain aperiodicity restriction. Courcelle in 1994 proposed a way to use logic to define functions over structures where the output structure is defined using logical formulas interpreted over the input structure. Engelfriet and Hoogeboom discovered the corresponding "automata connection" by showing that two-way generalised sequential machines capture the class of monadic-second order definable transformations. Alur and Cerny further refined the result by proposing a one-way deterministic transducer model with string variables---called the streaming string transducers---to capture the same class of transformations. In this paper we establish a transducer-logic correspondence for Courcelle's first-order definable string transformations. We propose a new notion of transition monoid for streaming string transducers that involves structural properties of both underlying input automata and variable dependencies. By putting an aperiodicity restriction on the transition monoids, we define a class of streaming string transducers that captures exactly the class of first-order definable transformations.Comment: 31 page

A Novel Antigen Sensitive to Calcium Chelation That is Associated with the Tip Links and Kinocilial Links of Sensory Hair Bundles

Tip links are extracellular, cell-surface-associated filaments of unknown molecular composition that are thought to gate the mechanotransducer channel of the sensory hair cell. They disappear from the hair bundle in response to calcium chelation and lanthanum treatment and resist degradation by the protease subtilisin. A monoclonal antibody derived from a hybridoma screen identified a novel antigen associated with tip links, the tip-link antigen. The tip-link antigen is also associated with kinocilial links, subtilisin-resistant filaments that are sensitive to calcium chelation and connect the kinocilium to the tallest stereocilia of the hair bundle. Furthermore, the tip-link antigen is expressed in the retina, where it is associated with the ciliary calyx, a ring of microvilli that surrounds the outer segment of the photoreceptor. The tip-link antigen rapidly disappears from the surface of the hair bundle in response to calcium chelation. It is also subtilisin resistant, relative to the ankle-link antigen, an antigen associated with another type of hair bundle link. The tip-link antigen is lanthanum sensitive and, like tip links, reappears on the surface of the hair bundle after calcium chelation. The monoclonal antibody to the tip-link antigen immunoprecipitates two concanavalin A-reactive polypeptides with apparent molecular masses of 200 and 250 kDa from detergent extracts of the retina. These results provide the first identification of a cell surface antigen associated with tip links, indicate that tip links share properties in common with kinocilial links, and reveal a second epitope that, along with the ankle-link antigen, is common to both sensory hair bundles and the ciliary calyx of photoreceptors

Jump-like unravelings for non-Markovian open quantum systems

Non-Markovian evolution of an open quantum system can be `unraveled' into pure state trajectories generated by a non-Markovian stochastic (diffusive) Schr\"odinger equation, as introduced by Di\'osi, Gisin, and Strunz. Recently we have shown that such equations can be derived using the modal (hidden variable) interpretation of quantum mechanics. In this paper we generalize this theory to treat jump-like unravelings. To illustrate the jump-like behavior we consider a simple system: A classically driven (at Rabi frequency $\Omega$) two-level atom coupled linearly to a three mode optical bath, with a central frequency equal to the frequency of the atom, $\omega_0$, and the two side bands have frequencies $\omega_0\pm\Omega$. In the large $\Omega$ limit we observed that the jump-like behavior is similar to that observed in this system with a Markovian (broad band) bath. This is expected as in the Markovian limit the fluorescence spectrum for a strongly driven two level atom takes the form of a Mollow triplet. However the length of time for which the Markovian-like behaviour persists depends upon {\em which} jump-like unraveling is used.Comment: 11 pages, 5 figure

Weighted estimates for powers and smoothing estimates of Schrödinger operators with inverse-square potentials

Let \La be a Schr\"odinger operator with inverse square potential $a|x|^{-2}$ on \Rd, d\geq 3. The main aim of this paper is to prove weighted estimates for fractional powers of \La. The proof is based on weighted Hardy inequalities and weighted inequalities for square functions associated to \La. As an application, we obtain smoothing estimates regarding the propagator e^{it\La}