Lower Bounds on the State Complexity of Geometric Goppa Codes

We reinterpret the state space dimension equations for geometric Goppa codes. An easy consequence is that if deg G less than or equal to n-2/2 or deg G greater than or equal to n-2/2 + 2g then the state complexity of C-L(D, G) is equal to the Wolf bound. For deg G is an element of [n-1/2, n-3/2 + 2g], we use Clifford's theorem to give a simple lower bound on the state complexity of C-L(D, G). We then derive two further lower bounds on the state space dimensions of C-L(D, G) in terms of the gonality sequence of F/F-q. (The gonality sequence is known for many of the function fields of interest for defining geometric Goppa codes.) One of the gonality bounds uses previous results on the generalised weight hierarchy of C-L(D, G) and one follows in a straightforward way from first principles; often they are equal. For Hermitian codes both gonality bounds are equal to the DLP lower bound on state space dimensions. We conclude by using these results to calculate the DLP lower bound on state complexity for Hermitian codes.

Automatic construction of explicit R matrices for the one-parameter families of irreducible typical highest weight (0(m)vertical bar alpha(n)) representations of U-q[gl(m vertical bar n)]

We detail the automatic construction of R matrices corresponding to (the tensor products of) the (O-m\alpha(n)) families of highest-weight representations of the quantum superalgebras Uq[gl(m\n)]. These representations are irreducible, contain a free complex parameter a, and are 2(mn)-dimensional. Our R matrices are actually (sparse) rank 4 tensors, containing a total of 2(4mn) components, each of which is in general an algebraic expression in the two complex variables q and a. Although the constructions are straightforward, we describe them in full here, to fill a perceived gap in the literature. As the algorithms are generally impracticable for manual calculation, we have implemented the entire process in MATHEMATICA; illustrating our results with U-q [gl(3\1)]. (C) 2002 Published by Elsevier Science B.V.

Attitudes of paediatric medical ward staff to a dog visitation programme

No previous studies regarding either structured, strictly controlled pet visitation programmes in paediatric hospital wards or hospital staff attitudes towards them have been conducted in Australia. Information regarding these is essential in order to minimize problems during implementation of such programmes. The aim of the study was to analyse hospital staff perceptions regarding the introduction of a pet visitation programme in an acute paediatric medical ward prior to and following implementation of the programme and to compare attitudes between the various professional groups. The study consisted of two cross-sectional surveys. A total of 224 anonymous questionnaires were distributed to administrators, doctors, nursing staff and therapists 6 weeks before and 195 were distributed 12 weeks after the introduction of a pet visitation programme. Responses were received from 115 respondents (before the programme introduction) and 45 respondents (after the programme introduction). Prior to the introduction of the dog visitation programme, there were high staff expectations that the programme would distract children from their illness, relax children and that it was a worthwhile project for the hospital to undertake. Following implementation of the programme these expectations were strongly endorsed, in addition to the perception that the ward was a happier place, the work environment was more interesting and that nurses accepted the dogs. After implementation staff were less concerned about the possibility of dog bites and dogs doing damage to equipment. Allied health staff and non-clinical staff were more positive about the programme with respect to ward climate and acceptance than were doctors and nurses. We conclude that well-planned dog visitation programmes result in positive anticipation among staff and high levels of satisfaction following programme impact.

One-dimensional quantum walk with unitary noise

The effect of unitary noise on the discrete one-dimensional quantum walk is studied using computer simulations. For the noiseless quantum walk, starting at the origin (n=0) at time t=0, the position distribution P-t(n) at time t is very different from the Gaussian distribution obtained for the classical random walk. Furthermore, its standard deviation, sigma(t) scales as sigma(t)similar tot, unlike the classical random walk for which sigma(t)similar toroott. It is shown that when the quantum walk is exposed to unitary noise, it exhibits a crossover from quantum behavior for short times to classical-like behavior for long times. The crossover time is found to be Tsimilar toalpha(-2), where alpha is the standard deviation of the noise.

gl(2 vertical bar 2) current superalgebra and non-unitary conformal field theory

Motivated by application of current superalgebras in the study of disordered systems such as the random XY and Dirac models, we investigate gl(2\2) current superalgebra at general level k. We construct its free field representation and corresponding Sugawara energy-momentum tensor in the non-standard basis. Three screen currents of the first kind are also presented. (C) 2003 Elsevier B.V. All rights reserved.

Entangled subspaces and quantum symmetries

Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt decomposition of the projection operator defines a string of Schmidt coefficients for each subspace, and this string is assumed to characterize its entanglement, so that a first subspace is more entangled than a second, if the Schmidt string of the second majorizes the Schmidt string of the first. The idea is applied to the antisymmetric and symmetric tensor products of a finite-dimensional Hilbert space with itself, and also to the tensor product of an angular momentum j with a spin 1/2. When adapted to the subspaces of states of the nonrelativistic hydrogen atom with definite total angular momentum (orbital plus spin), within the space of bound states with a given total energy, this leads to a complete ordering of those subspaces by their Schmidt strings.

Pseudo memory effects, majorization and entropy in quantum random walks

A quantum random walk on the integers exhibits pseudo memory effects, in that its probability distribution after N steps is determined by reshuffling the first N distributions that arise in a classical random walk with the same initial distribution. In a classical walk, entropy increase can be regarded as a consequence of the majorization ordering of successive distributions. The Lorenz curves of successive distributions for a symmetric quantum walk reveal no majorization ordering in general. Nevertheless, entropy can increase, and computer experiments show that it does so on average. Varying the stages at which the quantum coin system is traced out leads to new quantum walks, including a symmetric walk for which majorization ordering is valid but the spreading rate exceeds that of the usual symmetric quantum walk.

Coherent state construction of representations of osp(2|2) and primary fields of osp(2|2) conformal field theory

Representations of the superalgebra osp(2/2)(k)((1)) and current superalgebra. osp(2/2)k in the standard basis are investigated. All finite-dimensional typical and atypical representations of osp(2/2) are constructed by the vector coherent state method. Primary fields of the non-unitary conformal field theory associated with osp(2/2)(k)((1)) in the standard basis are obtained for arbitrary level k. (C) 2004 Elsevier B.V. All rights reserved.

Solution of the dual reflection equation for A(n-1)((1)) solid-on-solid model

We obtain a diagonal solution of the dual reflection equation for the elliptic A(n-1)((1)) solid-on-solid model. The isomorphism between the solutions of the reflection equation and its dual is studied. (C) 2004 American Institute of Physics.

Fungible dynamics: There are only two types of entangling multiple-qubit interactions

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? It has been shown that all two-body Hamiltonian evolutions can be simulated using any fixed two-body entangling n-qubit Hamiltonian and fast local unitaries. By entangling we mean that every qubit is coupled to every other qubit, if not directly, then indirectly via intermediate qubits. We extend this study to the case where interactions may involve more than two qubits at a time. We find necessary and sufficient conditions for an arbitrary n-qubit Hamiltonian to be dynamically universal, that is, able to simulate any other Hamiltonian acting on n qubits, possibly in an inefficient manner. We prove that an entangling Hamiltonian is dynamically universal if and only if it contains at least one coupling term involving an even number of interacting qubits. For odd entangling Hamiltonians, i.e., Hamiltonians with couplings that involve only an odd number of qubits, we prove that dynamic universality is possible on an encoded set of n-1 logical qubits. We further prove that an odd entangling Hamiltonian can simulate any other odd Hamiltonian and classify the algebras that such Hamiltonians generate. Thus, our results show that up to local unitary operations, there are only two fundamentally different types of entangling Hamiltonian on n qubits. We also demonstrate that, provided the number of qubits directly coupled by the Hamiltonian is bounded above by a constant, our techniques can be made efficient.

Do decomposing organic matter residues reduce phosphorus sorption in highly weathered soils?

Many studies have shown a reduction in P sorption in highly weathered soils when organic matter (OM) is applied, suggesting competition between OM decomposition products and P for sorption sites. However, such studies seldom consider the P released from the added OM. To delineate the effects of OM addition on P availability through sorption competition and P addition, water leachate from incubated soybean (SB) [Glycine mar (L.) Merr.] and Rhodes grass (RG) (Chloris gayana Knuth cv. Callide) was used in competitive P sorption studies both undiluted and after acidification (i.e., the fulvic acid [FA] component). Addition of two rates (0.2 and 2 mL) of SB leachate to an Oxisol significantly increased P sorption at the higher rate, while a similar trend was observed following RG leachate addition at the same rates. Extending the range of highly weathered soils examined (two Oxisols, an Ultisol, and an acidic Vertisol) resulted in no observed decrease in P sorption following addition of OM leachate. Surprisingly, SB leachate transiently increased P sorption in the two Oxisol soils. Addition of the FA component of the leachates resulted in a transient (< 6 d) decrease in P sorption in three of the four soils examined and constituted the only evidence in this study that decomposing OM residues reduced P sorption. This research provides further evidence contradicting the long held assumption that inhibition of P sorption by dissolved organic compounds, derived from decomposing OM, is responsible for increased P phytoavailability when P fertilizer and OM are applied together.

Assessment of P availability in heavily fertilized soils using the diffusive gradient in thin films (DGT) technique

Phosphorus-availability tests typically provide an indication of quantity of P available (Colwell bicarbonate-extractable P), or of the intensity of supply (0.01 M CaCl2-extractable P). The soil's capacity to buffer P is more difficult to assess, and is generally estimated using a P-adsorption curve. The diffusive gradient in thin films (DGT) approach may provide a simpler means of assessing a soil's ability to maintain soil solution P. Optimal extraction conditions were found to be 24 h exposure of DGT samplers to saturated soil. The DGT approach was evaluated on a range of 24 soils, some of which had high Colwell- (>100 mu g g(-1)) and Bray 1- (>30 mu g g(-1)) extractable P content, but showed a tomato (Lycopersicon esculentum Mill.) yield response to the addition of P fertilizer. The DGT approach provided an excellent separation of soils on which tomato showed a yield response, from those where fertilizer P did not increase dry-matter yield. Phosphorus accumulation was strongly correlated with soil solution P concentration and anion exchange resin-extractable P, but showed poor correlation with Colwell- or Bray 1-extractable P. The DGT P accumulation rate of 3.62 x 10(-7) to 4.79 x 10(-5) mol s(-1) m(-3) for the soils tested was comparable to the uptake rate of roots of tomato plants that were adequately supplied with P (2.25 x 10(-5) mol s(-1) m(-3)).

Competitive sorption reactions between phosphorus and organic matter in soil: a review

The incorporation of organic matter ( OM) in soils that are able to rapidly sorb applied phosphorus ( P) fertiliser reportedly increases P availability to plants. This effect has commonly been ascribed to competition between the decomposition products of OM and P for soil sorption sites resulting in increased soil solution P concentrations. The evidence for competitive inhibition of P sorption by dissolved organic carbon compounds, derived from the breakdown of OM, includes studies on the competition between P and (i) low molecular weight organic acids (LOAs), (ii) humic and fulvic acids, and (iii) OM leachates in soils with a high P sorption capacity. These studies, however, have often used LOAs at 1 - 100 mM, concentrations much higher than those in soils ( generally < 0.05 mM). The transience of LOAs in biologically active soils further suggests that neither their concentration nor their persistence would have a practical benefit in increasing P phytoavailability. Higher molecular weight compounds such as humic and fulvic acids also competitively inhibit P sorption; however, little consideration has been given to the potential of these compounds to increase the amount of P sorbed through metal - chelate linkages. We suggest that the magnitude of the inhibition of P sorption by the decomposition products of OM leachate is negligible at rates equivalent to those of OM applied in the field. Incubation of OM in soil has also commonly been reported as reducing P sorption in soil. However, we consider that the reported decreases in P sorption ( as measured by P in the soil solution) are not related to competition from the decomposition products of OM breakdown, but are the result of P release from the OM that was not accounted for when calculating the reduction in P sorption.

Primary Fields and Screening Currents of gl (2/2) non-unitary conformal field theory

The non-semisimple gl(2)k current superalgebra in the standard basis and the corresponding non-unitary conformal field theory are investigated. Infinite families of primary fields corresponding to all finite-dimensional irreducible typical and atypical representations of gl(212) and three (two even and one odd) screening currents of the first kind are constructed explicitly in terms of ten free fields. (C) 2004 Elsevier B.V All rights reserved.