Causal and localizable quantum operations

We examine constraints on quantum operations imposed by relativistic causality. A bipartite superoperator is said to be localizable if it can be implemented by two parties (Alice and Bob) who share entanglement but do not communicate, it is causal if the superoperator does not convey information from Alice to Bob or from Bob to Alice. We characterize the general structure of causal complete-measurement superoperators, and exhibit examples that are causal but not localizable. We construct another class of causal bipartite superoperators that are not localizable by invoking bounds on the strength of correlations among the parts of a quantum system. A bipartite superoperator is said to be semilocalizable if it can be implemented with one-way quantum communication from Alice to Bob, and it is semicausal if it conveys no information from Bob to Alice. We show that all semicausal complete-measurement superoperators are semi localizable, and we establish a general criterion for semicausality. In the multipartite case, we observe that a measurement superoperator that projects onto the eigenspaces of a stabilizer code is localizable.

Determining when the absolute state complexity of a Hermitian code achieves its DLP bound

Let g be the genus of the Hermitian function field H/F(q)2 and let C-L(D,mQ(infinity)) be a typical Hermitian code of length n. In [Des. Codes Cryptogr., to appear], we determined the dimension/length profile (DLP) lower bound on the state complexity of C-L(D,mQ(infinity)). Here we determine when this lower bound is tight and when it is not. For m less than or equal to n-2/2 or m greater than or equal to n-2/2 + 2g, the DLP lower bounds reach Wolf's upper bound on state complexity and thus are trivially tight. We begin by showing that for about half of the remaining values of m the DLP bounds cannot be tight. In these cases, we give a lower bound on the absolute state complexity of C-L(D,mQ(infinity)), which improves the DLP lower bound. Next we give a good coordinate order for C-L(D,mQ(infinity)). With this good order, the state complexity of C-L(D,mQ(infinity)) achieves its DLP bound (whenever this is possible). This coordinate order also provides an upper bound on the absolute state complexity of C-L(D,mQ(infinity)) (for those values of m for which the DLP bounds cannot be tight). Our bounds on absolute state complexity do not meet for some of these values of m, and this leaves open the question whether our coordinate order is best possible in these cases. A straightforward application of these results is that if C-L(D,mQ(infinity)) is self-dual, then its state complexity (with respect to the lexicographic coordinate order) achieves its DLP bound of n /2 - q(2)/4, and, in particular, so does its absolute state complexity.

Relationship of XIST expression and responses of ovarian cancer to chemotherapy

Expression profiling to characterize cancer pharmacology has become a new approach to discover novel molecular targets for prognostic markers and cancer therapy. In a study to compare the global RNA expression profiles between primary and recurrent ovarian tumors from the same patient, we have identified XIST (inactive X chromosome-specific transcripts) as the most differentially expressed gene that was down-regulated in the recurrent tumor. XIST encodes a spliced noncoding polyadenylated transcript that is unique in being expressed exclusively from the inactive X chromosome and is involved in the X-inactivation process. Subsequent characterization of XIST expression in a panel of female cancer cell lines showed that the expression level of XIST correlates significantly with Taxol sensitivity. The clinical relevance of this observation is demonstrated by the strong association between XIST RNA levels and disease-free periods of ovarian cancer patients in a group of 21 ovarian cancer cases with Taxol in the therapeutic regiments. Cytogenetic studies on ovarian cancer cell lines indicated that loss of inactive X chromosome is one mechanism for the loss of XIST transcripts in the cell lines. Our data suggest that XIST expression may be a potential marker for chemotherapeutic responses in ovarian cancer.

Synthesis of fluorinated 2-phenyl-4-quinolones from pyrrole-2,3-diones

A series of substituted 2-phenyl-4-quinolones 8-11 have been synthesized in good yields via ash vacuum thermolysis (FVT) of 1-aryl-4-cyano-5-phenylpyrrole-2,3-diones 7a-e and 1-aryl-4-methoxycarbonyl-5-phenylpyrrole-2,3-diones 7f-j. The pyrrolediones 7 were prepared from amines 3 and benzoylacetonitriles 5a-e or methyl 3-arylamino-3-phenylprop-2-enoates 5f-j.

Computation of the linear elastic properties of random porous materials with a wide variety of microstructure

A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.

Can the nitrogenous composition of xylem sap be used to assess salinity stress in Casuarina glauca?

It is predicted that dryland salinity will affect up to 17 Mha of the Australian landscape by 2050, and therefore, monitoring the health of tree plantings and remnant native vegetation in saline areas is increasingly important. Casuarina glauca Sieber ex Spreng. has considerable salinity tolerance and is commonly planted in areas with a shallow, saline water table. To evaluate the potential of using the nitrogenous composition of xylem sap to assess salinity stress in C. glauca, the responses of trees grown with various soil salinities in a greenhouse were compared with those of trees growing in field plots with different water table depths and groundwater salinities. In the greenhouse, increasing soil salinity led to increased allocation of nitrogen (N) to proline and arginine in both stem and root xylem sap, with coincident decreases in citrulline and asparagine. Although the field plots were ranked as increasingly saline-based on ground water salinity and depth-only the allocation of N to citrulline differed significantly between the field plots. Within each plot, temporal variation in the composition of the xylem sap was related to rainfall, rainfall infiltration and soil salinity. Periods of low rainfall and infiltration and higher soil salinity corresponded with increased allocation of N to proline and arginine in the xylem sap. The allocation of N to citrulline and asparagine increased following rainfall events where rain was calculated to have infiltrated sufficiently to decrease soil salinity. The relationship between nitrogenous composition of the xylem sap of C. glauca and soil salinity indicates that the analysis of xylem sap is an effective method for assessing changes in salinity stress in trees at a particular site over time. However, the composition of the xylem sap proved less useful as a comparative index of salinity stress in trees growing at different sites.

Two-dimensional balanced sampling plans excluding contiguous units

A balanced sampling plan excluding contiguous units (or BSEC for short) was first introduced by Hedayat, Rao and Stufken in 1988. These designs can be used for survey sampling when the units are arranged in one-dimensional ordering and the contiguous units in this ordering provide similar information. In this paper, we generalize the concept of a BSEC to the two-dimensional situation and give constructions of two-dimensional BSECs with block size 3. The existence problem is completely solved in the case where lambda = 1.

Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations

We study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which guarantee a priori bounds on first differences of solutions to the discretized problem. We establish existence results for solutions to the discretized boundary value problems subject to nonlinear boundary conditions. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. (C) 2002 Elsevier Science Ltd. All rights reserved.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

The nonexistence of spurious solutions to discrete, two-point boundary value problems

We investigate difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations. We formulate conditions under which all solutions to the discrete problem satisfy certain a priori bounds which axe independent of the step-size. As a result, the nonexistence of spurious solutions are guaranteed. Some existence and convergence theorems for solutions to the discrete problem are also presented. (C) 2002 Elsevier Science Ltd. All rights reserved.

Difference equations in Banach spaces

Difference equations which discretely approximate boundary value problems for second-order ordinary differential equations are analysed. It is well known that the existence of solutions to the continuous problem does not necessarily imply existence of solutions to the discrete problem and, even if solutions to the discrete problem are guaranteed, they may be unrelated and inapplicable to the continuous problem. Analogues to theorems for the continuous problem regarding a priori bounds and existence of solutions are formulated for the discrete problem. Solutions to the discrete problem are shown to converge to solutions of the continuous problem in an aggregate sense. An example which arises in the study of the finite deflections of an elastic string under a transverse load is investigated. The earlier results are applied to show the existence of a solution; the sufficient estimates on the step size are presented. (C) 2003 Elsevier Science Ltd. All rights reserved.

The spectrum of minimal defining sets of some Steiner systems

For a design D, define spec(D) = {\M\ \ M is a minimal defining set of D} to be the spectrum of minimal defining sets of D. In this note we give bounds on the size of an element in spec(D) when D is a Steiner system. We also show that the spectrum of minimal defining sets of the Steiner triple system given by the points and lines of PG(3,2) equals {16,17,18,19,20,21,22}, and point out some open questions concerning the Steiner triple systems associated with PG(n, 2) in general. (C) 2002 Elsevier Science B.V. All rights reserved.

Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

The tree cut and merge algorithm for estimation of network reliability

This article presents Monte Carlo techniques for estimating network reliability. For highly reliable networks, techniques based on graph evolution models provide very good performance. However, they are known to have significant simulation cost. An existing hybrid scheme (based on partitioning the time space) is available to speed up the simulations; however, there are difficulties with optimizing the important parameter associated with this scheme. To overcome these difficulties, a new hybrid scheme (based on partitioning the edge set) is proposed in this article. The proposed scheme shows orders of magnitude improvement of performance over the existing techniques in certain classes of network. It also provides reliability bounds with little overhead.

Influence of ageing, heat shock treatment and in vivo total antioxidant status on gene-expression profile and protein synthesis in human peripheral lymphocytes

Ageing results in a progressive, intrinsic and generalised imbalance of the control of regulatory systems. A key manifestation of this complex biological process includes the attenuation of the universal stress response. Here we provide the first global assessment of the ageing process as it affects the heat shock response, utilising human peripheral lymphocytes and cDNA microarray analysis. The genomic approach employed in our preliminary study was supplemented with a proteomic approach. In addition, the current study correlates the in vivo total antioxidant status with the age-related differential gene expression as well as the translational kinetics of heat shock proteins (hsps). Most of the genes encoding stress response proteins on the 4224 element microarray used in this study were significantly elevated after heat shock treatment of lymphocytes obtained from both young and old individuals albeit to a greater extent in the young. Cell signaling and signal transduction genes as well as some oxidoreductases showed varied response. Results from translational kinetics of induction of major hsps, from 0 to 24 It recovery period were broadly consistent with the differential expression of HSC 70 and HSP 40 genes. Total antioxidant levels in plasma from old individuals were found to be significantly lower by comparison with young, in agreement with the widely acknowledged role of oxidant homeostasis in the ageing process. (C) 2002 Elsevier Science Ireland Ltd. All rights reserved.