Generation of eigenstates using the phase-estimation algorithm

The phase estimation algorithm is so named because it allows an estimation of the eigenvalues associated with an operator. However, it has been proposed that the algorithm can also be used to generate eigenstates. Here we extend this proposal for small quantum systems, identifying the conditions under which the phase-estimation algorithm can successfully generate eigenstates. We then propose an implementation scheme based on an ion trap quantum computer. This scheme allows us to illustrate two simple examples, one in which the algorithm effectively generates eigenstates, and one in which it does not.

Observation of bound states of solitons in a passively mode-locked fiber laser

We report on an experimental observation of bound states of solitons in a passively mode-locked fiber soliton ring laser. The observed bound solitons are stable and have discrete, fixed soliton separations that are independent of the experimental conditions.

Lanczos subspace filter diagonalization: Homogeneous recursive filtering and a low-storage method for the calculation of matrix elements

We develop a new iterative filter diagonalization (FD) scheme based on Lanczos subspaces and demonstrate its application to the calculation of bound-state and resonance eigenvalues. The new scheme combines the Lanczos three-term vector recursion for the generation of a tridiagonal representation of the Hamiltonian with a three-term scalar recursion to generate filtered states within the Lanczos representation. Eigenstates in the energy windows of interest can then be obtained by solving a small generalized eigenvalue problem in the subspace spanned by the filtered states. The scalar filtering recursion is based on the homogeneous eigenvalue equation of the tridiagonal representation of the Hamiltonian, and is simpler and more efficient than our previous quasi-minimum-residual filter diagonalization (QMRFD) scheme (H. G. Yu and S. C. Smith, Chem. Phys. Lett., 1998, 283, 69), which was based on solving for the action of the Green operator via an inhomogeneous equation. A low-storage method for the construction of Hamiltonian and overlap matrix elements in the filtered-basis representation is devised, in which contributions to the matrix elements are computed simultaneously as the recursion proceeds, allowing coefficients of the filtered states to be discarded once their contribution has been evaluated. Application to the HO2 system shows that the new scheme is highly efficient and can generate eigenvalues with the same numerical accuracy as the basic Lanczos algorithm.

Growth regime map for liquid-bound granules: further development and experimental validation

An attempt was made to quantify the boundaries and validate the granule growth regime map for liquid-bound granules recently proposed by Iveson and Litster (AlChE J. 44 (1998) 1510). This regime map postulates that the type of granule growth behaviour is a function of only two dimensionless groups: the amount of granule deformation during collision (characterised by a Stokes deformation number, St(def)) and the maximum granule pore saturation, s(max). The results of experiments performed with a range of materials (glass ballotini, iron ore fines, copper chalcopyrite powder and a sodium sulphate and cellulose mixture) using both drum and high shear mixer granulators were examined. The drum granulation results gave good agreement with the proposed regime map. The boundary between crumb and steady growth occurs at St(def) of order 0.1 and the boundary between steady and induction growth occurs at St(def) of order 0.001. The nucleation only boundary occurs at pore saturations that increase from 70% to 80% with decreasing St(def). However, the high shear mixer results all had St(def) numbers which were too large. This is most likely to be because the chopper tip-speed is an over-estimate of the average impact velocity granules experience and possibly also due to the dynamic yield strength of the materials being significantly greater than the yield strengths measured at low strain rates. Hence, the map is only a useful tool for comparing the granulation behaviour of different materials in the same device. Until we have a better understanding of the flow patterns and impact velocities in granulators, it cannot be used to compare different types of equipment. Theoretical considerations also revealed that several of the regime boundaries are also functions of additional parameters not explicitly contained on the map, such as binder viscosity. (C) 2001 Elsevier Science B.V. All rights reserved.

An algorithm to predict 3 ' intron splice sites in Plasmodium falciparum genomic sequences

A new algorithm, PfAGSS, for predicting 3' splice sites in Plasmodium falciparum genomic sequences is described. Application of this program to the published P. falciparum chromosome 2 and 3 data suggests that existing programs result in a high error rate in assigning 3' intron boundaries. (C) 2001 Elsevier Science B.V. All rights reserved.

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.

A simulated annealing algorithm for finding consensus sequences

Motivation: A consensus sequence for a family of related sequences is, as the name suggests, a sequence that captures the features common to most members of the family. Consensus sequences are important in various DNA sequencing applications and are a convenient way to characterize a family of molecules. Results: This paper describes a new algorithm for finding a consensus sequence, using the popular optimization method known as simulated annealing. Unlike the conventional approach of finding a consensus sequence by first forming a multiple sequence alignment, this algorithm searches for a sequence that minimises the sum of pairwise distances to each of the input sequences. The resulting consensus sequence can then be used to induce a multiple sequence alignment. The time required by the algorithm scales linearly with the number of input sequences and quadratically with the length of the consensus sequence. We present results demonstrating the high quality of the consensus sequences and alignments produced by the new algorithm. For comparison, we also present similar results obtained using ClustalW. The new algorithm outperforms ClustalW in many cases.

Crystal structures of free, IMP-, and GMP-bound Escherichia coli hypoxanthine phosphoribosyltransferase

Crystal structures have been determined for free Escherichia coli hypoxanthine phosphoribosyltransferase (HPRT) (2.9 Angstrom resolution) and for the enzyme in complex with the reaction products, inosine 5'-monophosphate (IMP) and guanosine 5-monophosphate (GMP) (2.8 Angstrom resolution). Of the known 6-oxopurine phosphoribosyltransferase (PRTase) structures, E. coli HPRT is most similar in structure to that of Tritrichomonas foetus HGXPRT, with a rmsd for 150 Calpha atoms of 1.0 Angstrom. Comparison of the free and product bound structures shows that the side chain of Phe156 and the polypeptide backbone in this vicinity move to bind IMP or GMP. A nonproline cis peptide bond, also found in some other 6-oxopurine PRTases, is observed between Leu46 and Arg47 in both the free and complexed structures. For catalysis to occur, the 6-oxopurine PRTases have a requirement for divalent metal ion, Usually Mg2+ in vivo. In the free structure, a Mg2+, is coordinated to the side chains of Glu103 and Asp104. This interaction may be important for stabilization of the enzyme before catalysis. E. coli HPRT is unique among the known 6-oxopurine PRTases in that it exhibits a marked preference for hypoxanthine as substrate over both xanthine and guanine. The structures suggest that its substrate specificity is due to the modes of binding of the bases. In E. coli HPRT, the carbonyl oxygen of Asp 163 would likely form a hydrogen bond with the 2-exocyclic nitrogen of guanine (in the HPRT-guanine-PRib-PP-Mg2+ complex). However, hypoxanthine does not have a 2-exocyclic atom and the HPRT-IMP structure suggests that hypoxanthine is likely to occupy a different position in the purine-binding pocket.

A monolithic smoothing-gap algorithm for contact-impact based on the signed distance function

A new algorithm has been developed for smoothing the surfaces in finite element formulations of contact-impact. A key feature of this method is that the smoothing is done implicitly by constructing smooth signed distance functions for the bodies. These functions are then employed for the computation of the gap and other variables needed for implementation of contact-impact. The smoothed signed distance functions are constructed by a moving least-squares approximation with a polynomial basis. Results show that when nodes are placed on a surface, the surface can be reproduced with an error of about one per cent or less with either a quadratic or a linear basis. With a quadratic basis, the method exactly reproduces a circle or a sphere even for coarse meshes. Results are presented for contact problems involving the contact of circular bodies. Copyright (C) 2002 John Wiley Sons, Ltd.

A subset-oriented algorithm for minimizing the number of steps required for synthesis of cyclic-peptide libraries

Libraries of cyclic peptides are being synthesized using combinatorial chemistry for high throughput screening in the drug discovery process. This paper describes the min_syn_steps.cpp program (available at http://www.imb.uq.edu.au/groups/smythe/tran), which after inputting a list of cyclic peptides to be synthesized, removes cyclic redundant sequences and calculates synthetic strategies which minimize the synthetic steps as well as the reagent requirements. The synthetic steps and reagent requirements could be minimized by finding common subsets within the sequences for block synthesis. Since a brute-force approach to search for optimum synthetic strategies is impractically large, a subset-orientated approach is utilized here to limit the size of the search. (C) 2002 Elsevier Science Ltd. All rights reserved.