Subgeometric rates of convergence for a class of continuous-time Markov process

Let (Phi(t))(t is an element of R+) be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure pi. We investigate the rates of convergence of the transition function P-t(x, (.)) to pi; specifically, we find conditions under which r(t) vertical bar vertical bar P-t (x, (.)) - pi vertical bar vertical bar -> 0 as t -> infinity, for suitable subgeometric rate functions r(t), where vertical bar vertical bar - vertical bar vertical bar denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.

Measurement-based teleportation along quantum spin chains

We examine the teleportation of an unknown spin-1/2 quantum state along a quantum spin chain with an even number of sites. Our protocol, using a sequence of Bell measurements, may be viewed as an iterated version of the 2-qubit protocol of C. H. Bennett et al. [Phys. Rev. Lett. 70, 1895 (1993)]. A decomposition of the Hilbert space of the spin chain into 4 vector spaces, called Bell subspaces, is given. It is established that any state from a Bell subspace may be used as a channel to perform unit fidelity teleportation. The space of all spin-0 many-body states, which includes the ground states of many known antiferromagnetic systems, belongs to a common Bell subspace. A channel-dependent teleportation parameter O is introduced, and a bound on the teleportation fidelity is given in terms of O.

A theoretical comparison of two optimization methods for radiofrequency drive schemes in high frequency MRI resonators

In this paper, numerical simulations are used in an attempt to find optimal Source profiles for high frequency radiofrequency (RF) volume coils. Biologically loaded, shielded/unshielded circular and elliptical birdcage coils operating at 170 MHz, 300 MHz and 470 MHz are modelled using the FDTD method for both 2D and 3D cases. Taking advantage of the fact that some aspects of the electromagnetic system are linear, two approaches have been proposed for the determination of the drives for individual elements in the RF resonator. The first method is an iterative optimization technique with a kernel for the evaluation of RF fields inside an imaging plane of a human head model using pre-characterized sensitivity profiles of the individual rungs of a resonator; the second method is a regularization-based technique. In the second approach, a sensitivity matrix is explicitly constructed and a regularization procedure is employed to solve the ill-posed problem. Test simulations show that both methods can improve the B-1-field homogeneity in both focused and non-focused scenarios. While the regularization-based method is more efficient, the first optimization method is more flexible as it can take into account other issues such as controlling SAR or reshaping the resonator structures. It is hoped that these schemes and their extensions will be useful for the determination of multi-element RF drives in a variety of applications.

Folate: Methods of analysis

Folates and its derivatives occur as polyglutamates in nature. The multiplicity of forms and the generally low levels in foods makes quantitative analysis of folate a difficult task. The assay of folates from foods generally involves three steps: liberation of folates from the cellular matrix; deconjugation from the polyglutamate to the mono and di-glutamate forms; and the detection of the biological activity or chemical concentration of the resulting folates. The detection methods used are the microbiological assay relying on the turbidimetric bacterial growth of Lactobacillus rhamnosus which is by far the most commonly used method; the HPLC and LC/MS techniques and bio-specific procedures. This review attempts to describe the methods along with the merits and demerits of using each of these methods.

Matrix effects: The Achilles heel of quantitative high-performance liquid chromatography-electrospray-tandem mass spectrometry

High-performance liquid chromatography coupled by an electrospray ion source to a tandem mass spectrometer (HPLC-EST-MS/ MS) is the current analytical method of choice for quantitation of analytes in biological matrices. With HPLC-ESI-MS/MS having the characteristics of high selectivity, sensitivity, and throughput, this technology is being increasingly used in the clinical laboratory. An important issue to be addressed in method development, validation, and routine use of HPLC-ESI-MS/MS is matrix effects. Matrix effects are the alteration of ionization efficiency by the presence of coeluting substances. These effects are unseen in the chromatograrn but have deleterious impact on methods accuracy and sensitivity. The two common ways to assess matrix effects are either by the postextraction addition method or the postcolumn infusion method. To remove or minimize matrix effects, modification to the sample extraction methodology and improved chromatographic separation must be performed. These two parameters are linked together and form the basis of developing a successful and robust quantitative HPLC-EST-MS/MS method. Due to the heterogenous nature of the population being studied, the variability of a method must be assessed in samples taken from a variety of subjects. In this paper, the major aspects of matrix effects are discussed with an approach to address matrix effects during method validation proposed. (c) 2004 The Canadian Society of Clinical Chemists. All rights reserved.

Determining the effective dimensionality of the genetic variance-covariance matrix

Determining the dimensionality of G provides an important perspective on the genetic basis of a multivariate suite of traits. Since the introduction of Fisher's geometric model, the number of genetically independent traits underlying a set of functionally related phenotypic traits has been recognized as an important factor influencing the response to selection. Here, we show how the effective dimensionality of G can be established, using a method for the determination of the dimensionality of the effect space from a multivariate general linear model introduced by AMEMIYA (1985). We compare this approach with two other available methods, factor-analytic modeling and bootstrapping, using a half-sib experiment that estimated G for eight cuticular hydrocarbons of Drosophila serrata. In our example, eight pheromone traits were shown to be adequately represented by only two underlying genetic dimensions by Amemiya's approach and factor-analytic modeling of the covariance structure at the sire level. In, contrast, bootstrapping identified four dimensions with significant genetic variance. A simulation study indicated that while the performance of Amemiya's method was more sensitive to power constraints, it performed as well or better than factor-analytic modeling in correctly identifying the original genetic dimensions at moderate to high levels of heritability. The bootstrap approach consistently overestimated the number of dimensions in all cases and performed less well than Amemiya's method at subspace recovery.

Predicting residue-wise contact orders in proteins by support vector regression

Background: The residue-wise contact order (RWCO) describes the sequence separations between the residues of interest and its contacting residues in a protein sequence. It is a new kind of one-dimensional protein structure that represents the extent of long-range contacts and is considered as a generalization of contact order. Together with secondary structure, accessible surface area, the B factor, and contact number, RWCO provides comprehensive and indispensable important information to reconstructing the protein three-dimensional structure from a set of one-dimensional structural properties. Accurately predicting RWCO values could have many important applications in protein three-dimensional structure prediction and protein folding rate prediction, and give deep insights into protein sequence-structure relationships. Results: We developed a novel approach to predict residue-wise contact order values in proteins based on support vector regression (SVR), starting from primary amino acid sequences. We explored seven different sequence encoding schemes to examine their effects on the prediction performance, including local sequence in the form of PSI-BLAST profiles, local sequence plus amino acid composition, local sequence plus molecular weight, local sequence plus secondary structure predicted by PSIPRED, local sequence plus molecular weight and amino acid composition, local sequence plus molecular weight and predicted secondary structure, and local sequence plus molecular weight, amino acid composition and predicted secondary structure. When using local sequences with multiple sequence alignments in the form of PSI-BLAST profiles, we could predict the RWCO distribution with a Pearson correlation coefficient (CC) between the predicted and observed RWCO values of 0.55, and root mean square error (RMSE) of 0.82, based on a well-defined dataset with 680 protein sequences. Moreover, by incorporating global features such as molecular weight and amino acid composition we could further improve the prediction performance with the CC to 0.57 and an RMSE of 0.79. In addition, combining the predicted secondary structure by PSIPRED was found to significantly improve the prediction performance and could yield the best prediction accuracy with a CC of 0.60 and RMSE of 0.78, which provided at least comparable performance compared with the other existing methods. Conclusion: The SVR method shows a prediction performance competitive with or at least comparable to the previously developed linear regression-based methods for predicting RWCO values. In contrast to support vector classification (SVC), SVR is very good at estimating the raw value profiles of the samples. The successful application of the SVR approach in this study reinforces the fact that support vector regression is a powerful tool in extracting the protein sequence-structure relationship and in estimating the protein structural profiles from amino acid sequences.

Predicting the solvent accessibility of transmembrane residues from protein sequence

In this study, we propose a novel method to predict the solvent accessible surface areas of transmembrane residues. For both transmembrane alpha-helix and beta-barrel residues, the correlation coefficients between the predicted and observed accessible surface areas are around 0.65. On the basis of predicted accessible surface areas, residues exposed to the lipid environment or buried inside a protein can be identified by using certain cutoff thresholds. We have extensively examined our approach based on different definitions of accessible surface areas and a variety of sets of control parameters. Given that experimentally determining the structures of membrane proteins is very difficult and membrane proteins are actually abundant in nature, our approach is useful for theoretically modeling membrane protein tertiary structures, particularly for modeling the assembly of transmembrane domains. This approach can be used to annotate the membrane proteins in proteomes to provide extra structural and functional information.

Remodeling of extracellular matrix at ovulation of the bovine ovarian follicle

Using immunohistochemistry and RNA analyses we examined the fate of components of a newly identified matrix that develops between granulosa cells (focimatrix, abbreviated from focal intraepithelial matrix) and of the follicular basal lamina in ovulating bovine ovarian follicles. Pre- and postovulatory follicles were generated by treatment with estradiol (Day 1), progesterone (Days 1-10), and prostaglandin analogue (Day 9) with either no further treatment (Group 1, n = 6) and or with 25 mg porcine LH (Day 11, Group 2, n = 8 or Day 10, Group 3, n = 8) and ovariectomy on Day 12 (12-14 hr post LH in Group 2, 38-40.5 hr in Group 3). In the time frame examined no loss of follicular basal lamina laminin chains beta 2 and gamma 1 or nidogen 1 was observed. In the follicular basal lamina collagen type IV alpha 1 and perlecan were present prior to ovulation; after ovulation collagen type IV alpha 1 was discontinuously distributed and perlecan was absent. Versican in the theca interna adjacent to the follicular basal lamina in preovulatory follicles was not observed post ovulation, however, the granulosa cells then showed strong cytoplasmic staining for versican. Expression of versican isoforms V0, V1, and V3 was detected at all stages. Focimatrix was observed in preovulatory follicles. It contained collagen type IV alpha 1, laminins beta 2 and gamma 1, nidogen 1 and perlecan and underwent changes in composition similar to that of the follicular basal lamina. In conclusion focimatrix and the follicular basal lamina are degraded at ovulation. Individual components are lost at different times.

Arthritic disease suppression and cartilage protection with glycosaminoglycan polypeptide complexes (Peptacans) derived from the cartilage extracellular matrix: A novel approach to therapy

Molecular fragments of cartilage are antigenic and can stimulate an autoimmune response. Oral administration of type II collagen prevents disease onset in animal models of arthritis but the effects of other matrix components have not been reported. We evaluated glycosaminoglycan polypeptides (GAG-P) and matrix proteins (CaP) from cartilage for a) mitigating disease activity in rats with collagen-induced arthritis (CIA) and adjuvant-induced arthritis (AIA) and b) stimulating proteoglycan (PG) synthesis by chondrocytes in-vitro. CIA and AIA were established in Wistar rats using standard methods. Agents were administered orally (10–200 mg/kg), either for seven days prior to disease induction (toleragenic protocol), or continuously for 15 days after injecting the arthritigen (prophylactic protocol). Joint swelling and arthritis scores were determined on day 15. Histological sections of joint tissues were assessed post-necropsy. In chondrocyte cultures, CaP + / − interleukin-1 stimulated PG biosynthesis. CaP was also active in preventing arthritis onset at 3.3, 10 or 20 mg/kg in the rat CIA model using the toleragenic protocol. It was only active at 20 and 200 mg/kg in the CIA prophylactic protocol. GAG-P was active in the CIA toleragenic protocol at 20 mg/kg but chondroitin sulfate and glucosamine hydrochloride or glucosamine sulfate were all inactive. The efficacy of CaP in the rat AIA model was less than in the CIA model. These findings lead us to suggest that oral CaP could be used as a disease-modifying anti-arthritic drug.

Computational methods for the detection of facial palsy

We are developing a telemedicine application which offers automated diagnosis of facial (Bell's) palsy through a Web service. We used a test data set of 43 images of facial palsy patients and 44 normal people to develop the automatic recognition algorithm. Three different image pre-processing methods were used. Machine learning techniques (support vector machine, SVM) were used to examine the difference between the two halves of the face. If there was a sufficient difference, then the SVM recognized facial palsy. Otherwise, if the halves were roughly symmetrical, the SVM classified the image as normal. It was found that the facial palsy images had a greater Hamming Distance than the normal images, indicating greater asymmetry. The median distance in the normal group was 331 (interquartile range 277-435) and the median distance in the facial palsy group was 509 (interquartile range 334-703). This difference was significant (P

Authorship Attribution with Support Vector Machines

In this paper we explore the use of text-mining methods for the identification of the author of a text. We apply the support vector machine (SVM) to this problem, as it is able to cope with half a million of inputs it requires no feature selection and can process the frequency vector of all words of a text. We performed a number of experiments with texts from a German newspaper. With nearly perfect reliability the SVM was able to reject other authors and detected the target author in 60–80% of the cases. In a second experiment, we ignored nouns, verbs and adjectives and replaced them by grammatical tags and bigrams. This resulted in slightly reduced performance. Author detection with SVMs on full word forms was remarkably robust even if the author wrote about different topics.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

RGD-independent cell adhesion via a tissue transglutaminase-fibronectin matrix promotes fibronectin fibril deposition and requires syndecan-4/2 and α5β1 integrin co-signaling

Fibronectin (FN) deposition mediated by fibroblasts is an important process in matrix remodeling and wound healing. By monitoring the deposition of soluble biotinylated FN, we show that the stress-induced TG-FN matrix, a matrix complex of tissue transglutaminase (TG2) with its high affinity binding partner FN, can increase both exogenous and cellular FN deposition and also restore it when cell adhesion is interrupted via the presence of RGD-containing peptides. This mechanism does not require the transamidase activity of TG2 but is activated through an RGD-independent adhesion process requiring a heterocomplex of TG2 and FN and is mediated by a syndecan-4 and ß1 integrin co-signaling pathway. By using a5 null cells, ß1 integrin functional blocking antibody, and a a5ß1 integrin targeting peptide A5-1, we demonstrate that the a5 and ß1 integrins are essential for TG-FN to compensate RGD-induced loss of cell adhesion and FN deposition. The importance of syndecan-2 in this process was shown using targeting siRNAs, which abolished the compensation effect of TG-FN on the RGD-induced loss of cell adhesion, resulting in disruption of actin skeleton formation and FN deposition. Unlike syndecan-4, syndecan-2 does not interact directly with TG2 but acts as a downstream effector in regulating actin cytoskeleton organization through the ROCK pathway. We demonstrate that PKCa is likely to be the important link between syndecan-4 and syndecan-2 signaling and that TG2 is the functional component of the TG-FN heterocomplex in mediating cell adhesion via its direct interaction with heparan sulfate chains.

Splines and vector splines

The thrust of this report concerns spline theory and some of the background to spline theory and follows the development in (Wahba, 1991). We also review methods for determining hyper-parameters, such as the smoothing parameter, by Generalised Cross Validation. Splines have an advantage over Gaussian Process based procedures in that we can readily impose atmospherically sensible smoothness constraints and maintain computational efficiency. Vector splines enable us to penalise gradients of vorticity and divergence in wind fields. Two similar techniques are summarised and improvements based on robust error functions and restricted numbers of basis functions given. A final, brief discussion of the application of vector splines to the problem of scatterometer data assimilation highlights the problems of ambiguous solutions.