Scattering theory and the discrete linear optimal control problem

This paper deals with the interpretation of the discrete-time optimal control problem as a scattering process in a discrete medium. We treat the discrete optimal linear regulator, constrained end-point and servo and tracking problems, providing a unified approach to these problems. This approach results in an easy derivation of the desired results as well as several new ones.

The non-linear response of a gyrostabilized platform: Effects of correction torque time delay and of random inputs

First, the non-linear response of a gyrostabilized platform to a small constant input torque is analyzed in respect to the effect of the time delay (inherent or deliberately introduced) in the correction torque supplied by the servomotor, which itself may be non-linear to a certain extent. The equation of motion of the platform system is a third order nonlinear non-homogeneous differential equation. An approximate analytical method of solution of this equation is utilized. The value of the delay at which the platform response becomes unstable has been calculated by using this approximate analytical method. The procedure is illustrated by means of a numerical example. Second, the non-linear response of the platform to a random input has been obtained. The effects of several types of non-linearity on reducing the level of the mean square response have been investigated, by applying the technique of equivalent linearization and solving the resulting integral equations by using laguerre or Gaussian integration techniques. The mean square responses to white noise and band limited white noise, for various values of the non-linear parameter and for different types of non-linearity function, have been obtained. For positive values of the non-linear parameter the levels of the non-linear mean square responses to both white noise and band-limited white noise are low as compared to the linear mean square response. For negative values of the non-linear parameter the level of the non-linear mean square response at first increases slowly with increasing values of the non-linear parameter and then suddenly jumps to a high level, at a certain value of the non-linearity parameter.

The pulse response of non-linear third order systems

The response of a third order non-linear system subjected to a pulse excitation is analysed. A transformation of the displacement variable is effected. The transformation function chosen is the solution of the linear problem subjected to the same pulse. With this transformation the equation of motion is brought into a form in which the method of variation of parameters is applicable for the solution of the problem. The method is applied to a single axis gyrostabilized platform subjected to an exponentially decaying pulse. The analytical results are compared with digital and analog computer solutions.

Non-linear Transceiver Designs with Imperfect CSIT Using Convex Optimization

In this paper, we consider non-linear transceiver designs for multiuser multi-input multi-output (MIMO) down-link in the presence of imperfections in the channel state information at the transmitter (CSIT). The base station (BS) is equipped with multiple transmit antennas and each user terminal is equipped with multiple receive antennas. The BS employs Tomlinson-Harashima precoding (THP) for inter-user interference pre-cancellation at the transmitter. We investigate robust THP transceiver designs based on the minimization of BS transmit power with mean square error (MSE) constraints, and balancing of MSE among users with a constraint on the total BS transmit power. We show that these design problems can be solved by iterative algorithms, wherein each iteration involves a pair of convex optimization problems. The robustness of the proposed algorithms to imperfections in CSIT is illustrated through simulations.

Placental abruption : Studies on incidence, risk factors and potential predictive biomarkers

Placental abruption, one of the most significant causes of perinatal mortality and maternal morbidity, occurs in 0.5-1% of pregnancies. Its etiology is unknown, but defective trophoblastic invasion of the spiral arteries and consequent poor vascularization may play a role. The aim of this study was to define the prepregnancy risk factors of placental abruption, to define the risk factors during the index pregnancy, and to describe the clinical presentation of placental abruption. We also wanted to find a biochemical marker for predicting placental abruption early in pregnancy. Among women delivering at the University Hospital of Helsinki in 1997-2001 (n=46,742), 198 women with placental abruption and 396 control women were identified. The overall incidence of placental abruption was 0.42%. The prepregnancy risk factors were smoking (OR 1.7; 95% CI 1.1, 2.7), uterine malformation (OR 8.1; 1.7, 40), previous cesarean section (OR 1.7; 1.1, 2.8), and history of placental abruption (OR 4.5; 1.1, 18). The risk factors during the index pregnancy were maternal (adjusted OR 1.8; 95% CI 1.1, 2.9) and paternal smoking (2.2; 1.3, 3.6), use of alcohol (2.2; 1.1, 4.4), placenta previa (5.7; 1.4, 23.1), preeclampsia (2.7; 1.3, 5.6) and chorioamnionitis (3.3; 1.0, 10.0). Vaginal bleeding (70%), abdominal pain (51%), bloody amniotic fluid (50%) and fetal heart rate abnormalities (69%) were the most common clinical manifestations of placental abruption. Retroplacental blood clot was seen by ultrasound in 15% of the cases. Neither bleeding nor pain was present in 19% of the cases. Overall, 59% went into preterm labor (OR 12.9; 95% CI 8.3, 19.8), and 91% were delivered by cesarean section (34.7; 20.0, 60.1). Of the newborns, 25% were growth restricted. The perinatal mortality rate was 9.2% (OR 10.1; 95% CI 3.4, 30.1). We then tested selected biochemical markers for prediction of placental abruption. The median of the maternal serum alpha-fetoprotein (MSAFP) multiples of median (MoM) (1.21) was significantly higher in the abruption group (n=57) than in the control group (n=108) (1.07) (p=0.004) at 15-16 gestational weeks. In multivariate analysis, elevated MSAFP remained as an independent risk factor for placental abruption, adjusting for parity ≥ 3, smoking, previous placental abruption, preeclampsia, bleeding in II or III trimester, and placenta previa. MSAFP ≥ 1.5 MoM had a sensitivity of 29% and a false positive rate of 10%. The levels of the maternal serum free beta human chorionic gonadotrophin MoM did not differ between the cases and the controls. None of the angiogenic factors (soluble endoglin, soluble fms-like tyrosine kinase 1, or placental growth factor) showed any difference between the cases (n=42) and the controls (n=50) in the second trimester. The levels of C-reactive protein (CRP) showed no difference between the cases (n=181) and the controls (n=261) (median 2.35 mg/l [interquartile range {IQR} 1.09-5.93] versus 2.28 mg/l [IQR 0.92-5.01], not significant) when tested in the first trimester (mean 10.4 gestational weeks). Chlamydia pneumoniae specific immunoglobulin G (IgG) and immunoglobulin A (IgA) as well as C. trachomatis specific IgG, IgA and chlamydial heat-shock protein 60 antibody rates were similar between the groups. In conclusion, although univariate analysis identified many prepregnancy risk factors for placental abruption, only smoking, uterine malformation, previous cesarean section and history of placental abruption remained significant by multivariate analysis. During the index pregnancy maternal alcohol consumption and smoking and smoking by the partner turned out to be the major independent risk factors for placental abruption. Smoking by both partners multiplied the risk. The liberal use of ultrasound examination contributed little to the management of women with placental abruption. Although second-trimester MSAFP levels were higher in women with subsequent placental abruption, clinical usefulness of this test is limited due to low sensitivity and high false positive rate. Similarly, angiogenic factors in early second trimester, or CRP levels, or chlamydial antibodies in the first trimester failed to predict placental abruption.

Predicting the temporal response of seagrass meadows to dredging using Dynamic Bayesian Networks

Predicting temporal responses of ecosystems to disturbances associated with industrial activities is critical for their management and conservation. However, prediction of ecosystem responses is challenging due to the complexity and potential non-linearities stemming from interactions between system components and multiple environmental drivers. Prediction is particularly difficult for marine ecosystems due to their often highly variable and complex natures and large uncertainties surrounding their dynamic responses. Consequently, current management of such systems often rely on expert judgement and/or complex quantitative models that consider only a subset of the relevant ecological processes. Hence there exists an urgent need for the development of whole-of-systems predictive models to support decision and policy makers in managing complex marine systems in the context of industry based disturbances. This paper presents Dynamic Bayesian Networks (DBNs) for predicting the temporal response of a marine ecosystem to anthropogenic disturbances. The DBN provides a visual representation of the problem domain in terms of factors (parts of the ecosystem) and their relationships. These relationships are quantified via Conditional Probability Tables (CPTs), which estimate the variability and uncertainty in the distribution of each factor. The combination of qualitative visual and quantitative elements in a DBN facilitates the integration of a wide array of data, published and expert knowledge and other models. Such multiple sources are often essential as one single source of information is rarely sufficient to cover the diverse range of factors relevant to a management task. Here, a DBN model is developed for tropical, annual Halophila and temperate, persistent Amphibolis seagrass meadows to inform dredging management and help meet environmental guidelines. Specifically, the impacts of capital (e.g. new port development) and maintenance (e.g. maintaining channel depths in established ports) dredging is evaluated with respect to the risk of permanent loss, defined as no recovery within 5 years (Environmental Protection Agency guidelines). The model is developed using expert knowledge, existing literature, statistical models of environmental light, and experimental data. The model is then demonstrated in a case study through the analysis of a variety of dredging, environmental and seagrass ecosystem recovery scenarios. In spatial zones significantly affected by dredging, such as the zone of moderate impact, shoot density has a very high probability of being driven to zero by capital dredging due to the duration of such dredging. Here, fast growing Halophila species can recover, however, the probability of recovery depends on the presence of seed banks. On the other hand, slow growing Amphibolis meadows have a high probability of suffering permanent loss. However, in the maintenance dredging scenario, due to the shorter duration of dredging, Amphibolis is better able to resist the impacts of dredging. For both types of seagrass meadows, the probability of loss was strongly dependent on the biological and ecological status of the meadow, as well as environmental conditions post-dredging. The ability to predict the ecosystem response under cumulative, non-linear interactions across a complex ecosystem highlights the utility of DBNs for decision support and environmental management.

Two-level k-means clustering algorithm for k-tau relationship establishment and linear-time classification

Partitional clustering algorithms, which partition the dataset into a pre-defined number of clusters, can be broadly classified into two types: algorithms which explicitly take the number of clusters as input and algorithms that take the expected size of a cluster as input. In this paper, we propose a variant of the k-means algorithm and prove that it is more efficient than standard k-means algorithms. An important contribution of this paper is the establishment of a relation between the number of clusters and the size of the clusters in a dataset through the analysis of our algorithm. We also demonstrate that the integration of this algorithm as a pre-processing step in classification algorithms reduces their running-time complexity.

Low ML-Decoding Complexity, Large Coding Gain, Full-Rate, Full-Diversity STBCs for 2 x 2 and 4 x 2 MIMO Systems

This paper deals with low maximum-likelihood (ML)-decoding complexity, full-rate and full-diversity space-time block codes (STBCs), which also offer large coding gain, for the 2 transmit antenna, 2 receive antenna (2 x 2) and the 4 transmit antenna, 2 receive antenna (4 x 2) MIMO systems. Presently, the best known STBC for the 2 2 system is the Golden code and that for the 4 x 2 system is the DjABBA code. Following the approach by Biglieri, Hong, and Viterbo, a new STBC is presented in this paper for the 2 x 2 system. This code matches the Golden code in performance and ML-decoding complexity for square QAM constellations while it has lower ML-decoding complexity with the same performance for non-rectangular QAM constellations. This code is also shown to be information-lossless and diversity-multiplexing gain (DMG) tradeoff optimal. This design procedure is then extended to the 4 x 2 system and a code, which outperforms the DjABBA code for QAM constellations with lower ML-decoding complexity, is presented. So far, the Golden code has been reported to have an ML-decoding complexity of the order of for square QAM of size. In this paper, a scheme that reduces its ML-decoding complexity to M-2 root M is presented.

A Joint Source-Channel Coding Scheme for Transmission of Correlated Discrete Sources over a Gaussian Multiple Access Channel

We consider the problem of transmission of correlated discrete alphabet sources over a Gaussian Multiple Access Channel (GMAC). A distributed bit-to-Gaussian mapping is proposed which yields jointly Gaussian codewords. This can guarantee lossless transmission or lossy transmission with given distortions, if possible. The technique can be extended to the system with side information at the encoders and decoder.

Surveillance of Surgical Site Infections following Major Hip and Knee Surgery in Finland

Background and aims. Since 1999, hospitals in the Finnish Hospital Infection Program (SIRO) have reported data on surgical site infections (SSI) following major hip and knee surgery. The purpose of this study was to obtain detailed information to support prevention efforts by analyzing SIRO data on SSIs, to evaluate possible factors affecting the surveillance results, and to assess the disease burden of postoperative prosthetic joint infections in Finland. Methods. Procedures under surveillance included total hip (THA) and total knee arthroplasties (TKA), and the open reduction and internal fixation (ORIF) of femur fractures. Hospitals prospectively collected data using common definitions and written protocol, and also performed postdischarge surveillance. In the validation study, a blinded retrospective chart review was performed and infection control nurses were interviewed. Patient charts of deep incisional and organ/space SSIs were reviewed, and data from three sources (SIRO, the Finnish Arthroplasty Register, and the Finnish Patient Insurance Centre) were linked for capture-recapture analyses. Results. During 1999-2002, the overall SSI rate was 3.3% after 11,812 orthopedic procedures (median length of stay, eight days). Of all SSIs, 56% were detected after discharge. The majority of deep incisional and organ/space SSIs (65/108, 60%) were detected on readmission. Positive and negative predictive values, sensitivity, and specificity for SIRO surveillance were 94% (95% CI, 89-99%), 99% (99-100%), 75% (56-93%), and 100% (97-100%), respectively. Of the 9,831 total joint replacements performed during 2001-2004, 7.2% (THA 5.2% and TKA 9.9%) of the implants were inserted in a simultaneous bilateral operation. Patients who underwent bilateral operations were younger, healthier, and more often males than those who underwent unilateral procedures. The rates of deep SSIs or mortality did not differ between bi- and uni-lateral THAs or TKAs. Four deep SSIs were reported following bilateral operations (antimicrobial prophylaxis administered 48-218 minutes before incision). In the three registers, altogether 129 prosthetic joint infections were identified after 13,482 THA and TKA during 1999-2004. After correction with the positive predictive value of SIRO (91%), a log-linear model provided an estimated overall prosthetic joint infection rate of 1.6% after THA and 1.3% after TKA. The sensitivity of the SIRO surveillance ranged from 36% to 57%. According to the estimation, nearly 200 prosthetic joint infections could occur in Finland each year (the average from 1999 to 2004) after THA and TKA. Conclusions. Postdischarge surveillance had a major impact on SSI rates after major hip and knee surgery. A minority of deep incisional and organ/space SSIs would be missed, however, if postdischarge surveillance by questionnaire was not performed. According to the validation study, most SSIs reported to SIRO were true infections. Some SSIs were missed, revealing some weakness in case finding. Variation in diagnostic practices may also affect SSI rates. No differences were found in deep SSI rates or mortality between bi- and unilateral THA and TKA. However, patient materials between these two groups differed. Bilateral operations require specific attention paid to their antimicrobial prophylaxis as well as to data management in the surveillance database. The true disease burden of prosthetic joint infections may be heavier than the rates from national nosocomial surveillance systems usually suggest.

Membrane modifying linear polypeptide antibiotics

Peptides Possessing antibiotic activity isolated from microbial sources have been the subject of intensive structural and biological investigation over the past two decades. Perhaps, the discovery and widespread use of penicillin, a molecule biosynthetically derived from a tripeptide precursor, as a strong antibacterial agent, has provided the necessary impetus for the detailed study of microbial peptides. While many of these peptides have not been used clinically, They show unique metal binding properties and often possess the ability to modify the electrical properties or ion permeabilities of artificial lipid membranes. Hence, these peptides have been used extensively to study transmembrane ion transport processes in model and natural systems like mitochondria, chloroplasts and plasma membranes.

Formation of linear plasmid multimers promoted by the phage lambda Red-system in lon mutants of Escherichia coli

We report here the formation of plasmid linear multimers promoted by the Red-system of phage lambda using a multicopy plasmid comprised of lambda red alpha and red beta genes, under the control of the lambda cI857 repressor. Our observations have revealed that the multimerization of plasmid DNA is dependent on the red beta and recA genes, suggesting a concerted role for these functions in the formation of plasmid multimers. The formation of multimers occurred in a recBCD+ sbcB+ xthA+ lon genetic background at a higher frequency than in the isogenic lon+ host cells. The multimers comprised tandem repeats of monomer plasmid DNA. Treatment of purified plasmid DNA with exonuclease III revealed the presence of free double-chain ends in the molecules. Determination of the size of multimeric DNA, by pulse field gel electrophoresis, revealed that the bulk of the DNA was in the range 50-240 kb, representing approximately 5-24 unit lengths of monomeric plasmid DNA. We provide a conceptual framework for Red-system-promoted formation and enhanced accumulation of plasmid linear multimers in lon mutants of E. coli.

Homologous pairing between nucleosome cores on a linear duplex DNA and nucleoprotein filaments of RecA protein-single stranded DNA

The ability of E coli recA protein to promote homologous pairing with linear duplex DNA bound to HU protein (Nucleosome cores) was found to be differentially affected. The formation of paranemic joint molecules was not affected whereas the formation of plectomic joint molecules was inhibited from the start of the reaction. The formation of paranemic joint molecules between nucleoprotein filaments of recA protein-circular single stranded DNA and closed circular duplex DNA is believed to generate positive supercoiling in the duplex DNA. We found that the positively superhelical duplex DNA was inert in the formation of joint molecules but could be converted into an active substrate, in situ, by the action of wheat germ topoisomerase I. These observations initiate an understanding of the structural features of E coli chromosome such as DNA supercoiling and nucleosome-like structures in homologous recombination.

A Kalman filter based strategy for linear structural system identification based on multiple static and dynamic test data

The problem of identification of stiffness, mass and damping properties of linear structural systems, based on multiple sets of measurement data originating from static and dynamic tests is considered. A strategy, within the framework of Kalman filter based dynamic state estimation, is proposed to tackle this problem. The static tests consists of measurement of response of the structure to slowly moving loads, and to static loads whose magnitude are varied incrementally; the dynamic tests involve measurement of a few elements of the frequency response function (FRF) matrix. These measurements are taken to be contaminated by additive Gaussian noise. An artificial independent variable τ, that simultaneously parameterizes the point of application of the moving load, the magnitude of the incrementally varied static load and the driving frequency in the FRFs, is introduced. The state vector is taken to consist of system parameters to be identified. The fact that these parameters are independent of the variable τ is taken to constitute the set of ‘process’ equations. The measurement equations are derived based on the mechanics of the problem and, quantities, such as displacements and/or strains, are taken to be measured. A recursive algorithm that employs a linearization strategy based on Neumann’s expansion of structural static and dynamic stiffness matrices, and, which provides posterior estimates of the mean and covariance of the unknown system parameters, is developed. The satisfactory performance of the proposed approach is illustrated by considering the problem of the identification of the dynamic properties of an inhomogeneous beam and the axial rigidities of members of a truss structure.

A multistep transversal linearization (MTL) method in non-linear dynamics through a Magnus characterization

A new form of a multi-step transversal linearization (MTL) method is developed and numerically explored in this study for a numeric-analytical integration of non-linear dynamical systems under deterministic excitations. As with other transversal linearization methods, the present version also requires that the linearized solution manifold transversally intersects the non-linear solution manifold at a chosen set of points or cross-section in the state space. However, a major point of departure of the present method is that it has the flexibility of treating non-linear damping and stiffness terms of the original system as damping and stiffness terms in the transversally linearized system, even though these linearized terms become explicit functions of time. From this perspective, the present development is closely related to the popular practice of tangent-space linearization adopted in finite element (FE) based solutions of non-linear problems in structural dynamics. The only difference is that the MTL method would require construction of transversal system matrices in lieu of the tangent system matrices needed within an FE framework. The resulting time-varying linearized system matrix is then treated as a Lie element using Magnus’ characterization [W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math., VII (1954) 649–673] and the associated fundamental solution matrix (FSM) is obtained through repeated Lie-bracket operations (or nested commutators). An advantage of this approach is that the underlying exponential transformation could preserve certain intrinsic structural properties of the solution of the non-linear problem. Yet another advantage of the transversal linearization lies in the non-unique representation of the linearized vector field – an aspect that has been specifically exploited in this study to enhance the spectral stability of the proposed family of methods and thus contain the temporal propagation of local errors. A simple analysis of the formal orders of accuracy is provided within a finite dimensional framework. Only a limited numerical exploration of the method is presently provided for a couple of popularly known non-linear oscillators, viz. a hardening Duffing oscillator, which has a non-linear stiffness term, and the van der Pol oscillator, which is self-excited and has a non-linear damping term.