On the Filtering Problem for Continuous-Time Markov Jump Linear Systems with no Observation of the Markov Chain

We consider in this paper the optimal stationary dynamic linear filtering problem for continuous-time linear systems subject to Markovian jumps in the parameters (LSMJP) and additive noise (Wiener process). It is assumed that only an output of the system is available and therefore the values of the jump parameter are not accessible. It is a well known fact that in this setting the optimal nonlinear filter is infinite dimensional, which makes the linear filtering a natural numerically, treatable choice. The goal is to design a dynamic linear filter such that the closed loop system is mean square stable and minimizes the stationary expected value of the mean square estimation error. It is shown that an explicit analytical solution to this optimal filtering problem is obtained from the stationary solution associated to a certain Riccati equation. It is also shown that the problem can be formulated using a linear matrix inequalities (LMI) approach, which can be extended to consider convex polytopic uncertainties on the parameters of the possible modes of operation of the system and on the transition rate matrix of the Markov process. As far as the authors are aware of this is the first time that this stationary filtering problem (exact and robust versions) for LSMJP with no knowledge of the Markov jump parameters is considered in the literature. Finally, we illustrate the results with an example.

Synaptic compensation on Hopfield network: implications for memory rehabilitation

The discrete-time neural network proposed by Hopfield can be used for storing and recognizing binary patterns. Here, we investigate how the performance of this network on pattern recognition task is altered when neurons are removed and the weights of the synapses corresponding to these deleted neurons are divided among the remaining synapses. Five distinct ways of distributing such weights are evaluated. We speculate how this numerical work about synaptic compensation may help to guide experimental studies on memory rehabilitation interventions.

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

Different Approaches for Modeling Grouped Survival Data: A Mango Tree Study

Interval-censored survival data, in which the event of interest is not observed exactly but is only known to occur within some time interval, occur very frequently. In some situations, event times might be censored into different, possibly overlapping intervals of variable widths; however, in other situations, information is available for all units at the same observed visit time. In the latter cases, interval-censored data are termed grouped survival data. Here we present alternative approaches for analyzing interval-censored data. We illustrate these techniques using a survival data set involving mango tree lifetimes. This study is an example of grouped survival data.

Regression models for grouped survival data: Estimation and sensitivity analysis

In this study, regression models are evaluated for grouped survival data when the effect of censoring time is considered in the model and the regression structure is modeled through four link functions. The methodology for grouped survival data is based on life tables, and the times are grouped in k intervals so that ties are eliminated. Thus, the data modeling is performed by considering the discrete models of lifetime regression. The model parameters are estimated by using the maximum likelihood and jackknife methods. To detect influential observations in the proposed models, diagnostic measures based on case deletion, which are denominated global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to those measures, the local influence and the total influential estimate are also employed. Various simulation studies are performed and compared to the performance of the four link functions of the regression models for grouped survival data for different parameter settings, sample sizes and numbers of intervals. Finally, a data set is analyzed by using the proposed regression models. (C) 2010 Elsevier B.V. All rights reserved.

Sudden onset of log-periodicity and superdiffusion in non-Markovian random walks with amnestically induced persistence: exact results

Random walks can undergo transitions from normal diffusion to anomalous diffusion as some relevant parameter varies, for instance the L,vy index in L,vy flights. Here we derive the Fokker-Planck equation for a two-parameter family of non-Markovian random walks with amnestically induced persistence. We investigate two distinct transitions: one order parameter quantifies log-periodicity and discrete scale invariance in the first moment of the propagator, whereas the second order parameter, known as the Hurst exponent, describes the growth of the second moment. We report numerical and analytical results for six critical exponents, which together completely characterize the properties of the transitions. We find that the critical exponents related to the diffusion-superdiffusion transition are identical in the positive feedback and negative feedback branches of the critical line, even though the former leads to classical superdiffusion whereas the latter gives rise to log-periodic superdiffusion.

A valuation of patients` willingness-to-pay for insulin delivery in diabetes

Objectives: The aim of this study was to determine the insulin-delivery system and the attributes of insulin therapy that best meet patients` preferences, and to estimate patients` willingness-to-pay (WTP) for them. Methods: This was a cross-sectional discrete choice experiment (DCE) study involving 378 Canadian patients with type 1 or type 2 diabetes. Patients were asked to choose between two hypothetical insulin treatment options made up of different combinations of the attribute levels. Regression coefficients derived using conditional logit models were used to calculate patients` WTP. Stratification of the sample was performed to evaluate WTP by predefined subgroups. Results: A total of 274 patients successfully completed the survey. Overall, patients were willing to pay the most for better blood glucose control followed by weight gain. Surprisingly, route of insulin administration was the least important attribute overall. Segmented models indicated that insulin naive diabetics were willing to pay significantly more for both oral and inhaled short-acting insulin compared with insulin users. Surprisingly, type 1 diabetics were willing to pay $C11.53 for subcutaneous short-acting insulin, while type 2 diabetics were willing to pay $C47.23 to avoid subcutaneous short-acting insulin (p < .05). These findings support the hypothesis of a psychological barrier to initiating insulin therapy, but once that this barrier has been overcome, they accommodate and accept injectable therapy as a treatment option. Conclusions: By understanding and addressing patients` preferences for insulin therapy, diabetes educators can use this information to find an optimal treatment approach for each individual patient, which may ultimately lead to improved control, through improved compliance, and better diabetes outcomes.

Determination of coalescence kernels for high-shear granulation using DEM simulations

Discrete element method (DEM) modeling is used in parallel with a model for coalescence of deformable surface wet granules. This produces a method capable of predicting both collision rates and coalescence efficiencies for use in derivation of an overall coalescence kernel. These coalescence kernels can then be used in computationally efficient meso-scale models such as population balance equation (PBE) models. A soft-sphere DEM model using periodic boundary conditions and a unique boxing scheme was utilized to simulate particle flow inside a high-shear mixer. Analysis of the simulation results provided collision frequency, aggregation frequency, kinetic energy, coalescence efficiency and compaction rates for the granulation process. This information can be used to bridge the gap in multi-scale modeling of granulation processes between the micro-scale DEM/coalescence modeling approach and a meso-scale PBE modeling approach.

Constructing and Deconstructing Latin Trades

This paper discusses existence results for latin trades and provides a Glueing Construction which is subsequently used to construct all latin trades of finite order greater than three.

Probabilistic Action System Trace Semantics

Action systems are a construct for reasoning about concurrent, reactive systems, in which concurrent behaviour is described by interleaving atomic actions. Sere and Troubitsyna have proposed an extension to action systems in which actions may be expressed and composed using discrete probabilistic choice as well as demonic nondeterministic choice. In this paper we develop a trace-based semantics for probabilistic action systems. This semantics provides a simple theoretical base on which practical refinement rules for probabilistic action systems may be justified.

Superconducting Correlations in Metallic Nanoparticles: Exact Solution of the BCS Model by the Algebraic Bethe Ansatz

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced Bardeen, Cooper, and Schrieffer model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors and correlation functions that describe superconducting pairing.

Magma Flow Instabilities in a Volcanic Conduit: Implications for Long-Period Seismicity

Silicic volcanic eruptions are typically accompanied by repetitive Long-Period (LP) seismicity that originates from a small region of the upper conduit. These signals have the capability to advance eruption prediction, since they commonly precede a change in the eruption vigour. Shear bands forming along the conduit wall, where the shear stresses are highest, have been linked to providing the seismic trigger. However, existing computational models are unable to generate shear bands at the depths where the LP signals originate using simple magma strength models. Presented here is a model in which the magma strength is determined from a constitutive relationship dependent upon crystallinity and pressure. This results in a depth-dependent magma strength, analogous to planetary lithospheres. Hence, in shallow highly-crystalline regions a macroscopically discontinuous brittle type of deformation will prevail, whilst in deeper crystal-poor regions there will be a macroscopically continuous plastic deformation mechanism. This will result in a depth where the brittle-ductile transition occurs, and here shear bands disconnected from the free-surface may develop. We utilize the Finite Element Method and use axi-symmetric coordinates to model magma flow as a viscoplastic material, simulating quasi-static shear bands along the walls of a volcanic conduit. Model results constrained to the Soufrière Hills Volcano, Montserrat, show the generation of two types of shear bands: upper-conduit shear bands that form between the free-surface to a few 100 metres below it and discrete shear bands that form at the depths where LP seismicity is measured to occur corresponding to the brittle-ductile transition and the plastic shear region. It is beyond the limitation of the model to simulate a seismic event, although the modelled viscosity within the discrete shear bands suggests a failure and healing cycle time that supports the observed LP seismicity repeat times. However, due to the paucity of data and large parameter space available these results can only be considered to be qualitative rather than quantitative at this stage.

Integrating infection control into the dental curriculum

The dental profession has possessed traditional standards of cross-infection control but the recent expression of real concerns by both the public and the profession over the transmissibility of infectious diseases in the dental surgery has demanded a formalized and extended approach to teaching cross-infection control in the dental curriculum. Clear curriculum content must be formulated within contemporary Workplace Health and Safety Guidelines and the Strategic Plan of the Dental School or academic health centre. The full integration demands that the area is taught as a discrete entity but recognized as an intrinsic part of each clinical encounter. This paper discusses the structure and integration of cross-infection control into the curriculum at the University of Queensland Dental School.

Bifurcation in growth patterns for arrays of parallel Griffith, edge and sliding cracks

This paper presents the recent finding by Muhlhaus et al [1] that bifurcation of crack growth patterns exists for arrays of two-dimensional cracks. This bifurcation is a result of the nonlinear effect due to crack interaction, which is, in the present analysis, approximated by the dipole asymptotic or pseudo-traction method. The nonlinear parameter for the problem is the crack length/ spacing ratio lambda = a/h. For parallel and edge crack arrays under far field tension, uniform crack growth patterns (all cracks having same size) yield to nonuniform crack growth patterns (i.e. bifurcation) if lambda is larger than a critical value lambda(cr) (note that such bifurcation is not found for collinear crack arrays). For parallel and edge crack arrays respectively, the value of lambda(cr) decreases monotonically from (2/9)(1/2) and (2/15.096)(1/2) for arrays of 2 cracks, to (2/3)(1/2)/pi and (2/5.032)(1/2)/pi for infinite arrays of cracks. The critical parameter lambda(cr) is calculated numerically for arrays of up to 100 cracks, whilst discrete Fourier transform is used to obtain the exact solution of lambda(cr) for infinite crack arrays. For geomaterials, bifurcation can also occurs when array of sliding cracks are under compression.

Evolutionary distinctiveness and status of the endangered Lake Eacham rainbowfish (Melanotaenia eachamensis)

The Lake Eacham rainbowfish (Melanotaenia eachamensis) was declared extinct in the wild in the late 1980s after it disappeared from its only known locality, an isolated crater lake in northeast Queensland. Doubts have been raised about whether this taxon is distinct from surrounding populations of the eastern rainbowfish (Melanotaenia splendida splendida). We examined the evolutionary distinctiveness of M. eachamensis, obtained from captive stocks, relative to M. s. splendida through analysis of variation in mtDNA sequences, nuclear microsatellites, and morphometric characters Captive M. eachamensis had mtDNAs that were highly divergent from those in most populations of M. s. splendida. A broader geographic survey using RFLPs revealed some populations initially identified as M. s. splendida, that carried eachamensis mtDNA, whereas some others had mixtures of eachamensis and splendida mtDNA. The presence of eachamensis-like mtDNA in these populations could in principle be due to (1) sorting of ancestral polymorphisms, (2) introgression of M. eachamensis mtDNA into M. s. splendida, or (3) incorrect species boundaries, such that some populations currently assigned to M. s. splendida are M. eachamensis or are mixtures of the two species. These alternatives hypotheses were evaluated through comparisons of four nuclear microsatellite loci and morphometrics and meristics. In analyses of both data sets, populations of M. s. splendida with eachamensis mtDNA were more similar to captive M. eachamensis than to M. s. splendida with splendida mtDNA, supporting hypothesis 3. These results are significant for the management of M. eachamensis in several respects. First the combined molecular and morphological evidence indicates that M. eachamensis is a distinct species and a discrete evolutionarily significant unit worthy of conservation effort. Second it appears that the species boundary between M. eachamensis and M. s. splendida has been misdiagnosed such that there are extant populations on the Atherton Tableland as well as areas where both forms coexist. Accordingly we suggest that M. eachamensis be listed as vulnerable, rather than critical (or extinct in the wild). Third, the discovery of extant but genetically divergent populations of M. eachamensis on the Atherton Tableland broadens the options for future reintroductions to Lake Eacham.