A novel continuous time representation for the scheduling of pipeline systems with pumping yield rate constraints

Pipeline systems play a key role in the petroleum business. These operational systems provide connection between ports and/or oil fields and refineries (upstream), as well as between these and consumer markets (downstream). The purpose of this work is to propose a novel MINLP formulation based on a continuous time representation for the scheduling of multiproduct pipeline systems that must supply multiple consumer markets. Moreover, it also considers that the pipeline operates intermittently and that the pumping costs depend on the booster stations yield rates, which in turn may generate different flow rates. The proposed continuous time representation is compared with a previously developed discrete time representation [Rejowski, R., Jr., & Pinto, J. M. (2004). Efficient MILP formulations and valid cuts for multiproduct pipeline scheduling. Computers and Chemical Engineering, 28, 1511] in terms of solution quality and computational performance. The influence of the number of time intervals that represents the transfer operation is studied and several configurations for the booster stations are tested. Finally, the proposed formulation is applied to a larger case, in which several booster configurations with different numbers of stages are tested. (C) 2007 Elsevier Ltd. All rights reserved.

A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

In this paper, we devise a separation principle for the finite horizon quadratic optimal control problem of continuous-time Markovian jump linear systems driven by a Wiener process and with partial observations. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati differential equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a separation principle for the finite horizon quadratic optimal control problem for continuous-time Markovian jump linear systems. For the case in which the matrices are all time-invariant we analyze the asymptotic behavior of the solution of the derived interconnected Riccati differential equations to the solution of the associated set of coupled algebraic Riccati equations as well as the mean square stabilizing property of this limiting solution. When there is only one mode of operation our results coincide with the traditional ones for the LQG control of continuous-time linear systems.

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.

Stability and ergodicity of piecewise deterministic Markov processes

The main goal of this paper is to establish some equivalence results on stability, recurrence, and ergodicity between a piecewise deterministic Markov process ( PDMP) {X( t)} and an embedded discrete-time Markov chain {Theta(n)} generated by a Markov kernel G that can be explicitly characterized in terms of the three local characteristics of the PDMP, leading to tractable criterion results. First we establish some important results characterizing {Theta(n)} as a sampling of the PDMP {X( t)} and deriving a connection between the probability of the first return time to a set for the discrete-time Markov chains generated by G and the resolvent kernel R of the PDMP. From these results we obtain equivalence results regarding irreducibility, existence of sigma-finite invariant measures, and ( positive) recurrence and ( positive) Harris recurrence between {X( t)} and {Theta(n)}, generalizing the results of [ F. Dufour and O. L. V. Costa, SIAM J. Control Optim., 37 ( 1999), pp. 1483-1502] in several directions. Sufficient conditions in terms of a modified Foster-Lyapunov criterion are also presented to ensure positive Harris recurrence and ergodicity of the PDMP. We illustrate the use of these conditions by showing the ergodicity of a capacity expansion model.

AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs) taking values in a general Borel space and with compact action space depending on the state variable. The control variable acts on the jump rate and transition measure of the PDMP, and the running and boundary costs are assumed to be positive but not necessarily bounded. Our first main result is to obtain an optimality equation for the long run average cost in terms of a discrete-time optimality equation related to the embedded Markov chain given by the postjump location of the PDMP. Our second main result guarantees the existence of a feedback measurable selector for the discrete-time optimality equation by establishing a connection between this equation and an integro-differential equation. Our final main result is to obtain some sufficient conditions for the existence of a solution for a discrete-time optimality inequality and an ordinary optimal feedback control for the long run average cost using the so-called vanishing discount approach. Two examples are presented illustrating the possible applications of the results developed in the paper.

Directed Abelian algebras and their application to stochastic models

With each directed acyclic graph (this includes some D-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent sigma(tau)=3/2). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found sigma(tau)=1.780 +/- 0.005.

The Policy Iteration Algorithm for Average Continuous Control of Piecewise Deterministic Markov Processes

The main goal of this paper is to apply the so-called policy iteration algorithm (PIA) for the long run average continuous control problem of piecewise deterministic Markov processes (PDMP`s) taking values in a general Borel space and with compact action space depending on the state variable. In order to do that we first derive some important properties for a pseudo-Poisson equation associated to the problem. In the sequence it is shown that the convergence of the PIA to a solution satisfying the optimality equation holds under some classical hypotheses and that this optimal solution yields to an optimal control strategy for the average control problem for the continuous-time PDMP in a feedback form.

THE VANISHING DISCOUNT APPROACH FOR THE AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This work is concerned with the existence of an optimal control strategy for the long-run average continuous control problem of piecewise-deterministic Markov processes (PDMPs). In Costa and Dufour (2008), sufficient conditions were derived to ensure the existence of an optimal control by using the vanishing discount approach. These conditions were mainly expressed in terms of the relative difference of the alpha-discount value functions. The main goal of this paper is to derive tractable conditions directly related to the primitive data of the PDMP to ensure the existence of an optimal control. The present work can be seen as a continuation of the results derived in Costa and Dufour (2008). Our main assumptions are written in terms of some integro-differential inequalities related to the so-called expected growth condition, and geometric convergence of the post-jump location kernel associated to the PDMP. An example based on the capacity expansion problem is presented, illustrating the possible applications of the results developed in the paper.

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.

Billiards in a General Domain with Random Reflections

We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain D R(d) until it hits the boundary and bounces randomly inside, according to some reflection law. We assume that the boundary of the domain is locally Lipschitz and almost everywhere continuously differentiable. The angle of the outgoing velocity with the inner normal vector has a specified, absolutely continuous density. We construct the discrete time and the continuous time processes recording the sequence of hitting points on the boundary and the pair location/velocity. We mainly focus on the case of bounded domains. Then, we prove exponential ergodicity of these two Markov processes, we study their invariant distribution and their normal (Gaussian) fluctuations. Of particular interest is the case of the cosine reflection law: the stationary distributions for the two processes are uniform in this case, the discrete time chain is reversible though the continuous time process is quasi-reversible. Also in this case, we give a natural construction of a chord ""picked at random"" in D, and we study the angle of intersection of the process with a (d - 1) -dimensional manifold contained in D.

QUASISTATIONARY DISTRIBUTIONS AND FLEMING-VIOT PROCESSES IN FINITE SPACES

Consider a continuous-time Markov process with transition rates matrix Q in the state space Lambda boolean OR {0}. In In the associated Fleming-Viot process N particles evolve independently in A with transition rates matrix Q until one of them attempts to jump to state 0. At this moment the particle jumps to one of the positions of the other particles, chosen uniformly at random. When Lambda is finite, we show that the empirical distribution of the particles at a fixed time converges as N -> infinity to the distribution of a single particle at the same time conditioned on not touching {0}. Furthermore, the empirical profile of the unique invariant measure for the Fleming-Viot process with N particles converges as N -> infinity to the unique quasistationary distribution of the one-particle motion. A key element of the approach is to show that the two-particle correlations are of order 1/N.

Modulation of Mediotemporal and Ventrostriatal Function in Humans by Delta 9-Tetrahydrocannabinol A Neural Basis for the Effects of Cannabis sativa on Learning and Psychosis

Context: Cannabis sativa use can impair verbal learning, provoke acute psychosis, and increase the risk of schizophrenia. It is unclear where C sativa acts in the human brain to modulate verbal learning and to induce psychotic symptoms. Objectives: To investigate the effects of 2 main psychoactive constituents of C sativa, Delta 9-tetrahydrocannabinol (Delta 9-THC) and cannabidiol, on regional brain function during verbal paired associate learning. Design: Subjects were studied on 3 separate occasions using a block design functional magnetic resonance imaging paradigm while performing a verbal paired associate learning task. Each imaging session was preceded by the ingestion of Delta 9-THC (10 mg), cannabidiol (600 mg), or placebo in a double-blind, randomized, placebo-controlled, repeated-measures, within-subject design. Setting: University research center. Participants: Fifteen healthy, native English-speaking, right-handed men of white race/ethnicity who had used C sativa 15 times or less and had minimal exposure to other illicit drugs in their lifetime. Main Outcome Measures: Regional brain activation ( blood oxygen level-dependent response), performance in a verbal learning task, and objective and subjective ratings of psychotic symptoms, anxiety, intoxication, and sedation. Results: Delta 9-Tetrahydrocannabinol increased psychotic symptoms and levels of anxiety, intoxication, and sedation, whereas no significant effect was noted on these parameters following administration of cannabidiol. Performance in the verbal learning task was not significantly modulated by either drug. Administration of Delta 9-THC augmented activation in the parahippocampal gyrus during blocks 2 and 3 such that the normal linear decrement in activation across repeated encoding blocks was no longer evident. Delta 9-Tetrahydrocannabinol also attenuated the normal time-dependent change in ventrostriatal activation during retrieval of word pairs, which was directly correlated with concurrently induced psychotic symptoms. In contrast, administration of cannabidiol had no such effect. Conclusion: The modulation of mediotemporal and ventrostriatal function by Delta 9-THC may underlie the effects of C sativa on verbal learning and psychotic symptoms, respectively.

Facies, delta(13)C, delta(15)N and C/N analyses in a late Quaternary compound estuarine fill, northern Brazil and relation to sea level

The present work integrates sedimentary facies, (14)C dating, delta(13)C, delta(15)N, and C/N with geologic and geomorphologic data available from literature. The aim was to characterize the depositional settings of a late Quaternary estuary in northeastern Marajo Island and analyze its evolution within the context of relative sea level fluctuations. The data derive from four continuous cores along a proximal-to-distal transect of a paleoestuary, previously recognized using remote sensing information. Fifteen sediment samples recorded ages ranging from 42,580 +/- 1430 to 3184 +/- 37 (14)C yr B.P. Fades analysis indicated fine- to coarse-grained sands with parallel lamination or cross stratification, massive or laminated muds and heterolithic deposits. delta(13)C (-28.1 parts per thousand to -19.7 parts per thousand, mean = -23.0 parts per thousand), delta(15)N (+ 14.8 parts per thousand to + 4.7 parts per thousand, mean = + 9.2 parts per thousand) and C/N (14.5 to 1.5, mean = 7.9) indicate mostly marine and freshwater phytoplankton sources for the organic matter. The results confirm a large late Quaternary paleoestuary in northeastern Marajo Island. The distribution of delta(13)C, delta(15)N, and C/N, together with fades associations, led to identify depositional settings related to fluvial channel, floodplain, tidal channel/tidal flat, central basin, tidal delta, and tidal inlet/sand barrier. These deposits are consistent with a wave-dominated estuary. Variations in stratigraphy and geochemistry are controlled by changes in relative sea level, revealing a main transgression from an undetermined time around 42,000 (14)C yr B.P. and 29,340 (+/- 200) (14)C yr B.P., which is synchronous to the overall drop in sea level after the last interglacial. Following this period, and probably until 9110 +/- 37 (14)C yr B.P., i.e., during a time interval encompassing two glacial episodes including the Last Glacial and the Younger Dryas, there was a pronounced drop in sea level, recorded by the development of a major erosional discontinuity due to valley re-incision. Sea level rose again until 5464 +/- 40 (14)C yr B.P, just before the main worldwide mid-Holocene transgressive peak. Mid to late Holocene coastal progradation ended the Marajo paleoestuarine history, and promoted the establishment of continental conditions throughout the island. The divergence comparing the Marajo sea level behavior with the eustatic curve allows hypothesizing that post-rifting tectonics along the Brazilian Equatorial margin influenced the sedimentary evolution of the studied paleoestuary. Considering that sedimentary facies in estuarine settings are highly variable both laterally and vertically, the present integration of facies with isotope and elemental analyses was crucial to provide a more precise interpretation of the Late Pleistocene and Holocene Marajo paleoestuary, and analyze its sea level history within the eustatic and tectonic context. (C) 2010 Elsevier B.V. All rights reserved.

Tonal Modulation and Subjective Time

This work investigated listeners` sense of the temporal expression of tonal modulation. One experiment described the effects on retrospective reproductions of sudden and gradual modulations to close and distant keys. The results showed that modulations elicit time underestimations as an inverse function of interkey distances, with a major impact for sudden modulations. A proposed vectorial model - ""Expected Development Fraction"" (EDF) - describes the development of expectations when an interkey distance is traversed during a certain time interval. This expected development is longer than the perceived duration, leading to underestimation of the time.

Qualitative and Quantitative Real Time Myocardial Contrast Echocardiography for Detecting Hibernating Myocardium

Background: Real time myocardial contrast echocardiography (RTMCE) is an emerging imaging modality for assessing myocardial perfusion that allows for noninvasive quantification of regional myocardial blood flow (MBF). Aim: We sought to assess the value of qualitative analysis of myocardial perfusion and quantitative assessment of myocardial blood flow (MBF) by RTMCE for predicting regional function recovery in patients with ischemic heart disease who underwent coronary artery bypass grafting (CABG). Methods: Twenty-four patients with coronary disease and left ventricular systolic dysfunction (ejection fraction < 45%) underwent RTMCE before and 3 months after CABG. RTMCE was performed using continuous intravenous infusion of commercially available contrast agent with low mechanical index power modulation imaging. Viability was defined by qualitative assessment of myocardial perfusion as homogenous opacification at rest in >= 2 segments of anterior or >= 1 segment of posterior territory. Viability by quantitative assessment of MBF was determined by receiver-operating characteristics curve analysis. Results: Regional function recovery was observed in 74% of territories considered viable by qualitative analysis of myocardial perfusion and 40% of nonviable (P = 0.03). Sensitivity, specificity, positive and negative predictive values of qualitative RTMCE for detecting regional function recovery were 74%, 60%, 77%, and 56%, respectively. Cutoff value of MBF for predicting regional function recovery was 1.76 (AUC = 0.77; 95% CI = 0.62-0.92). MBF obtained by RTMCE had sensitivity of 91%, specificity of 50%, positive predictive value of 75%, and negative predictive value of 78%. Conclusion: Qualitative and quantitative RTMCE provide good accuracy for predicting regional function recovery after CABG. Determination of MBF increases the sensitivity for detecting hibernating myocardium. (Echocardiography 2011;28:342-349).