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"Krawczyk, Jacek B"
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Controlling the thickness of the atherosclerotic plaque by statin medication
Atherosclerosis, a chronic inflammatory disorder of the arterial wall, is a complex process whose dynamics are affected by multiple factors. The disease control consists of restraining it by administering statins. Slowing down or halting the plaque growth depends on the patient age at which the statin treatment begins and on the thickness of the intima-media (IMT) at that time. In this paper, we propose a mathematical model to estimate the sets of atherosclerosis states, from which the use of statins can restrain the disease. Our model is control-theoretic, and the estimated sets are the viability kernels, in the parlance of viability theory. To our best knowledge, this way of modelling the atherosclerosis progression is original. We compute two viability kernels, each for a different statin-treatment dose. Each kernel is composed of the vector [age, IMT] from which the disease can be restrained. By extension, the disease can't be restrained from the kernel complements, this being mainly because of the disease and patient-age advancement. The kernels visualise tradeoffs between early and late treatments, which helps the clinician to decide when to start the statin treatment and which statin dose may be sufficient.
Journal Article
A qualitative game of interest rate adjustments with a nuisance agent
A qualitative game describes a situation in which antagonistic players strive to keep the evolutions of their state variables in predetermined constraint sets. We argue that a qualitative game model is a suitable mathematical representation of the struggle between a domestic central bank of a small open economy and a foreign central bank of a large economy to maintain their respective state variables within an acceptable band regardless of the other player's choices. The actions of the foreign central bank affect the domestic exchange rate and, hence, domestic inflation, output gap and interest rate. However, these actions do not necessarily aim to destabilise the small open economy, nor do they take into account the state of the latter. The domestic bank's problem, therefore, is similar to that of a game against nature. We refer to this type of qualitative game as a nuisance-agent game (or NA-game). We use viability theory to derive satisficing rules (in the sense of Simon) of nominal interest-rate adjustments for the domestic central bank of a small open economy in a qualitative NA-game against the foreign central bank.
Journal Article
Sustainable Emission Control Policies: Viability Theory Approach
Our interest is in the relationship between the environment and economic growth. Because various interest groups see this issue differently, the typical optimization approach based on representative agent is not suitable. This is mainly because assessing the relative weight between consumption and environment in the utility function in a democracy is a sensitive political process. On the other hand, constraints on capital, consumption, and pollution levels should be agreed considerably easier than the aforementioned weight because the constraints refer to quantifiable measures. We propose that a regulator can look for a feasible strategy for emission control that will maintain capital, consumption, and pollution in a closed set of constraints. Such a strategy is called viable in viability theory. Viability theory is the study of dynamic systems that asks what set of initial conditions will generate evolutions that obey the laws of motion of a system and remain in a certain state constraints set for the duration of the evolution. We apply viability theory to a neoclassical model to identify which current economic states are sustainable under smooth adjustments of abatement-rate in the future. Among many observations, we note that countries that embark on an ambitious abatement program may fail to maintain their economies within the state constraints if their present levels of capital and consumption are low.
Journal Article
Delivering left-skewed portfolio payoff distributions in the presence of transaction costs
For pension-savers, a low payoff is a financial disaster. Such investors will most likely prefer left-skewed payoff distributions over right-skewed payoff distributions. We explore how such distributions can be delivered. Cautious-relaxed utility measures are cautious in ensuring that payoffs don't fall much below a reference value, but relaxed about exceeding it. We find that the payoff distribution delivered by a cautious-relaxed utility measure has appealing features which payoff distributions delivered by traditional utility functions don't. In particular, cautious-relaxed distributions can have the mass concentrated on the left, hence be left-skewed. However, cautious-relaxed strategies prescribe frequent portfolio adjustments which may be expensive if transaction costs are charged. In contrast, more traditional strategies can be time-invariant. Thus we investigate the impact of transaction costs on the appeal of cautious-relaxed strategies. We find that relatively high transaction fees are required for the cautious-relaxed strategy to lose its appeal. This paper contributes to the literature which compares utility measures by the payoff distributions they produce and finds that a cautious-relaxed utility measure will deliver payoffs that many investors will prefer.
Journal Article
A Control-Theoretic Model of Atherosclerosis
We propose a control-theoretic aggregate model of the progression of atherosclerosis plaque, a chronic inflammatory disease of the arterial wall, to study the basic features of this disease. In the model, we exploit the role of inflammation in the disease progression, and use statins—drugs commonly recommended in atherosclerosis—to control this progression. We use a logistic function to allow for constrained growth of plaque. In the model, both the patient’s age and overall health impact the plaque growth and its sensitivity to statins. The model parameters are estimated using original data, or calibrated using published research as well as our own clinical and laboratory studies. We contend that our model helps to gauge the statins’ impact on a patient’s plaque thickness, hence the disease’s progression and cardiovascular risk, without requiring artery scans.
Journal Article
Playing Pollution Games with Thermal Electricity Generators
This paper discusses the economic and environmental implications of a stylised electricity market with transmission grid constraints and shared temporal pollution standards that restrict the joint strategy space of the agents. These are problematic to enforce if individual monitoring is impossible or very expensive. For such situations, we propose a time-dependent (or “open-loop dynamic”), game-theoretic model capable of analysing coupled constraints equilibria, also known as generalised Nash. We compute these equilibria for thermal generators subjected to annual pollution limits and instantaneous grid restrictions for a three-node dc model with a two-period load duration curve. The model illustrates the possibility that well-meaning environmental regulation might harm consumer surplus. It also highlights the cost to efficiency of regulatory attempts to ease the burden of compliance.
Journal Article
Management of High-Risk Atherosclerotic Patients by Statins May Be Supported by Logistic Model of Intima-Media Thickening
While the use of statins in treating patients with atherosclerosis is an undisputed success, the questions regarding an optimal starting time for treatment and its strength remain open. We proposed in our earlier paper published in Int. J. Mol. Sci. (2019, 20) that the growth of intima-media thickness of the carotid artery follows an S-shape (i.e., logistic) curve. In our subsequent paper in PLoS ONE (2020, 15), we incorporated this feature into a logistic control-theoretic model of atherosclerosis progression and showed that some combinations of patient age and intima-media thickness are better suited than others to start treatment. In this study, we perform a new and comprehensive calibration of our logistic model using a recent clinical database. This allows us to propose a procedure for inferring an optimal age to start statin treatment for a particular group of patients. We argue that a decrease in the slope of the IMT logistic growth curve, induced by statin treatment, is most efficient where the curve is at its steepest, whereby the efficiency means lowering the future IMT levels. Using the procedure on an aggregate group of severely sick men, 38 years of age is observed to correlate with the steepest point of the logistic curve, and, thus, it is the preferred time to start statin treatment. We believe that detecting the logistic curve’s steepest fragment and commencing statin administration on that fragment are courses of action that agree with clinician intuition and may support decision-making processes.
Journal Article
Sustainability screw: role of relative production and abatement time scales
We postulate that reasonable notions of sustainability must include a time-scale synchronization of both the processes of human development and those of the natural environment. We perform our analysis within a simple system of five differential equations where non-renewable and renewable resources are coupled with production capacities, abatement and human capital as functions of time. A 'sustainability screw' phenomenon is demonstrated describing a spiral like trajectory of three key variables-the non-renewable resources, the renewable resources and the production capital. This spiral may tend to an undesirable steady state, however, by adjusting a ratio of intensity parameters, time scales of production and natural recovery processes can be altered to produce more sustainable trajectories.
Journal Article
Computation of viability kernels: a case study of by-catch fisheries
Traditional means of studying environmental economics and management problems consist of optimal control and dynamic game models that are solved for optimal or equilibrium strategies. Notwithstanding the possibility of multiple equilibria, the models’ users—managers or planners—will usually be provided with a single optimal or equilibrium strategy no matter how reliable, or unreliable, the underlying models and their parameters are. In this paper we follow an alternative approach to policy making that is based on viability theory. It establishes “satisficing” (in the sense of Simon), or viable, policies that keep the dynamic system in a constraint set and are, generically, multiple and amenable to each manager’s own prioritisation. Moreover, they can depend on fewer parameters than the optimal or equilibrium strategies and hence be more robust. For the determination of these (viable) policies, computation of “viability kernels” is crucial. We introduce a MATLAB application, under the name of VIKAASA, which allows us to compute approximations to viability kernels. We discuss two algorithms implemented in VIKAASA. One approximates the viability kernel by the locus of state space positions for which solutions to an auxiliary cost-minimising optimal control problem can be found. The lack of any solution implies the infinite value function and indicates an evolution which leaves the constraint set in finite time, therefore defining the point from which the evolution originates as belonging to the kernel’s complement. The other algorithm accepts a point as viable if the system’s dynamics can be stabilised from this point. We comment on the pros and cons of each algorithm. We apply viability theory and the VIKAASA software to a problem of by-catch fisheries exploited by one or two fleets and provide rules concerning the proportion of fish biomass and the fishing effort that a sustainable fishery’s exploitation should follow.
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