Proceedings of the ... IEEE Conference on Decision & Control. IEEE Conference on Decision & Control最新文献

Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such signal. Meanwhile, the diffusion of the signal is itself affected by the changes in shape and size of the organism. In other words, there is a complete coupling between the diffusion of the signal and the change of the shapes. In this paper, we introduce a mathematical model to investigate such coupling. The shape is given by a manifold, that varies in time as the result of a deformation given by a transport equation. The signal is represented by a density, diffusing on the manifold via a diffusion equation. We show the non-commutativity of the transport and diffusion evolution by introducing a new concept of Lie bracket between the diffusion and the transport operator. We also provide numerical simulations showing this phenomenon.

Numerical computation of the expected information content of a prospective experimental design is computationally expensive, requiring calculating the Kullback-Leibler divergence of the posterior distribution from the prior for simulated data from a large sample of points from the prior distribution. In this work, we investigate whether the Unscented Transform (UT) of the prior distribution can provide an adequate estimate of the expected information content in the context of experiment design for a previously validated HIV-1 2-LTR model. Three different schedules with evenly distributed time points have been used to generate the experimental data along with the incorporation of qPCR noise for the study. The UT shows promise in estimating information content by preserving the optimal ordering of 2-LTR sample collection schedules, when compared to completely stochastic sampling from the underlying multivariate distributions.

We propose a new stochastic global optimization method targeting protein docking problems. The method is based on finding a general convex polynomial underestimator to the binding energy function in a permissive subspace that possesses a funnel-like structure. We use Principal Component Analysis (PCA) to determine such permissive subspaces. The problem of finding the general convex polynomial underestimator is reduced into the problem of ensuring that a certain polynomial is a Sum-of-Squares (SOS), which can be done via semi-definite programming. The underestimator is then used to bias sampling of the energy function in order to recover a deep minimum. We show that the proposed method significantly improves the quality of docked conformations compared to existing methods.

A zone model predictive control (zone-MPC) algorithm that utilizes the Moving Horizon State Estimator (MHSE) is presented. The control application is an artificial pancreas for treating people with type 1 diabetes mellitus. During the meal challenge, the prediction quality of the zone-MPC algorithm with the MHSE was significantly better than when using the current Luenberger observer to provide the state estimate. Consequently, the controller using the MHSE rejected the meal disturbance faster and without inducing extra hypoglycemia risk (e.g., lower postprandial blood glucose peak by 10 mg/dL and higher postprandial minimum blood glucose by 11 mg/dL). The faster rejection of the meal disturbance led to a longer time in the clinically accepted safe region (70-180 mg/dL) by 13%, and this may reduce the likelihood of the complications related to type 1 diabetes mellitus.

An extension of a novel state estimation scheme is presented. The proposed method is developed for model predictive control (MPC) of an artificial pancreas for automatic insulin delivery to people with type 1 diabetes mellitus; specifically, glycemia control based on feedback by a continuous glucose monitor. The state estimation strategy is akin to moving-horizon estimation, but effectively exploits knowledge of sensor recalibrations, ameliorates the effects of delays between measurements and the controller call, and accommodates irregularly sampled output measurements. The method performs a function fit and a sampling action to synthesize a mock output trajectory for constructing the state. In this paper the structure of the fitted function prototype is divorced from the structure of the function that is sampled, facilitating the strategic elimination of prediction artifacts that are not observed in the actual plant. The proposed estimation strategy is demonstrated using clinical data collected by a Dexcom G4 Platinum continuous glucose monitor.

In this paper we consider the problem of minimization of a cost function that depends on the location and poses of one or more rigid bodies, or bodies that consist of rigid parts hinged together. We present a unified setting for formulating this problem as an optimization on an appropriately defined manifold for which efficient manifold optimizations can be developed. This setting is based on a Lie group representation of the rigid movements of a body that is different from what is commonly used for this purpose. We illustrate this approach by using the steepest descent algorithm on the manifold of the search space and specify conditions for its convergence.

Bivalirudin is used in patients with heparin-induced thrombocytopenia and is a direct thrombin inhibitor. Since it is a rarely used drug, clinical experience with its dosing is sparse. We develop a model that predicts the effect of bivalirudin, measured by the Partial Thromboplastin Time (PTT), based on its past fusion rates. We learn population-wide model parameters by solving a nonlinear optimization problem that uses a training set of patient data. More interestingly, we devise an adaptive algorithm based on the extended Kalman filter that can adapt model parameters to individual patients. The latter adaptive model emerges as the most promising as it reduces both the mean error and, drastically, the per-patient error variance. The model accuracy we demonstrate on actual patient measurements is sufficient to be useful in guiding optimal therapy.

Side-chain positioning (SCP) is an important component of computational protein docking methods. Existing SCP methods and available software have been designed for protein folding applications where side-chain positioning is also important. As a result they do not take into account significant special structure that SCP for docking exhibits. We propose a new algorithm which poses SCP as a Maximum Weighted Independent Set (MWIS) problem on an appropriately constructed graph. We develop an approximate algorithm which solves a relaxation of the MWIS and then rounds the solution to obtain a high-quality feasible solution to the problem. The algorithm is fully distributed and can be executed on a large network of processing nodes requiring only local information and message-passing between neighboring nodes. Motivated by the special structure in docking, we establish optimality guarantees for a certain class of graphs. Our results on a benchmark set of enzyme-inhibitor protein complexes show that our predictions are close to the native structure and are comparable to the ones obtained by a state-of-the-art method. The results are substantially improved if rotamers from unbound protein structures are included in the search. We also establish that the use of our SCP algorithm substantially improves docking results.

Our work is motivated by energy minimization of biological macromolecules, an essential step in computational docking. By allowing some ligand flexibility, we generalize a recently introduced novel representation of rigid body minimization as an optimization on the [Formula: see text] manifold, rather than on the commonly used Special Euclidean group SE(3). We show that the resulting flexible docking can also be formulated as an optimization on a Lie group that is the direct product of simpler Lie groups for which geodesics and exponential maps can be easily obtained. Our computational results for a local optimization algorithm developed based on this formulation show that it is about an order of magnitude faster than the state-of-the-art local minimization algorithms for computational protein-small molecule docking.