Process design in SISO systems with input multiplicity using bifurcation analysis and optimisation

This paper presents an approach using continuation and optimisation methods for modifying a process design to avoid control difficulties caused by input multiplicity. The approach assumes an initial design, with a preassigned SISO control structure, has been obtained and is useful where there is an input multiplicity in the operating region. The condition for input multiplicity is obtained by inflating the state space model with a state representing the locus of the point of zero gain. The multiplicity condition is determined using the bifurcation analysis package, AUTO, which allows the study of the influence of operating conditions and parameters on input multiplicity behaviour to obtain an expression for the point of zero gain as a function of the design and disturbance variables. A process modification problem is formulated within an optimisation framework and solved to determine the minimal design parameter changes necessary to avoid input multiplicity given an assumed maximal disturbance. Results are presented for the application of the algorithm to a CSTR system demonstrating that small changes in some design variables can avoid input multiplicity problems in this case, and that the method can determine the changes necessary

Biclustering via optimal re-ordering of data matrices in systems biology: rigorous methods and comparative studies

<p>Abstract</p> <p>Background</p> <p>The analysis of large-scale data sets via clustering techniques is utilized in a number of applications. Biclustering in particular has emerged as an important problem in the analysis of gene expression data since genes may only jointly respond over a subset of conditions. Biclustering algorithms also have important applications in sample classification where, for instance, tissue samples can be classified as cancerous or normal. Many of the methods for biclustering, and clustering algorithms in general, utilize simplified models or heuristic strategies for identifying the "best" grouping of elements according to some metric and cluster definition and thus result in suboptimal clusters.</p> <p>Results</p> <p>In this article, we present a rigorous approach to biclustering, OREO, which is based on the Optimal RE-Ordering of the rows and columns of a data matrix so as to globally minimize the dissimilarity metric. The physical permutations of the rows and columns of the data matrix can be modeled as either a network flow problem or a traveling salesman problem. Cluster boundaries in one dimension are used to partition and re-order the other dimensions of the corresponding submatrices to generate biclusters. The performance of OREO is tested on (a) metabolite concentration data, (b) an image reconstruction matrix, (c) synthetic data with implanted biclusters, and gene expression data for (d) colon cancer data, (e) breast cancer data, as well as (f) yeast segregant data to validate the ability of the proposed method and compare it to existing biclustering and clustering methods.</p> <p>Conclusion</p> <p>We demonstrate that this rigorous global optimization method for biclustering produces clusters with more insightful groupings of similar entities, such as genes or metabolites sharing common functions, than other clustering and biclustering algorithms and can reconstruct underlying fundamental patterns in the data for several distinct sets of data matrices arising in important biological applications.</p

Accelerating tube-based model predictive control by constraint removal

Tube-based model predictive control (MPC) is a variant of MPC that is suitable for constrained linear systems subject to additive bounded disturbances. We extend constraint removal, a technique recently introduced to accelerate nominal MPC, to tube-based MPC. Constraint removal detects inactive constraints before actually solving the MPC problem. By removing constraints that are known to be inactive from the optimization problem, the computational time required to solve it can be reduced considerably. We show that the number of constraints to be considered in the optimization problem decreases along any trajectory of the closed-loop system, until only the unconstrained optimization problem remains. The proposed variant of constraint removal is easy to apply. Since it does not depend on details of the optimization algorithm, it can easily be added to existing implementations of tube-based MPC

Nucleocytoplasmic shuttling of persistently activated STAT3.

Persistent activation of the transcription factor STAT3 has been detected in many types of cancer and plays an important role in tumor progression, immune evasion and metastasis. To analyze persistent STAT3 activation we coexpressed STAT3 with v-Src. We found that tyrosine phosphorylation of STAT3 by v-Src is independent of Janus kinases (Jaks), the canonical activators of STATs. The STAT3-induced feedback inhibitor, suppressor of cytokine signaling 3 (SOCS3), did not interfere with STAT3 activation by v-Src. However, the protein inhibitor of activated STAT3 (PIAS3) suppressed gene induction by persistently activated STAT3. We measured nucleocytoplasmic shuttling of STAT3 in single cells by bleaching the YFP moiety of double-labelled STAT3-CFP-YFP in the cytoplasm. Analysis of the subcellular distribution of CFP and YFP fluorescence over time by mathematical modeling and computational parameter estimation revealed that activated STAT3 shuttles more rapidly than non-activated STAT3. Inhibition of exportin-1-mediated nuclear export slowed down nucleocytoplasmic shuttling of v-Src-activated STAT3 resulting in reduced tyrosine phosphorylation, decreased induction of STAT3 target genes and increased apoptosis. We propose passage of persistently activated STAT3 through the nuclear pore complex as a new target for intervention in cancer