scholarly journals A Convex Optimization Approach to Multiple Stopping: Pricing Chooser Caps and Swing Options

2019 ◽  
Author(s):  
Shyam Sundar Chandramouli
Keyword(s):  
Convex Optimization ◽  
Optimization Approach ◽  
Swing Options ◽  
Multiple Stopping

scholarly journals Maximizing protein translation rate in the non-homogeneous ribosome flow model: a convex optimization approach

2014 ◽  
Vol 11 (100) ◽  
pp. 20140713 ◽  
Author(s):  
Gilad Poker ◽  
Yoram Zarai ◽  
Michael Margaliot ◽  
Tamir Tuller
Keyword(s):  
Synthetic Biology ◽  
Convex Optimization ◽  
Production Rate ◽  
Protein Production ◽  
Flow Model ◽  
Protein Translation ◽  
Optimization Approach ◽  
Initiation Rate ◽  
Translation Rate ◽  
Protein Production Rate

Translation is an important stage in gene expression. During this stage, macro-molecules called ribosomes travel along the mRNA strand linking amino acids together in a specific order to create a functioning protein. An important question, related to many biomedical disciplines, is how to maximize protein production. Indeed, translation is known to be one of the most energy-consuming processes in the cell, and it is natural to assume that evolution shaped this process so that it maximizes the protein production rate. If this is indeed so then one can estimate various parameters of the translation machinery by solving an appropriate mathematical optimization problem. The same problem also arises in the context of synthetic biology, namely, re-engineer heterologous genes in order to maximize their translation rate in a host organism. We consider the problem of maximizing the protein production rate using a computational model for translation–elongation called the ribosome flow model (RFM). This model describes the flow of the ribosomes along an mRNA chain of length n using a set of n first-order nonlinear ordinary differential equations. It also includes n + 1 positive parameters: the ribosomal initiation rate into the mRNA chain, and n elongation rates along the chain sites. We show that the steady-state translation rate in the RFM is a strictly concave function of its parameters. This means that the problem of maximizing the translation rate under a suitable constraint always admits a unique solution, and that this solution can be determined using highly efficient algorithms for solving convex optimization problems even for large values of n . Furthermore, our analysis shows that the optimal translation rate can be computed based only on the optimal initiation rate and the elongation rate of the codons near the beginning of the ORF. We discuss some applications of the theoretical results to synthetic biology, molecular evolution, and functional genomics.

Segregation of Heterogeneous Robotics Swarms via Convex Optimization

2016 ◽  
Author(s):  
Victoria Edwards ◽  
Paulo Rezeck ◽  
Luiz Chaimowicz ◽  
M. Ani Hsieh
Keyword(s):  
Convex Optimization ◽  
Division Of Labor ◽  
Optimization Approach ◽  
Control Methods ◽  
Natural Phenomena ◽  
The Past ◽  
Robotic Swarms ◽  
Theoretical Results

The division of labor amongst a heterogeneous swarm of robots increases the range and sophistication of the tasks the swarm can accomplish. To efficiently execute a task the swarm of robots must have some starting organization. Over the past decade segregation of robotic swarms has grown as a field of research drawing inspiration from natural phenomena such as cellular segregation. A variety of different approaches have been undertaken to devise control methods to organize a heterogeneous swarm of robots. In this work, we present a convex optimization approach to segregate a heterogeneous swarm into a set of homogeneous collectives. We present theoretical results that show our approach is guaranteed to achieve complete segregation and validate our strategy in simulation and experiments.

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