Turnpike Property and Convergence Rate for an Investment Model with General Utility Functions

In this paper we aim to address two questions faced by a long-term investor with a power-type utility at high levels of wealth: one is whether the turnpike property still holds for a general utility that is not necessarily differentiable or strictly concave, the other is whether the error and the convergence rate of the turnpike property can be estimated. We give positive answers to both questions. To achieve these results, we first show that there is a classical solution to the HJB equation and give a representation of the solution in terms of the dual function of the solution to the dual HJB equation. We demonstrate the usefulness of that representation with some nontrivial examples that would be difficult to solve with the trial and error method. We then combine the dual method and the partial differential equation method to give a direct proof to the turnpike property and to estimate the error and the convergence rate of the optimal policy when the utility function is continuously differentiable and strictly concave. We finally relax the conditions of the utility function and provide some sufficient conditions that guarantee the turnpike property and the convergence rate in terms of both primal and dual utility functions.Comment: 29 page

Design and Functional Assembly of Synthetic Biological Parts and Devices

Programming living cells with synthetic gene circuits to perform desired tasks has been a major theme in the emerging field of synthetic biology. However, gene circuit engineering currently lacks the same predictability and reliability as seen in other mature engineering disciplines. This thesis focuses on the design and engineering of novel modular and orthogonal biological devices, and the predictable functional assembly of modular biological elements (BioParts) into customisable larger biological devices. The thesis introduces the design methodology for engineering modular and orthogonal biological devices. A set of modular biological devices with digital logic functions, including the AND, NOT and combinatorial NAND gates, were constructed and quantitatively characterised. In particular, a novel genetic AND gate was engineered in Escherichia coli by redesigning the natural HrpR/HrpS heteroregulation motif in the hrp system of Pseudomonas syringae. The AND gate is orthogonal to E. coli chassis, and employs the alternative σ54-dependent gene transcription to achieve tight transcriptional control. Results obtained show that context has a large impact on part and device behaviour, established through the systematic characterisation of a series of biological parts and devices in various biophysical and genetic contexts. A new, effective strategy is presented for the assembly of BioParts into functional customised systems using engineered ‘incontext’ characterised modules aided by modelling, which can significantly increase the predictability of circuit construction by characterising the component parts and modules in the same biophysical and genetic contexts as anticipated in their final systems. Finally, the thesis presents the design and construction of an application-oriented integrated system – the cell density-dependent microbe-based biosensor. The in vivo biosensor was programmed to be able to integrate its own cell density signal through an engineered cell-cell communication module and a second environmental signal through an environment-responsive promoter in the logic AND manner, with GFP as the output readout

Smooth Value Functions for a Class of Nonsmooth Utility Maximization Problems

In this paper we prove that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave. The value function is smooth if admissible controls satisfy an integrability condition or if it is continuous on the closure of its domain. The key idea is to work on the dual control problem and the dual HJB equation. We construct a smooth, strictly convex solution to the dual HJB equation and show that its conjugate function is a smooth, strictly concave solution to the primal HJB equation satisfying the terminal and boundary conditions.Comment: 18 page

Generalized Yule-Walker Estimation for Spatio-Temporal Models with Unknown Diagonal Coefficients

We consider a class of spatio-temporal models which extend popular econometric spatial autoregressive panel data models by allowing the scalar coefficients for each location (or panel) different from each other. To overcome the innate endogeneity, we propose a generalized Yule-Walker estimation method which applies the least squares estimation to a Yule-Walker equation. The asymptotic theory is developed under the setting that both the sample size and the number of locations (or panels) tend to infinity under a general setting for stationary and alpha-mixing processes, which includes spatial autoregressive panel data models driven by i.i.d. innovations as special cases. The proposed methods are illustrated using both simulated and real data

Software defect prediction based on association rule classification.

In software defect prediction, predictive models are estimated based on various code attributes to assess the likelihood of software modules containing errors. Many classification methods have been suggested to accomplish this task. However, association based classification methods have not been investigated so far in this context. This paper assesses the use of such a classification method, CBA2, and compares it to other rule based classification methods. Furthermore, we investigate whether rule sets generated on data from one software project can be used to predict defective software modules in other, similar software projects. It is found that applying the CBA2 algorithm results in both accurate and comprehensible rule sets.Software defect prediction; Association rule classification; CBA2; AUC;

Rice microtubule‐associated protein IQ67‐DOMAIN14 regulates rice grain shape by modulating microtubule cytoskeleton dynamics

Cortical microtubule (MT) arrays play a critical role in plant cell shape determination by defining the direction of cell expansion. As plants continuously adapt to ever‐changing environmental conditions, multiple environmental and developmental inputs need to be translated into changes of the MT cytoskeleton. Here, we identify and functionally characterize an auxin‐inducible and MT‐localized protein OsIQ67‐DOMAIN14 (OsIQD14), which is highly expressed in rice seed hull cells. We show that while deficiency of OsIQD14 results in short and wide seeds and increases overall yield, overexpression leads to narrow and long seeds, caused by changed MT alignment. We further show that OsIQD14‐mediated MT reordering is regulated by specifically affecting MT dynamics, and ectopic expression of OsIQD14 in Arabidopsis could change the cell shape both in pavement cells and hypocotyl cells. Additionally, OsIQD14 activity is tightly controlled by calmodulin proteins, providing an alternative way to modify the OsIQD14 activity. Our results indicate that OsIQD14 acts as a key factor in regulating MT rearrangements in rice hull cells and hence the grain shape, and allows effective local cell shape manipulation to improve the rice yield trait