Dynamic Programming for General Linear Quadratic Optimal Stochastic Control with Random Coefficients

We are concerned with the linear-quadratic optimal stochastic control problem with random coefficients. Under suitable conditions, we prove that the value field $V(t,x,\omega), (t,x,\omega)\in [0,T]\times R^n\times \Omega$, is quadratic in $x$, and has the following form: $V(t,x)=\langle K_tx, x\rangle$ where $K$ is an essentially bounded nonnegative symmetric matrix-valued adapted processes. Using the dynamic programming principle (DPP), we prove that $K$ is a continuous semi-martingale of the form $$K_t=K_0+\int_0^t \, dk_s+\sum_{i=1}^d\int_0^tL_s^i\, dW_s^i, \quad t\in [0,T]$$ with $k$ being a continuous process of bounded variation and $$E\left[\left(\int_0^T|L_s|^2\, ds\right)^p\right] <\infty, \quad \forall p\ge 2;$$ and that $(K, L)$ with $L:=(L^1, \cdots, L^d)$ is a solution to the associated backward stochastic Riccati equation (BSRE), whose generator is highly nonlinear in the unknown pair of processes. The uniqueness is also proved via a localized completion of squares in a self-contained manner for a general BSRE. The existence and uniqueness of adapted solution to a general BSRE was initially proposed by the French mathematician J. M. Bismut (1976, 1978). It had been solved by the author (2003) via the stochastic maximum principle with a viewpoint of stochastic flow for the associated stochastic Hamiltonian system. The present paper is its companion, and gives the {\it second but more comprehensive} adapted solution to a general BSRE via the DDP. Further extensions to the jump-diffusion control system and to the general nonlinear control system are possible.Comment: 16 page

Comparing Income Distributions Between Economies That Reward Innovation And Those That Reward Knowledge

In this paper, we develop an optimal control model of labor allocation in two types of economy - one economy is for innovative workers and the other one for knowledge workers. In both economies, workers allocate time between learning and discovering new knowledge. Both markets consist of a continuum of heterogeneous agents that are distinguished by their learning ability. Workers are rewarded for the knowledge they possess in the knowledge economy, and only for the new knowledge they create in the innovative economy. We show that, at steady state, while human capital accumulation is higher in the knowledge economy, the rate of knowledge creation is not necessarily higher in the innovative economy. Secondly, we prove that when the cost of learning is sufficiently high, the distribution of net wage income in the knowledge economy dominates that in the innovative economy in the first degree.

Uniform fractional factorial designs

The minimum aberration criterion has been frequently used in the selection of fractional factorial designs with nominal factors. For designs with quantitative factors, however, level permutation of factors could alter their geometrical structures and statistical properties. In this paper uniformity is used to further distinguish fractional factorial designs, besides the minimum aberration criterion. We show that minimum aberration designs have low discrepancies on average. An efficient method for constructing uniform minimum aberration designs is proposed and optimal designs with 27 and 81 runs are obtained for practical use. These designs have good uniformity and are effective for studying quantitative factors.Comment: Published in at http://dx.doi.org/10.1214/12-AOS987 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Generation of spin current and polarization under dynamic gate control of spin-orbit interaction in low-dimensional semiconductor systems

Based on the Keldysh formalism, the Boltzmann kinetic equation and the drift diffusion equation have been derived for studying spin polarization flow and spin accumulation under effect of the time dependent Rashba spin-orbit interaction in a semiconductor quantum well. The time dependent Rashba interaction is provided by time dependent electric gates of appropriate shapes. Several examples of spin manipulation by gates have been considered. Mechanisms and conditions for obtaining the stationary spin density and the induced rectified DC spin current are studied.Comment: 10 pages, 3 figures, RevTeX

Deductive Optimization of Relational Data Storage

Optimizing the physical data storage and retrieval of data are two key database management problems. In this paper, we propose a language that can express a wide range of physical database layouts, going well beyond the row- and column-based methods that are widely used in database management systems. We use deductive synthesis to turn a high-level relational representation of a database query into a highly optimized low-level implementation which operates on a specialized layout of the dataset. We build a compiler for this language and conduct experiments using a popular database benchmark, which shows that the performance of these specialized queries is competitive with a state-of-the-art in memory compiled database system

Effects of the complex mass distribution of dark matter halos on weak lensing cluster surveys

Gravitational lensing effects arise from the light ray deflection by all of the mass distribution along the line of sight. It is then expected that weak lensing cluster surveys can provide us true mass-selected cluster samples. With numerical simulations, we analyze the correspondence between peaks in the lensing convergence $\kappa$-map and dark matter halos. Particularly we emphasize the difference between the peak $\kappa$ value expected from a dark matter halo modeled as an isolated and spherical one, which exhibits a one-to-one correspondence with the halo mass at a given redshift, and that of the associated $\kappa$-peak from simulations. For halos with the same expected $\kappa$, their corresponding peak signals in the $\kappa$-map present a wide dispersion. At an angular smoothing scale of $\theta_G=1\hbox{arcmin}$, our study shows that for relatively large clusters, the complex mass distribution of individual clusters is the main reason for the dispersion. The projection effect of uncorrelated structures does not play significant roles. The triaxiality of dark matter halos accounts for a large part of the dispersion, especially for the tail at high $\kappa$ side. Thus lensing-selected clusters are not really mass-selected. (abridged)Comment: ApJ accepte

Effect of mental training on short-term psychomotor skill acquisition in laparoscopic surgery - a pilot study

Aim: The mental demands of laparoscopic surgery create a steep learning curve for surgical trainees. Experienced surgeons informally conduct mental training prior to starting a complex laparoscopic procedure. Reconstructing haptic feedback to mentally observe surgeon-instrument-tissue interaction is considered to be acquired only with experience. An experiment was devised to implement mental training for the haptic feedback reconstruction and its effect on laparoscopic task performance was observed.Methods: Twenty laparoscopy novice medical students with normal/corrected visual acuity and normal hearing were randomised into two groups. Both groups were asked to apply a pre-established consistent force by means of retracting a laparoscopic grasper fixed to an electronic weight scale. Studied group underwent mental training while control group conducted a laparoscopic task as a distraction exercise. Accuracy of the task performance was measured as primary outcome. Performance between dominant and non-dominant hands was the secondary outcome.Results: Baseline assessment of both dominant and non-dominant hands between groups were similar (P &gt; 0.05). Mental training group improved their performance (0.66 ± 0.04) vs. (1.06 ± 0.14) with dominant hand (P &lt; 0.01) and (0.73 ± 0.04) vs. (1.10 ± 0.20) with non-dominant hand (P &lt; 0.05), when compared with control group.Conclusion: In a laparoscopic task performance, skill transfer is significantly accurate if mental haptic feedback reconstruction is achieved through mental training