Optimal Output Feedback Architecture for Triangular LQG Problems

Distributed control problems under some specific information constraints can be formulated as (possibly infinite dimensional) convex optimization problems. The underlying motivation of this work is to develop an understanding of the optimal decision making architecture for such problems. In this paper, we particularly focus on the N-player triangular LQG problems and show that the optimal output feedback controllers have attractive state space realizations. The optimal controller can be synthesized using a set of stabilizing solutions to 2N linearly coupled algebraic Riccati equations, which turn out to be easily solvable under reasonable assumptions.Comment: To be presented at 2014 American Control Conferenc

Random walks on Galton-Watson trees with infinite variance offspring distribution conditioned to survive

We establish a variety of properties of the discrete time simple random walk on a Galton-Watson tree conditioned to survive when the offspring distribution, Z say, is in the domain of attraction of a stable law with index alpha is an element of (1,2]. In particular, we are able to prove a quenched version of the result that the spectral dimension of the random walk is 2 alpha/(2 alpha-1). Furthermore, we demonstrate that when alpha is an element of (1,2) there are logarithmic fluctuations in the quenched transition density of the simple random walk, which contrasts with the log-logarithmic fluctuations seen when alpha=2. In the course of our arguments, we obtain tail bounds for the distribution of the nth generation size of a Galton-Watson branching process with offspring distribution Z conditioned to survive, as well as tail bounds for the distribution of the total number of individuals born up to the nth generation, that are uniform in n

Human stem cells and articular cartilage regeneration.

The regeneration of articular cartilage damaged due to trauma and posttraumatic osteoarthritis is an unmet medical need. Current approaches to regeneration and tissue engineering of articular cartilage include the use of chondrocytes, stem cells, scaffolds and signals, including morphogens and growth factors. Stem cells, as a source of cells for articular cartilage regeneration, are a critical factor for articular cartilage regeneration. This is because articular cartilage tissue has a low cell turnover and does not heal spontaneously. Adult stem cells have been isolated from various tissues, such as bone marrow, adipose, synovial tissue, muscle and periosteum. Signals of the transforming growth factor beta superfamily play critical roles in chondrogenesis. However, adult stem cells derived from various tissues tend to differ in their chondrogenic potential. Pluripotent stem cells have unlimited proliferative capacity compared to adult stem cells. Chondrogenesis from embryonic stem (ES) cells has been studied for more than a decade. However, establishment of ES cells requires embryos and leads to ethical issues for clinical applications. Induced pluripotent stem (iPS) cells are generated by cellular reprogramming of adult cells by transcription factors. Although iPS cells have chondrogenic potential, optimization, generation and differentiation toward articular chondrocytes are currently under intense investigation

Biased random walk on critical Galton-Watson trees conditioned to survive

We consider the biased random walk on a critical Galton-Watson tree conditioned to survive, and confirm that this model with trapping belongs to the same universality class as certain one-dimensional trapping models with slowly-varying tails. Indeed, in each of these two settings, we establish closely-related functional limit theorems involving an extremal process and also demonstrate extremal aging occurs

Thermodynamic black di-rings

Previously the five dimensional $S^1$-rotating black rings have been superposed in a concentric way by some solitonic methods, and regular systems of two $S^1$-rotating black rings were constructed by the authors and then Evslin and Krishnan (we called these solutions "black di-rings"). In this place we show some characteristics of the solutions of five dimensional black di-rings, especially in thermodynamic equilibrium. After the summary of the di-ring expressions and their physical quantities, first we comment on the equivalence of the two different solution sets of the black di-rings. Then the existence of thermodynamic black di-rings is shown, in which both isothermality and isorotation between the inner black ring and the outer black ring are realized. We also give detailed analysis of peculiar properties of the thermodynamic black di-ring including discussion about a certain kind of thermodynamic stability (instability) of the system.Comment: 26 pages,10 figures; references added, typos corredte