In this paper, we consider a distributed stochastic computation of AXB=C with local set constraints over an multi-agent system, where each agent over the network only knows a few rows or columns of matrixes. Through formulating an equivalent distributed optimization problem for seeking least-squares solutions of AXB=C, we propose a distributed stochastic mirror-descent algorithm for solving the equivalent distributed problem. Then, we provide the sublinear convergence of the proposed algorithm. Moreover, a numerical example is also given to illustrate the effectiveness of the proposed algorithm.
Maintaining liquid asset portfolios involves a high carry cost and is mandatory by law for most financial institutions. Taking this into account a financial institution's aim is to manage a liquid asset portfolio in an "optimal" way, such that it keeps the minimum required liquid assets to comply with regulations. In this paper we propose a multi-stage dynamic stochastic programming model for liquid asset portfolio management. The model allows for portfolio rebalancing decisions over a multi-period horizon, as well as for flexible risk management decisions, such as reinvesting coupons, at intermediate time steps. We show how our problem closely relates to insurance products with guarantees and utilize this in the formulation. We will discuss our formulation and implementation of a multi-stage stochastic programming model that minimizes the down-side risk of these portfolios. The model is back-tested on real market data over a period of two years
In a Discounted Markov Decision Process (DMDP) with finite action sets the Value Iteration Algorithm, under suitable conditions, leads to an optimal policy in a finite number of steps. Determining an upper bound on the necessary number of steps till gaining convergence is an issue of great theoretical and practical interest as it would provide a computationally feasible stopping rule for value iteration as an algorithm for finding an optimal policy. In this paper we find such a bound depending only on structural properties of the Markov Decision Process, under mild standard conditions and an additional "individuality" condition, which is of interest in its own. It should be mentioned that other authors find such kind of constants using non-structural information, i.e., information not immediately apparent from the Decision Process itself. The DMDP is required to fulfill an ergodicity condition and the corresponding ergodicity index plays a critical role in the upper bound.
In this paper we obtain a strong invariance principle for negatively associated random fields, under the assumptions that the field has a finite $(2+\delta )$th moment and the covariance coefficient $u(n)$ exponentially decreases to $0$. The main tools are the Berkes-Morrow multi-parameter blocking technique and the Csörgő-Révész quantile transform method.
BACKGROUND: Radio frequency (RF) and chemical peels have been used for nonablative skin rejuvenation. Both of these cause collagen remodeling in the dermis and neo-collagen formation resulting in facial rejuvenation. There is limited literature on the evaluation of collagen remodeling by objective methods. OBJECTIVE: To compare the benefits of monopolar radiofrequency and glycolic acid peels in facial rejuvenation with regards to histopathology and Ultrabiomicroscopic sonography (UBM). METHODOLOGY: In this study, forty patients with mild to moderate photoaging received four treatments with 3 weeks interval of monopolar radiofrequency on one side of face and glycolic acid peels in increasing concentrations (NeostrataR) on the other side. Pre and post treatment, 2 mm biopsies were taken from both preauricular areas and Ultrasonography using a 35 MHz probe was done from outer canthus of eye and nasolabial folds from both sides of face. A blinded assessment was done to measure the increase in the grenz zone and dermal thickness. RESULTS: In 35/40 patients there was a significant increase in the grenz zone on histopathology and decrease in subepidermal low-echogenic band (SLEB) on UBM of the nasolabial folds on both sides of the face (p < 0.05). CONCLUSION: Radiofrequency and chemical peels showed equal efficacy in the treatment of facial rejuvenation. and D. V. Wakade, C. S. Nayak, K. D. Bhatt