On the Convergence of Alternating Direction Lagrangian Methods for Nonconvex Structured Optimization Problems

Nonconvex and structured optimization problems arise in many engineering applications that demand scalable and distributed solution methods. The study of the convergence properties of these methods is in general difficult due to the nonconvexity of the problem. In this paper, two distributed solution methods that combine the fast convergence properties of augmented Lagrangian-based methods with the separability properties of alternating optimization are investigated. The first method is adapted from the classic quadratic penalty function method and is called the Alternating Direction Penalty Method (ADPM). Unlike the original quadratic penalty function method, in which single-step optimizations are adopted, ADPM uses an alternating optimization, which in turn makes it scalable. The second method is the well-known Alternating Direction Method of Multipliers (ADMM). It is shown that ADPM for nonconvex problems asymptotically converges to a primal feasible point under mild conditions and an additional condition ensuring that it asymptotically reaches the standard first order necessary conditions for local optimality are introduced. In the case of the ADMM, novel sufficient conditions under which the algorithm asymptotically reaches the standard first order necessary conditions are established. Based on this, complete convergence of ADMM for a class of low dimensional problems are characterized. Finally, the results are illustrated by applying ADPM and ADMM to a nonconvex localization problem in wireless sensor networks.Comment: 13 pages, 6 figure

An Adaptive Inventory Management System for Hospital Supply Chain

In healthcare, delivering high quality care to the patients typically requires significant investment in supply chain management systems. Inventory management is an important part of any supply chain system. Researchers have indicated great potential for optimizing existing healthcare inventory systems, especially within hospitals. With ever changing needs, product prices and policies, managing inventory of products in hospitals becomes difficult. As time progresses, the inventory policies of products become sub-optimal. In this research, we study multiple echelons of a hospital supply chain considering the distributors, to address the need for an efficient and effective hospital inventory management system. We propose a method consisting of two components: (1) system design and optimization; and (2) system monitoring, evaluation, and forecasting. The system design and optimization methodology includes a sim-heuristic approach where optimization of inventory levels and hospital operations is considered. As time evolves, to monitor the relevant system performance measures over time, control-chart like methods are used. When significant deviations in system performance occur, a re-evaluation of the inventory decision variables and/or system operations is conducted to maintain an efficient inventory system. A hierarchical procedure is used to determine the extent of evaluation of the system. Experimental results are presented to demonstrate the effectiveness of this methodology

In silico identification of potential inhibitors for human aurora kinase b

Cell cycle progression through mitosis and meiosis involves regulation by serine/threonine kinases from the aurora family. Aurora kinase b (Aurkb) is mainly involved in the proper segregation of chromosomes during mitosis as well as meiosis. However, over expression of Aurkb leads to the unequal distribution of genetic information creating aneuploid cells, a hallmark of cancer. Thus, Aurkb can be used as an effective molecular target for computer-aided drug discovery against cancer. Existing Aurkb inhibitors are less efficient, hence an in silico work was carried out to identify novel potent inhibitors. Three published inhibitors azd1152, zm447439 and N-(4-{[6-methoxy-7-(3-morpholin-4-ylpropoxy) quinazolin- 4-yl] amino} phenyl) benzamide were subjected to high throughput virtual screening of over 1 million entries from a ligand info meta database, to generate a 1161 compound library. The crystal structure was optimized and energy was minimized applying an OPLS force field in Maestro v9.0. Molecular docking using Glide was performed to predict the binding orientation of the prepared ligand molecule into a grid of 20*20*20 Å created around the centroid of the optimized human Aurkb protein. Nine lead molecules with good binding affinity with human Aurkb were identified. In silico pharmacokinetics study for these nine lead molecules has shown no ADME violation. Analysis of lead ‘1’- human Aurkb docking complex has revealed a XP Gscore of -10.20 kcal/mol with a highly stabilized hydrogen bond network with Asp218 and Ala157 and good Van der wall interactions. The docking complex coincides well with the native co- crystallized human Aurkb and inhibitor zm447439 complex. Thus, lead 1 would be highly useful for developing potential drug molecules for the treatment of cancer

In silico identification of potential inhibitors for human aurora kinase b

Cell cycle progression through mitosis and meiosis involves regulation by serine/threonine kinases from the aurora family. Aurora kinase b (Aurkb) is mainly involved in the proper segregation of chromosomes during mitosis as well as meiosis. However, over expression of Aurkb leads to the unequal distribution of genetic information creating aneuploid cells, a hallmark of cancer. Thus, Aurkb can be used as an effective molecular target for computer-aided drug discovery against cancer. Existing Aurkb inhibitors are less efficient, hence an in silico work was carried out to identify novel potent inhibitors. Three published inhibitors azd1152, zm447439 and N-(4-{[6-methoxy-7-(3-morpholin-4-ylpropoxy) quinazolin- 4-yl] amino} phenyl) benzamide were subjected to high throughput virtual screening of over 1 million entries from a ligand info meta database, to generate a 1161 compound library. The crystal structure was optimized and energy was minimized applying an OPLS force field in Maestro v9.0. Molecular docking using Glide was performed to predict the binding orientation of the prepared ligand molecule into a grid of 20*20*20 Å created around the centroid of the optimized human Aurkb protein. Nine lead molecules with good binding affinity with human Aurkb were identified. In silico pharmacokinetics study for these nine lead molecules has shown no ADME violation. Analysis of lead ‘1’- human Aurkb docking complex has revealed a XP Gscore of -10.20 kcal/mol with a highly stabilized hydrogen bond network with Asp218 and Ala157 and good Van der wall interactions. The docking complex coincides well with the native co- crystallized human Aurkb and inhibitor zm447439 complex. Thus, lead 1 would be highly useful for developing potential drug molecules for the treatment of cancer

Million frames per second infrared imaging system

An infrared imaging system has been developed for measuring the temperature increase during the dynamic deformation of materials. The system consists of an 8×8 HgCdTe focal plane array, each with its own preamplifier. Outputs from the 64 detector/preamplifiers are digitized using a row-parallel scheme. In this approach, all 64 signals are simultaneously acquired and held using a bank of track and hold amplifiers. An array of eight 8:1 multiplexers then routes the signals to eight 10 MHz digitizers, acquiring data from each row of detectors in parallel. The maximum rate is one million frames per second. A fully reflective lens system was developed, consisting of two Schwarszchild objectives operating at infinite conjugation ratio. The ratio of the focal lengths of the objectives determines the lens magnification. The system has been used to image the distribution of temperature rise near the tip of a notch in a high strength steel sample (C-300) subjected to impact loading by a drop weight testing machine. The results show temperature rises at the crack tip up to around 70 K. Localization of temperature, and hence, of deformation into "U" shaped zones emanating from the notch tip is clearly seen, as is the onset of crack propagation

Pattern formation during de novo assembly of the Arabidopsis shoot meristem

Most multicellular organisms have a capacity to regenerate tissue after wounding. Few, however, have the ability to regenerate an entire new body from adult tissue. Induction of new shoot meristems from cultured root explants is a widely used, but poorly understood, process in which apical plant tissues are regenerated from adult somatic tissue through the de novo formation of shoot meristems. We characterize early patterning during de novo development of the Arabidopsis shoot meristem using fluorescent reporters of known gene and protein activities required for shoot meristem development and maintenance. We find that a small number of progenitor cells initiate development of new shoot meristems through stereotypical stages of reporter expression and activity of CUP-SHAPED COTYLEDON 2 (CUC2), WUSCHEL (WUS), PIN-FORMED 1 (PIN1), SHOOT-MERISTEMLESS (STM), FILAMENTOUS FLOWER (FIL, also known as AFO), REVOLUTA (REV), ARABIDOPSIS THALIANA MERISTEM L1 LAYER (ATML1) and CLAVATA 3 (CLV3). Furthermore, we demonstrate a functional requirement for WUS activity during de novo shoot meristem initiation. We propose that de novo shoot meristem induction is an easily accessible system for the study of patterning and self-organization in the well-studied model organism Arabidopsis

EFFICACY OF VRUNO-HEAL OIL IN THE MANAGEMENT OF DUSHTA VRUNA (NON HEALING WOUND)

Vruna is the commonest problem we face in practice. The wound in and out itself is the biggest challenge to medical practitioners, even more, when it's a non-healing type. In practice, Dushta vrana is that the most typically encountered problem faced by a health professional. Wound healing is a major problem in surgical practice also. Acharya Sushruta, has explained Vrana very well in “Sushruta Samhita” as a concourse of wound healing procedures described by Sushruta still holds its place today. Sushruta has described Shashti Upakrama (60 measures) for the great management of Vruna (wound). Here is a case report- of 57 Years male presented with complaints of an ulcer/ non healing wound on medial aspect and on lateral malleolus of right foot with pain, discharge, foul smell, edema, discoloration, and pus discharge. The case was treated with Vruno-heal oil as local application, and with few internal medications. Among these 60 Upakramas - Parisheka, Lekhana, Kashaya, Mrudukarma, Bandha modalities were used to treat the wound