Network Cournot Competition

Cournot competition is a fundamental economic model that represents firms competing in a single market of a homogeneous good. Each firm tries to maximize its utility---a function of the production cost as well as market price of the product---by deciding on the amount of production. In today's dynamic and diverse economy, many firms often compete in more than one market simultaneously, i.e., each market might be shared among a subset of these firms. In this situation, a bipartite graph models the access restriction where firms are on one side, markets are on the other side, and edges demonstrate whether a firm has access to a market or not. We call this game \emph{Network Cournot Competition} (NCC). In this paper, we propose algorithms for finding pure Nash equilibria of NCC games in different situations. First, we carefully design a potential function for NCC, when the price functions for markets are linear functions of the production in that market. However, for nonlinear price functions, this approach is not feasible. We model the problem as a nonlinear complementarity problem in this case, and design a polynomial-time algorithm that finds an equilibrium of the game for strongly convex cost functions and strongly monotone revenue functions. We also explore the class of price functions that ensures strong monotonicity of the revenue function, and show it consists of a broad class of functions. Moreover, we discuss the uniqueness of equilibria in both of these cases which means our algorithms find the unique equilibria of the games. Last but not least, when the cost of production in one market is independent from the cost of production in other markets for all firms, the problem can be separated into several independent classical \emph{Cournot Oligopoly} problems. We give the first combinatorial algorithm for this widely studied problem

A new polynomial-time implementation of the out-of-kilter algorithm using Minty’s lemma

It is less well known how to use the out-of-kilter idea to solve the min-cost flow problem because the generic version of the out-of-kilter algorithm runs in exponential time, although it is the sort of algorithm that computers can do easily. Ciupala (2005) presented a scaling out-of-kilter algorithm that runs in polynomial time using the shortest path computation in each phase. In this paper, we present a new polynomial time implementation of out-of-kilter idea. The algorithm uses a scaling method that is different from Ciupala’s scaling method. Each phase of Ciupala’s method needs a shortest path computation, while our algorithm uses Minty’s lemma to transform all the out-of-kilter arcs into in-kilter arcs. When the given network is infeasible, Ciupala’s algorithm does not work, but our algorithm presents some information that helps to repair the infeasible network

Simultaneous Detemination of Atorvastatin Calcium and Amlodipine Besylate by Spectrophotometry and Multivariate Calibration Methods in Pharmaceutical Formulations

Resolution of binary mixture of atorvastatin (ATV) and amlodipine (AML) with minimum sample pretreatment and without analyte separation has been successfully achieved using a rapid method based on partial least square analysis of UV–spectral data. Multivariate calibration modeling procedures, traditional partial least squares (PLS-2), interval partial least squares (iPLS) and synergy partial least squares (siPLS), were applied to select a spectral range that provided the lowest prediction error in comparison to the full-spectrum model. The simultaneous determination of both analytes was possible by PLS processing of sample absorbance between 220-425 nm. The correlation coefficients (R) and root mean squared error of cross validation (RMSECV) for ATV and AML in synthetic mixture were 0.9991, 0.9958 and 0.4538, 0.2411 in best siPLS models respectively. The optimized method has been used for determination of ATV and AML in amostatin commercial tablets. The proposed method are simple, fast, inexpensive and do not need any separation or preparation methods

Sphingosine 1 phosphate agonists (SPI): A potential agent to prevent acute lung injury in COVID-19

SARS-CoV-2 is a worldwide pandemic, that has led to the morbidity and mortality of millions of people. This virus rapidly proliferates and destroys lung epithelial cells directly, which is worsened by a subsequent cytokine storm. This cytokine storm diffusely damages the alveolar barriers and leads to fibrin and fluid exudation, hyaline membrane formation, and infiltration of inflammatory cells into the lung causing acute respiratory distress syndrome (ARDS). To date, there exists no medication to treat SARS-CoV-2 infection and novel new therapeutics are still being explored to prevent or limit the damage to the lung. Sphingosine 1-phosphate (S1P) is an effective bioactive lipid mediator and its related signaling pathways are vital for endothelial cell integrity. Stabilizing the pulmonary endothelial barrier and decreasing the inflammatory infiltrate by S1P analogs such as Fingolimod (FTY720-P) would be a new therapeutic approach for the hindrance of pulmonary exudation and subsequent ARDS. Copyright © 2021 The Author(s); Published by Nickan Research Institute. This is an open-access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]