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

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

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

Computing violated sets in a market equilibrium problem with constant prices

AbstractConsider Fisher’s and Arrow-Debreu’s market equilibrium models for a linear utilities case consisting of a set B of buyers and a set G of divisible goods. Supposing that a vector of prices P=(p1,…,p|G|) for goods is given and there are some buyers with surplus money, but, by the politics of the market, prices P are constant and cannot be changed in order to compute an equilibrium. In this paper, a set of buyers with surplus money is called a violated set. First, we define a kind of violated set called maximum mean, then compute a set of buyers with maximum surplus money corresponding to the definition of a maximum mean violated set. We show a maximum mean set is found in O(mnlog(n2/m)) time, where n=|B|+|G|, and m is the number of pairs (i,j), such that buyer i has some utility for purchasing goods j

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]

Expression profile of miR-15 and miR-16 in peripheral blood mononuclear cells of patients with steroid-resistant nephrotic syndrome

Introduction: Steroids are considered first-line therapeutic opportunities in cases with idiopathic nephrotic syndrome (INS). The trustworthy biomarkers for steroid-resistant NS (SRNS) would permit more precise decisions in the treatment of INS. Objectives: This study aimed to evaluate the miR-15 and miR-16 levels in NS cases. Patients and Methods: Adult cases with primary NS (n=60) including 30 FSGS (Focal segmental glomerulosclerosis) and 30 membranous glomerulonephritis (MGN) patients and 24 healthy individuals were included. The evaluation of miR-15 and miR-16 expression in blood cells was performed using real-time polymerase chain reaction (qPCR). Moreover, gene ontology analysis and prediction of the miRNA targets were completed to recognize the biological procedures and signaling pathways involved in the pathophysiology of NS. Results: A significant increase was observed in miR-15a-5p expression in cases with primary MGN and FSGS compared with healthy subjects. Conversely, the miR-16-5p expression was significantly decreased in both conditions compared with healthy controls. In the clinical subdivision of FSGS group to steroid-resistant-FSGS and steroid-responsive-FSGS, significant elevated levels of miR-15a-5p and diminished levels of miR-16-5p were observed in both groups compared to normal controls. Gene annotation demonstrated that these miRNAs contribute to cell cycle, ion transport, biological adhesion, cation transport, cellular response to endogenous stimulus, and regulation of small GTPase-related signal transduction. Conclusion: Dysregulated levels of miR-15 and miR-16 may be involved in the pathogenesis and response to steroid therapy in patients with INS. </jats:p