Using of Rectangular Stochastic Matrices for the Problem of Evaluating and Ranking Alternatives

The paper investigates the issue related to a possible generalization of the “state-probability of choice” model so that the generalized model could be applied to the problem of ranking alternatives, either individual or by a group of agents. It is shown that the results obtained before for the problem of multi-agent choice and decision making by majority of votes can be easily transferred to the problem of multi-agent alternatives ranking. On the basis of distributions of importance values for the problem of ranking alternatives, we can move on to similar models for the choice and voting with the help of well-known exponential normalization of rows.So we regard two types of matrices, both of which belonging to the sort of matrices named balanced rectangular stochastic matrices. For such matrices, sums of elements in each row equal 1, and all columns have equal sums of elements. Both types are involved in a two-level procedure regarded in this paper. Firstly a matrix representing all possible distributions of importance among alternatives should be formed, and secondly a “state-probability of choice” matrix should be obtained on its base. For forming a matrix of states, which belongs and the rows of which correspond to possible distributions of importance, applying pairwise comparisons and the Analytic Hierarchy Method is suggested. Parameterized transitive scales with the parameter affecting the spread of importance between the best and the worst alternatives are regarded. For further getting the matrices of choice probabilities, another parameter which reflects the degree of the agent’s decisiveness is also introduced. The role of both parameters is discussed and illustrated with examples in the paper.The results are reported regarding some numerical experiments which illustrate getting distributions of importance on the basis of the Analytic Hierarchy Process and which are connected to gaining the situation of dynamic equilibrium of alternatives, i.e. the situation when alternatives are considered as those of equal value.

Electromagnetic energy (670 nm) stimulates vasodilation through activation of the large conductance potassium channel (BKCa)

Introduction Peripheral artery disease (PAD) is a highly morbid condition in which impaired blood flow to the limbs leads to pain and tissue loss. Previously we identified 670 nm electromagnetic energy (R/NIR) to increase nitric oxide levels in cells and tissue. NO elicits relaxation of smooth muscle (SMC) by stimulating potassium efflux and membrane hyperpolarization. The actions of energy on ion channel activity have yet to be explored. Here we hypothesized R/NIR stimulates vasodilation through activation of potassium channels in SMC. Methods Femoral arteries or facial arteries from C57Bl/6 and Slo1-/- mice were isolated, pressurized to 60 mmHg, pre-constricted with U46619, and irradiated twice with energy R/NIR (10 mW/cm2 for 5 min) with a 10 min dark period between irradiations. Single-channel K+ currents were recorded at room temperature from cell-attached and excised inside-out membrane patches of freshly isolated mouse femoral arterial muscle cells using the patch-clamp technique. Results R/NIR stimulated vasodilation requires functional activation of the large conductance potassium channels. There is a voltage dependent outward current in SMC with light stimulation, which is due to increases in the open state probability of channel opening. R/NIR modulation of channel opening is eliminated pharmacologically (paxilline) and genetically (BKca α subunit knockout). There is no direct action of light to modulate channel activity as excised patches did not increase the open state probability of channel opening. Conclusion R/NIR vasodilation requires indirect activation of the BKca channel.

A M/M/1 Queueing Network with Classical Retrial Policy

In this paper we study the M/M/1 queueing model with retrial on network. We derive the steady state probability of customers in the network, the average number of customers in the all the three nodes in the system, the queue length, system length using little’s formula. The particular case is derived (no retrial). The numerical examples are given to test the correctness of the model.

Reliability Analysis of a Complex Multistate System Based on a Cloud Bayesian Network

This study focused on mixed uncertainty of the state information in each unit caused by a lack of data, complex structures, and insufficient understanding in a complex multistate system as well as common-cause failure between units. This study combined a cloud model, Bayesian network, and common-cause failure theory to expand a Bayesian network by incorporating cloud model theory. The cloud model and Bayesian network were combined to form a reliable cloud Bayesian network analysis method. First, the qualitative language for each unit state performance level in the multistate system was converted into quantitative values through the cloud, and cloud theory was then used to express the uncertainty of the probability of each state of the root node. Then, the β-factor method was used to analyze reliability digital characteristic values when there was common-cause failure between the system units and when each unit failed independently. The accuracy and feasibility of the method are demonstrated using an example of the steering hydraulic system of a pipelayer. This study solves the reliability analysis problem of mixed uncertainty in the state probability information of each unit in a multistate system under the condition of common-cause failure. The multistate system, mixed uncertainty of the state probability information of each unit, and common-cause failure between the units were integrated to provide new ideas and methods for reliability analysis to avoid large errors in engineering and provide guidance for actual engineering projects.

Buffer Allocation via Bottleneck-Based Variable Neighborhood Search

This study addresses the challenging problem of efficient buffer allocation in production lines. Suitable locations for buffer allocation are determined to satisfy the desired throughput, while a suitable balance between solution quality and computation time is achieved. A throughput calculation approach that yields the state probability of production lines is adopted to evaluate the effectiveness of candidate buffer allocation solutions. To generate candidate buffer allocation solutions, an active probability index based on state probability is proposed to rapidly detect suitable locations of buffer allocations. A variable neighborhood search algorithm is used to maintain acceptable solution quality; an additional neighborhood structure is used in the case where no satisfactory solution is generated in the initial neighborhood structure. Extensive numerical experiments demonstrate the efficacy of the proposed approach. The proposed approach can facilitate agile design of production lines in industry by rapidly estimating production line topologies.