OPTIMIZATION PROBLEMS OF MODERNIZATION OF THE CAPACITY OF ARCS OF FAULT-TOLERANT NETWORKS

Mathematical models of two classes of problems of modernization of the capacity of arcs of fault-tolerant oriented networks are considered. A network is considered to be fault-tolerant for which it is possible to satisfy all the demands for the transmission of flows when there will be one, but any failure, from all possible single network failures. For the first class of problems (problem A), all possible paths in the network can be used for the transmission of flows. For the second class of problems (problem P), only paths from a predetermined set of paths are used to transfer flows. Mathematical models are represented by linear, Boolean and nonlinear programming problems with a block structure of the constraint matrix.The material of the article is presented in five sections. The first section describes the concepts of a single failure and the scenario of network failures, the content of optimization problems A and P for modernization of capacity of arcs of a fault-tolerant network, a test network (6 vertices and 19 arcs) to test algorithms for solving the problems of modernization of fault-tolerant networks. In the second section, basic models of linear programming problems for finding the capacities of arcs of the fault-tolerant physical structure of a network (problem A) and the fault-tolerant logical structure of a network (problem P) are described, and their properties are considered. The third section describes problems A and P in the form of mixed Boolean linear programming models. Optimal solutions of problem A for various failure scenarios are given for the example of the test network. The solutions were found using the Gurobi program from the NEOS server, where the mathematical model of problem A is described in the AMPL modeling language.The fourth section describes nonlinear convex programming models for problems A and P, developed to find the optimal capacities of fault-tolerant networks according to the selected criterion, and a decomposition algorithm for their solution. The fifth section describes software in the FORTRAN programming language for the decomposition algorithm based on efficient implementations of Shor’s r-algorithms. The decomposition algorithm is compared with the IPOPT program based on the results of solving test problems.

Librarians participation in professional development workshops using Zoom in Nigeria

The purpose of this study is to investigate the extent to which librarians in Nigeria engaged in professional development workshops during the COVID-19 era. The study adopted a survey method using an online questionnaire. Factors such as saving money, the free nature of workshops, eliminating travel risk, in the comfort of the home, and providing an opportunity for all were mentioned as the benefits of participating in online workshops using Zoom. Buying data bundle, lack of computer/Android phone/smartphone, ignorance or lack of awareness of up-coming workshops, lack of time, power outage, nonchalant attitude towards technology, and network failures were identified as challenges of participation. The Zoom platform can be adopted for organizing workshops and meetings, and for teaching and learning in the post COVID-19 era.

Underground MV Network Failures’ Waveform Characteristics—An Investigation

The authors seek to investigate the characteristics of outage-causing faults that can be observed in a short time frame after their occurrence: waveform of the voltages and currents. The aim is to identify which characteristics can be used to estimate the failure type immediately after its occurrence. This paper lays the groundwork to determine which features display a stronger relation to four failure types with the aim of using this information in a later work, not presented in this paper, aimed at designing a reliable failure type estimator from readily available data. This paper focuses on the most common failures of the underground cable MV networks in Portugal: cable insulation; cable joint; secondary substation busbar; and excavation-motivated failures. A set of 206 waveform records of real underground MV network failures was available for analysis. After investigating the waveforms, the authors identified seven waveform characteristics which can be used for failure type estimation. Fault type characteristics can be used to distinguish secondary substation failures from the remaining failure types. Fault evolution does not yield relevant information. Fault self-extinction phenomenon was not observed in excavation-caused failures. There are differences for self-extinction characteristics between secondary substation busbar failures and the cable insulation and joint failures. Fault inception instant and arc voltage are two characteristics which are shown to have a promising merit to the identification process of failure types. Finally, fault intra-cycle repetitive extinction results have been found to be very similar for cable insulation failures and joint failures, but otherwise different regarding the remaining failure types.

Tau and Amyloid Relationships with Resting-state Functional Connectivity in Atypical Alzheimer’s Disease

The mechanisms through which tau and amyloid-beta (Aβ) accumulate in the brain of Alzheimer’s disease patients may differ but both are related to neuronal networks. We examined such mechanisms on neuroimaging in 58 participants with atypical Alzheimer’s disease (posterior cortical atrophy or logopenic progressive aphasia). Participants underwent Aβ-PET, longitudinal tau-PET, structural MRI and resting-state functional MRI, which was analyzed with graph theory. Regions with high levels of Aβ were more likely to be functional hubs, with a high number of functional connections important for resilience to cascading network failures. Regions with high levels of tau were more likely to have low clustering coefficients and degrees, suggesting a lack of trophic support or vulnerability to local network failures. Regions strongly functionally connected to the disease epicenters were more likely to have higher levels of tau and, less strongly, of Aβ. The regional rate of tau accumulation was associated with tau levels in functionally connected regions, in support of tau accumulation in a functional network. This study elucidates the relations of tau and Aβ to functional connectivity metrics in atypical Alzheimer’s disease, strengthening the hypothesis that the spread of the 2 proteins is driven by different biological mechanisms related to functional networks.

Transmission of Information in Channels Specified by Structures of Partial Erasure. Part 1

We investigate covert channels that use players moves to transmit information. We assume that there exits noise generated by periods of invisiblility of the transmitting player (due to network failures, game mechanics, etc.); thus there arises the problem of reliable transmission of information over a noisy channel. The formal model that addresses this problem is referred to as a structure of partial erasure. In the framework of the model we prove the criterion of equivalence of a pair of trajectories on the receiving end of the channel. We also discuss a number of methods that prevent organization of covert channels of the type considered.