New dualities from old: generating geometric, Petrie, and Wilson dualities and trialities of ribbon graphs

We define a new ribbon group action on ribbon graphs that uses a semidirect product of a permutation group and the original ribbon group of Ellis-Monaghan and Moffatt to take (partial) twists and duals, or twuals, of ribbon graphs. A ribbon graph is a fixed point of this new ribbon group action if and only if it is isomorphic to one of its (partial) twuals. This extends the original ribbon group action, which only used the canonical identification of edges, to the more natural setting of self-twuality up to isomorphism. We then show that every ribbon graph has in its orbit an orientable embedded bouquet and prove that the (partial) twuality properties of these bouquets propagate through their orbits. Thus, we can determine (partial) twualities via these one vertex graphs, for which checking isomorphism reduces simply to checking dihedral group symmetries. Finally, we apply the new ribbon group action to generate all self-trial ribbon graphs on up to seven edges, in contrast with the few, large, very high-genus, self-trial regular maps found by Wilson, and by Jones and Poultin. We also show how the automorphism group of a ribbon graph yields self-dual, -petrial or –trial graphs in its orbit, and produce an infinite family of self-trial graphs that do not arise as covers or parallel connections of regular maps, thus answering a question of Jones and Poulton.

A Canonical Scheme of Bottom-Up and Top-Down Information Flows in the Frontoparietal Network

Goal-directed behavior often involves temporal separation and flexible context-dependent association between sensory input and motor output. The control of goal-directed behavior is proposed to lie in the frontoparietal network, but the computational architecture of this network remains elusive. Based on recent rodent studies that measured and manipulated projection neurons in the frontoparietal network together with findings from earlier primate studies, we propose a canonical scheme of information flows in this network. The parietofrontal pathway transmits the spatial information of a sensory stimulus or internal motor bias to drive motor programs in the frontal areas. This pathway might consist of multiple parallel connections, each controlling distinct motor effectors. The frontoparietal pathway sends the spatial information of cognitively processed motor plans through multiple parallel connections. Each of these connections could support distinct spatial functions that use the motor target information, including attention allocation, multi-body part coordination, and forward estimation of movement state (i.e., forward models). The parallel pathways in the frontoparietal network enable dynamic interactions between regions that are tuned for specific goal-directed behaviors. This scheme offers a promising framework within which the computational architecture of the frontoparietal network and the underlying circuit mechanisms can be delineated in a systematic way, providing a holistic understanding of information processing in this network. Clarifying this network may also improve the diagnosis and treatment of behavioral deficits associated with dysfunctional frontoparietal connectivity in various neurological disorders including Alzheimer’s disease.

Model for evaluating the end runouts of a rotor with parallel connections of parts

The existing methods for calculating the assembly dimensional chains of aircraft engine rotors are analyzed. The factors that have a significant impact on the reliability of the calculation of the controlled assembly parameters of the product are identified. One of these factors is the existence of parallel connections of parts in the rotor. In the drum disk rotors, parallel rotor connections are formed by mating their parts along several end surfaces in the axial direction. A mathematical model is proposed that allows taking into account the parallel connections of the rotor parts. The form of relationship between rotor end run-outs and amplitudes of deviations of the shape of the mating surfaces of the parts and their angular positions in the unit is determined. The determined dependence includes many coefficients that allow taking into account the amplitudes of deviations of the shape of the mating surfaces, parallel connections of parts in the rotor, and their angular position. Determination of dependence coefficients values is solved as a problem of regression analysis. The initial data for obtaining the dependence are formed using the developed parameterized finite element model (FEM) of a part of the rotor of an aircraft engine high-pressure compressor (HPC). The results of research of end run-outs of control surfaces of disks of the considered HPC rotor assembly part are presented. The values of the dependence coefficients for assessing the end run-outs of the rotor are determined.

Design of Five Port Router for 3x3 Mesh Network Using Verilog

With technological advancements, a large number of intellectual property (IP) cores can be integrated into a single chip. As a result, communication between these cores is critical. Such communication is achieved using Network on Chip (NoC) technology. NoC is an on-chip packet-switched network with IP cores connected to the network via interfaces, and packets are sent to their destinations via a multi-chip routing path. A router is the essential component of the NoC architecture, it must be designed efficiently to build a competitive NoC architecture. Verilog is used to design the router which supports five parallel connections. It uses store and forward type of flow control, round-robin arbitration, and deterministic XY routing. The building blocks of the router are FIFO, arbiter, and crossbar. The proposed architecture of the five port router is targeted to the Spartan 6 XC6SLX45 FPGA design platform and simulated in Xilinx ISE 14.5 software.

System Availability Study Results in the Example of Radio Communication System in the Underground Mine

The availability rating of any system is the probability that it will be able to operate for a given time in other words, to restore the system in the case of a system failure, or during the failure it is a measure of the availability index of resource system. We aimed to complete the study for the reasons as below. The rating and upgrading of underground mine radio communication system availability is to ensure operation reliability of the underground mine and to establish reliable radio communication system for miner’s safety during failure. Therefore, our study is contributed to reveal system availability rating of single resource (with two parallel connections) system and two resources (with three parallel connections) system. The study is related to not only practical contribution but also reliability engineering theory. To achieve this result, we have used Exponential, Weibull, and Poisson distributions. The readiness rating of single resource (with two parallel connections) and two resources (with three parallel connections) systems were calculated using Matlab software and the simulation results were introduced. This result confirms that any system has a resource system, which increases its readiness rating. The study was in examples of single resource radio communication system on the two shafts of the underground mine and two resource radio communication system for three shafts. During the initial system reliability enhancement study, the readiness of the dual resource system was assessed. The rating shows a 99 percent result, which is very meaningless for systems with more than two n-resources and we have revealed that it can show more than 100 percent result. In the process of the study on system reliability improvement the rating availability of system which has two resources was 99 % result. It is very meaningless for systems with more than two n-resources or more than 100% result.

Iodide Electrolyte-Based Hybrid Supercapacitor for Compact Photo-Rechargeable Energy Storage System Utilising Silicon Solar Cells

The one of the most important issues in constructing light-harvesting photovoltaic (PV) systems with a charge storage element is its reliable and uninterrupted use in highly variable and weather-dependent conditions in everyday applications. Herein, we report the construction and applicability evaluation of a ready-to-use portable solar charger comprising a silicon solar cell and an enhanced energy hybrid supercapacitor using activated carbon electrodes and iodide-based aqueous electrolyte to stabilise the PV power under fluctuating light conditions. The optimised electrode/electrolyte combination of a supercapacitor was used for the construction of a 60 F/3 V module by a proper adjustment of the series and parallel connections between the CR2032 coin cells. The final photo-rechargeable device was tested as a potential supporting system for pulse electronic applications under various laboratory conditions (temperature of 15 and 25 °C, solar irradiation of 600 and 1000 W m−2).

CALCULATION OF PARAMETERS OF BRANCHED MECHANICAL SYSTEMS WITH HARMONIC VIBRATIONS. Continuation

Parallel-series and series-parallel connections of mechanical power consumers are considered. According to the known parameters of systems and the disturbing harmonic effect, the velocities of the elements of mechanical systems and the forces applied to them are algebraically determined. For the considered branched mechanical schemes, the classical methods based on solving second-order differential equations become many times more complicated and require solving systems of equations that reduce to higher-order differential equations. The use of a symbolic (complex) description of mechanical processes and systems makes it possible to use instead simple and compact algebraic methods, the complexity of which is ten times less. Vector diagrams, not being a necessary component of the study of mechanical systems, are of significant methodological importance, since they show quantitative and phase relationships between the parameters of systems.