A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number γt(G). The graph G is 3t-critical if γt(G)=3 and γt(G+e)=2 for every edge e in the complement of G. We show that no bipartite graph is 3t-critical. The tripartite 3 t-critical graphs are characterized. For every k<3, we prove that there are only a finite number of 3t-critical k-partite graphs. We show that the 5-cycle is the only 3t-critical K3-free graph and that there are only a finite number of 3t-critical K4-free graphs.

A connected graph is total domination stable upon edge removal, if the removal of an arbitrary edge does not change the total domination number. We determine the minimum number of edges required for a total domination stable graph in terms of its order and total domination number.

A graph G is diameter 2-critical if its diameter is 2, and the deletion of any edge increases the diameter. Murty and Simon conjectured that the number of edges in a diameter 2-critical graph of order n is at most n24 and that the extremal graphs are complete bipartite graphs with equal size partite sets. We use an important association with total domination to prove the conjecture for the graphs whose complements are claw-free.

Most of the research on domination focuses on vertices dominating other vertices. In this paper we consider vertexedge domination where a vertex dominates the edges incident to it as well as the edges adjacent to these incident edges. The minimum cardinality of a vertex-edge dominating set of a graph G is the vertex-edge domination number γve(G). We present bounds on γve(G) and relationships between γve(G) and other domination related parameters. Since any ordinary dominating set is also a vertex-edge dominating set, it follows that γve(G) is bounded above by the domination number of G. Our main result characterizes the trees having equal domination and vertex-edge domination numbers.

Let G be a nontrivial connected, edge-colored graph. An edge-cut R of G is called a rainbow cut if no two edges in R are colored the same. An edge-coloring of G is a rainbow disconnection coloring if for every two distinct vertices u and v of G, there exists a rainbow cut in G, where u and v belong to different components of G − R. We introduce and study the rainbow disconnection number rd(G) of G, which is defined as the minimum number of colors required of a rainbow disconnection coloring of G. It is shown that the rainbow disconnection number of a nontrivial connected graph G equals the maximum rainbow disconnection number among the blocks of G. It is also shown that for a nontrivial connected graph G of order n, rd(G) = n−1 if and only if G contains at least two vertices of degree n − 1. The rainbow disconnection numbers of all grids Pm Pn are determined. Furthermore, it is shown for integers k and n with 1 ≤ k ≤ n − 1 that the minimum size of a connected graph of order n having rainbow disconnection number k is n + k − 2. Other results and a conjecture are also presented.

Using specialized hardware to accelerate workloads have the potential to bring great performance lifts in various applications. Using specialized hardware to speed up the slowest executing component in an application will make the whole application execute faster, since it cannot be faster than it's slowest part. This work investigates two modifications to improve an existing virtual reality application with the help of more hardware support. The existing virtual reality application uses a server computer which handles virtual object rendering, these are later sent to the mobile phone, which is the end user. In this project the server part of the application, where the Simultaneous Localization And Mapping (SLAM) library is run was modified to use a Compute Unified Device Architecture (CUDA) accelerated variant. The software encoder and decoder used for the video streaming were modified to use specialized hardware. Small changes were made to the client-side application to allow the latency measurement to work when changing the server-side encoder. Accelerating SLAM with CUDA showed an increase in the number of processed frames each second, and frame processing time, at the cost of latency between the end and edge device. Using the hardware encoder and decoder resulted in no improvement considering latency or processed frames, in fact, the hardware encoders and decoder performed worse than the baseline configuration. The reduced frame processing time indicates that the CUDA platform is beneficial provided that the additional latency that occurred from the implementation is reduced or removed.

PURPOSE: To analyze surface roughness, the edge chipping of different CAD/CAM bur milled dental materials (bar and crown design of 1.0mm and 1.5mm thickness), correlate the effect of machining damage on the material strength, compare the flexural strength of bur milled versus sectioned CAD/CAM blocks and evaluate the tool wear after milling. MATERIALS AND METHODS: Five dental CAD/CAM materials were used: Lithium disilicate glass-ceramic (IPS e.max CAD), Leucite-reinforced glass-ceramic (IPS Empress CAD), Feldspathic porcelain (Vitablocs Mark II), Feldspar ceramic-polymer infiltrated (Enamic), and composite resin (Lava Ultimate). Ten rectangular bars with dimensions of 4 mm × 2 mm × 14 mm were milled using a new set of burs for each material. Then, ten crowns of each material with thicknesses of 1.0 mm and 1.5 mm were milled after scanning a standard aluminum die with corresponding marginal thickness. The bars surface roughness was measured. Then, three specimens were selected for the edge chipping analysis using (SEM). Thereafter, 3-point bend test was used to test the flexural strength of bur milled and saw cut bars with the same dimensions. For the crowns, load to failure test was used. One-way ANOVA and Tukey HSD post hoc tests to determine the difference between the groups using JMP13.0 with α=0.05. RESULTS AND CONCLUSIONS: The surface roughness and edge chipping was significantly affected by the material composition. Comparison of the flexural strength of bur milled to sectioned bars, IPS e.max CAD and IPS Empress CAD show statistically significant less flexural strength (p<0.001). A strong correlation was found between the decrease in flexural strength and the chipping length on the central tensile side of the bur milled materials (R2=0.62, p=0.01). Crown thickness significantly affects the edge chipping as 1.5 mm crown thickness has more edge chipping than 1.0 mm crowns. However, no correlation is found between the load to failure test for the crown design and the edge chipping for 1.5mm and 1.0 mm thickness crowns. Tool wear is significantly affected by the material type. / 2021-07-31

Indiana University-Purdue University Indianapolis (IUPUI) / The Internet has substantially embraced mobility since last decade. Cellular data network carries majority of Internet mobile access traffic and become the de facto solution of accessing Internet in mobile fashion, while many clean-slate Internet mobility solutions were proposed but none of them has been largely deployed. Internet mobile users increasingly concern more about their privacy as both researches and real-world incidents show leaking of communication and location privacy could lead to serious consequences. Just the communication itself between mobile user and their peer users or websites could leak considerable privacy of mobile user, such as location history, to other parties. Additionally, comparing to ordinary Internet access, connecting through cellular network yet provides equivalent connection stability or longevity. In this research we proposed a novelty paradigm that leverages concurrent far-side proxies to maximize network location privacy protection and minimize interruption and performance penalty brought by mobility.To avoid the deployment feasibility hurdle we also investigated the root causes impeding popularity of existing Internet mobility proposals and proposed guidelines on how to create an economical feasible solution for this goal. Based on these findings we designed a mobility support system offered as a value-added service by mobility service providers and built on elastic infrastructure that leverages various cloud aided designs, to satisfy economic feasibility and explore the architectural trade-offs among service QoS, economic viability, security and privacy.

Indiana University-Purdue University Indianapolis (IUPUI) / Due to the increasing demand from mobile devices for the real-time response of cloud computing services, federated edge learning (FEL) emerges as a new computing paradigm, which utilizes edge devices to achieve efficient machine learning while protecting their data privacy. Implementing efficient FEL suffers from the challenges of devices' limited computing and communication resources, as well as unevenly distributed datasets, which inspires several existing research focusing on device selection to optimize time consumption and data diversity. However, these studies fail to consider the energy consumption of edge devices given their limited power supply, which can seriously affect the cost-efficiency of FEL with unexpected device dropouts. To fill this gap, we propose a device selection model capturing both energy consumption and data diversity optimization, under the constraints of time consumption and training data amount. Then we solve the optimization problem by reformulating the original model and designing a novel algorithm, named E2DS, to reduce the time complexity greatly. By comparing with two classical FEL schemes, we validate the superiority of our proposed device selection mechanism for FEL with extensive experimental results. Furthermore, for each device in a real FEL environment, it is the fact that multiple tasks will occupy the CPU at the same time, so the frequency of the CPU used for training fluctuates all the time, which may lead to large errors in computing energy consumption. To solve this problem, we deploy reinforcement learning to learn the frequency so as to approach real value. And compared to increasing data diversity, we consider a more direct way to improve the convergence speed using loss values. Then we formulate the optimization problem that minimizes the energy consumption and maximizes the loss values to select the appropriate set of devices. After reformulating the problem, we design a new algorithm FCE2DS as the solution to have better performance on convergence speed and accuracy. Finally, we compare the performance of this proposed scheme with the previous scheme and the traditional scheme to verify the improvement of the proposed scheme in multiple aspects.

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