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Minimally tough series–parallel graphs with toughness more than ½
No full textLet t be a positive real number. A graph is called t-tough if the removal of any vertex set S that disconnects the graph leaves at most |S|/t components. The toughness of a graph is the largest t for which the graph is t-tough. A graph is minimally t-tough if the toughness of the graph is t, and the deletion of any edge from the graph decreases the toughness. Series–parallel graphs are graphs with two distinguished vertices called terminals, formed recursively by two simple composition operations, series and parallel joins. They can be used to model series and parallel electric circuits. We characterize minimally t-tough series–parallel graphs for all t > 1/2. It is clear that there is no minimally t-tough series– parallel graph if t > 1. We show that for 1 ≥ t > 1/2, most of the series–parallel graphs with toughness t are minimally t-tough. We conjecture that the situation is very different if the toughness is 1/2. We show a family of minimally 1/2-tough graphs, and conjecture that these are the only such graphs
Regeneration of Ultrasound Tongue Images using Tongue Position Values towards Articulatory-to-Acoustic Mapping
Full text linkSilent Speech Interfaces (SSI) aim to help people communicate by using articulatory data, supporting those who cannot speak aloud or need to communicate in noisy or silent environments. Ultrasound Tongue Imaging (UTI) is a widely used, safe, and cost-effective method for studying tongue movements during speech. UTI provides real-time views of tongue shapes and dynamics, making it useful for Articulation-to-Speech (ATS) synthesis. However, challenges such as probe misalignment, incomplete tongue images, and differences between speakers can affect data quality. Recent advancements, such as neural vocoders like WaveGlow and adaptations of Tacotron2, have improved ATS synthesis, producing more natural and accurate speech. UTI has also been used to enhance text-to-speech (TTS) systems, showing potential for applications like speech training. To address limitations, studies have explored techniques like dynamic time warping (DTW) and data augmentation, aiming to mitigate alignment issues and enrich training datasets. This study investigates the optimal representation of tongue shape using UTI, employing DeepLabCut for pose estimation and tongue image regeneration from tongue position values towards articulatory-to-acoustic mapping (AAM). The findings aim to refine UTI-based speech synthesis systems and expand their applicability
Analysis of the Entanglement Assistance Effect on Quality of Service of multi-Class IoT Networks
No full textInternet of Things (IoT) technologies have allowed the connection of devices worldwide through the Internet. these tiny, intelligent, and mixed devices must be able to send, receive, and analyze data with different service requirements. It is recognized as one of the most rapidly growing technologies, with a rising number of nodes daily. Quality of service (QoS) is one of the crucial issues in these networks due to the large volume of data transferred or received across networks. Numerous QoS metrics exist, and network layer Parameters containing delay, throughput, efficiency, and packet loss are the focus of our study. In this paper, we concentrate on studying the distribution of quantum entanglement effect on QoS for heterogeneous IoT networks. Besides this, we also presented an analytical approach to demonstrate the method's performance, side by side with the comparison of slotted ALOHA systems
