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Artigos de revistas sobre o tema "Connectivity"

Autor: Grafiati

Publicado: 4 de junho de 2021

Última modificação: 9 de junho de 2025

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1

Farahani, Mohammad Reza. "The Second-Connectivity and Second-Sum-Connectivity Indices of Armchair Polyhex Nanotubes TUAC₆[m,n]." International Letters of Chemistry, Physics and Astronomy 30 (March 2014): 74–80. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.30.74.

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The m-connectivety and m-sum connectivity indices of G are defined as to be and where runs over all paths of length m in G and di is the degree of vertex νi. In this paper, we give explicit formulas for the second-connectivity and second-sum-connectivity indices of an infinite class of Armchair Polyhex Nanotubes TUAC6[m,n].

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Farahani, Mohammad Reza. "The Second-Connectivity and Second-Sum-Connectivity Indices of Armchair Polyhex Nanotubes TUAC<sub>6</sub>[m,n]." International Letters of Chemistry, Physics and Astronomy 30 (March 12, 2014): 74–80. http://dx.doi.org/10.56431/p-f068h3.

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The m-connectivety and m-sum connectivity indices of G are defined as to be and where runs over all paths of length m in G and di is the degree of vertex νi. In this paper, we give explicit formulas for the second-connectivity and second-sum-connectivity indices of an infinite class of Armchair Polyhex Nanotubes TUAC6[m,n].

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3

Farahani, Mohammad Reza. "The General Connectivity and General Sum-Connectivity Indices of Nanostructures." International Letters of Chemistry, Physics and Astronomy 44 (January 2015): 73–80. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.44.73.

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Let G be a simple graph with vertex set V(G) and edge set E(G). For ∀νi∈V(G),di denotes the degree of νi in G. The Randić connectivity index of the graph G is defined as [1-3] χ(G)=∑e=v1v2є(G)(d1d2)-1/2. The sum-connectivity index is defined as χ(G)=∑e=v1v2є(G)(d1+d2)-1/2. The sum-connectivity index is a new variant of the famous Randić connectivity index usable in quantitative structure-property relationship and quantitative structure-activity relationship studies. The general m-connectivety and general m-sum connectivity indices of G are defined as mχ(G)=∑e=v1v2...vim+1(1/√(di1di2...dim+1)) and mχ(G)=∑e=v1v2...vim+1(1/√(di1+di2+...+dim+1)) where vi1vi2...vim+1 runs over all paths of length m in G. In this paper, we introduce a closed formula of the third-connectivity index and third-sum-connectivity index of nanostructure "Armchair Polyhex Nanotubes TUAC6[m,n]" (m,n≥1).

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4

Farahani, Mohammad Reza. "The General Connectivity and General Sum-Connectivity Indices of Nanostructures." International Letters of Chemistry, Physics and Astronomy 44 (January 14, 2015): 73–80. http://dx.doi.org/10.56431/p-892ddt.

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Let G be a simple graph with vertex set V(G) and edge set E(G). For ∀νi∈V(G),di denotes the degree of νi in G. The Randić connectivity index of the graph G is defined as [1-3] χ(G)=∑e=v1v2є(G)(d1d2)-1/2. The sum-connectivity index is defined as χ(G)=∑e=v1v2є(G)(d1+d2)-1/2. The sum-connectivity index is a new variant of the famous Randić connectivity index usable in quantitative structure-property relationship and quantitative structure-activity relationship studies. The general m-connectivety and general m-sum connectivity indices of G are defined as mχ(G)=∑e=v1v2...vim+1(1/√(di1di2...dim+1)) and mχ(G)=∑e=v1v2...vim+1(1/√(di1+di2+...+dim+1)) where vi1vi2...vim+1 runs over all paths of length m in G. In this paper, we introduce a closed formula of the third-connectivity index and third-sum-connectivity index of nanostructure "Armchair Polyhex Nanotubes TUAC6[m,n]" (m,n≥1).

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5

Grone, Robert, and Russell Merris. "Algebraic connectivity of trees." Czechoslovak Mathematical Journal 37, no. 4 (1987): 660–70. http://dx.doi.org/10.21136/cmj.1987.102192.

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6

John, Lizy Kurian. "Connectivity! Connectivity! Connectivity! May You Be More Connected Than Ever!!" IEEE Micro 40, no. 1 (January 1, 2020): 4–5. http://dx.doi.org/10.1109/mm.2019.2961722.

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7

Kost, Gerald J. "Connectivity." Archives of Pathology & Laboratory Medicine 124, no. 8 (August 1, 2000): 1108–10. http://dx.doi.org/10.5858/2000-124-1108-c.

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8

Angelopulo, George. "Connectivity." Communicatio 40, no. 3 (July 3, 2014): 209–22. http://dx.doi.org/10.1080/02500167.2014.953561.

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9

Das, Pritha, and Jim Lagopoulos. "Connectivity." Acta Neuropsychiatrica 21, no. 2 (April 2009): 91–92. http://dx.doi.org/10.1111/j.1601-5215.2009.00374.x.

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10

Hodgetts, Timothy. "Connectivity." Environmental Humanities 9, no. 2 (November 1, 2017): 456–59. http://dx.doi.org/10.1215/22011919-4215412.

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11

DuBois, Jeffrey A. "Connectivity." Point of Care: The Journal of Near-Patient Testing & Technology 3, no. 1 (March 2004): 30–32. http://dx.doi.org/10.1097/00134384-200403000-00009.

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12

Schaffner, Marilyn. "Connectivity." Gastroenterology Nursing 28, no. 2 (March 2005): 148–49. http://dx.doi.org/10.1097/00001610-200503000-00012.

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13

Peckham, Haley. "Connectivity." Neuropsychotherapist, no. 5 (April 1, 2014): 82–85. http://dx.doi.org/10.12744/tnpt(5)082-085.

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14

Ramani, Ramachandran. "Connectivity." Current Opinion in Anaesthesiology 28, no. 5 (October 2015): 498–504. http://dx.doi.org/10.1097/aco.0000000000000237.

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15

Galil, Zvi, and Giuseppe F. Italiano. "Reducing edge connectivity to vertex connectivity." ACM SIGACT News 22, no. 1 (March 1991): 57–61. http://dx.doi.org/10.1145/122413.122416.

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16

Mukungunugwa, Vivian, and Simon Mukwembi. "On Eccentric Connectivity Index and Connectivity." Acta Mathematica Sinica, English Series 35, no. 7 (April 16, 2019): 1205–16. http://dx.doi.org/10.1007/s10114-019-7320-1.

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17

Ferreira, Kecia Aline M., Mariza A. S. Bigonha, and Roberto S. Bigonha. "Reestruturação de Software Dirigida por Conectividade para Redução de Custo de Manutenção." Revista de Informática Teórica e Aplicada 15, no. 2 (December 12, 2008): 155–80. http://dx.doi.org/10.22456/2175-2745.7031.

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Most of the software cost is due to maintenance. In the last years, there has been a great deal of interest in developing cost estimation and effort prediction instruments for software maintenance. This work proposes that module connectivityis a key factor to predict maintenance cost and uses this thesis as the basis to develop a Connectivity Evaluation Model in OO Systems (MACSOO), which is a refactoring model based on connectivity whose aim is to minimize maintenance cost. We describe experiments whose results provide an example of the model application and expose the correlation between connectivity and maintainability.

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18

Borowiecki, Mieczysław. "Partition numbers, connectivity and Hamiltonicity." Časopis pro pěstování matematiky 112, no. 2 (1987): 173–76. http://dx.doi.org/10.21136/cpm.1987.118305.

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19

AlDahdouh, Alaa A. "Does Artificial Neural Network Support Connectivism's Assumptions?" International Journal of Instructional Technology and Distance Learning 14, no. 3 (March 1, 2017): 3–26. https://doi.org/10.5281/zenodo.545695.

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Connectivism was presented as a learning theory for the digital age and connectivists claim that recent developments in Artificial Intelligence (AI) and, more specifically, Artificial Neural Network (ANN) support their assumptions of knowledge connectivity. Yet, very little has been done to investigate this brave allegation. Does the advancement in artificial neural network studies support connectivism’s assumptions? And if yes, to what extent? This paper addresses the aforementioned question by tackling the core concepts of ANN and matching them with connectivist's assumptions. The study employed the qualitative content analysis approach where the researcher started with purposely selected and relatively small content samples in connectivism and ANN literature. The results revealed that ANN partially supports connectivism’s assumptions but this does not mean that other learning theories such as behaviorism and constructivism are not supported as well. The findings enlighten our understanding of connectivism and where it may be applied.

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20

Li, Shi. "Faculty of Applied & Creative Arts, Universiti Malaysia Sarawak." Studies in Social Science & Humanities 2, no. 9 (September 2023): 35–39. http://dx.doi.org/10.56397/sssh.2023.09.07.

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The advent of globalised connectivity has intricately linked local communities with worldwide information dissemination, forming a global consciousness among individuals. This essay explores the interplay between globalised connectivity and the “risk society,” analyzing its impact on democracy. Through cases such as Cambridge Analytica, the Arab Spring, and the ICIJ, it reveals the dual nature of globalised connectivity, fostering democratic advancement while compromising data privacy. The essay underscores the need for active democratic participation while managing associated risks. As society navigates this transformative phase, harnessing globalised connectivity’s potential to amplify voices and ensure accountability is crucial for a balanced future of enhanced global democracy and personal information security.

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21

Kende, Michael, Sonia Livingstone, Scott Minehane, Michael Minges, Simon Molloy, and George Sciadas. "GLOBAL CONNECTIVTY REPORT 2022. CHAPTER 1. UNIVERSAL AND MEANINGFUL CONNECTIVITY: THE NEW IMPERATIVE." SYNCHROINFO JOURNAL 8, no. 2 (2022): 35–45. http://dx.doi.org/10.36724/2664-066x-2022-8-2-35-45.

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In the 30 years since the creation of the ITU Telecommunication Development Sector in 1992, the number of Internet users surged from a few million to almost five billion. This trend has enabled a digital transformation that has been, and is, transforming our societies and our economies. Yet the potential of the Internet for social and economic good remains largely untapped: one-third of humanity (2.9 billion people) remains offline and many users only enjoy basic connectivity. Universal and meaningful connectivity – defined as the possibility of a safe, satisfying, enriching, productive, and affordable online experience for everyone – has become the new imperative for the 2020-2030 Decade of Action to deliver on the Sustainable Development Goals (SDGs). The Global Connectivity Report 2022 takes stock of the progress in digital connectivity over the past three decades. It provides a detailed assessment of the current state of connectivity and how close the world is to achieving universal and meaningful connectivity, using a unique analytical framework. It goes on to showcase solutions and good practices to accelerate progress. This article presents a short version of the report (Part I).

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22

Zhao, Yang, Shicun Zhao, Yi Zhang, and Da Wang. "On the Connectivity Measurement of the Fractal Julia Sets Generated from Polynomial Maps: A Novel Escape-Time Algorithm." Fractal and Fractional 5, no. 2 (June 13, 2021): 55. http://dx.doi.org/10.3390/fractalfract5020055.

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In this paper, a novel escape-time algorithm is proposed to calculate the connectivity’s degree of Julia sets generated from polynomial maps. The proposed algorithm contains both quantitative analysis and visual display to measure the connectivity of Julia sets. For the quantitative part, a connectivity criterion method is designed by exploring the distribution rule of the connected regions, with an output value Co in the range of [0,1]. The smaller the Co value outputs, the better the connectivity is. For the visual part, we modify the classical escape-time algorithm by highlighting and separating the initial point of each connected area. Finally, the Julia set is drawn into different brightnesses according to different Co values. The darker the color, the better the connectivity of the Julia set. Numerical results are included to assess the efficiency of the algorithm.

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Kende, Michael, Sonia Livingstone, Scott Minehane, Michael Minges, Simon Molloy, and George Sciadas. "GLOBAL CONNECTIVTY REPORT 2022. CHAPTERS 3-4. ACCELERATING PROGRESS TOWARDS UNIVERSAL AND MEANINGFUL CONNECTIVITY & THE CRITICAL ROLE OF MIDDLE-MILE CONNECTIVITY." SYNCHROINFO JOURNAL 8, no. 4 (2022): 22–32. http://dx.doi.org/10.36724/2664-066x-2022-8-4-22-32.

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The Global Connectivity Report 2022 takes stock of the progress in digital connectivity over the past three decades. It provides a detailed assessment of the current state of connectivity and how close the world is to achieving universal and meaningful connectivity, using a unique analytical framework. It goes on to showcase solutions and good practices to accelerate progress. The second part of the report consists of seven thematic deep dives on infrastructure, affordability, financing, the pandemic, regulation, youth, and data. Chapter 3 explores options to accelerate progress towards universal and meaningful connectivity. Expanding broadband networks is needed to eliminate the remaining blind spots and improve the quality of connectivity. Measures include reducing constraints on foreign direct investment to attract capital for upgrading and expanding digital infrastructure; ensuring sound ICT sector regulation to help build competitive markets and enhance predictability; promoting infrastructure sharing to reduce costs; ensuring the supply of adequate, inexpensive spectrum to help reduce coverage gaps; and ensuring sufficient capacity and a shift to new generations of mobile broadband. Solutions to ensure an adequate energy provision to power ICT infrastructure include policy incentives, reducing duties and taxes on green power equipment and allowing independent power producers. Chapter 4 explores the importance of middle-mile connectivity as countries develop digital economies – achieving better quality, lower costs and greater redundancy. The “middle mile” consists of infrastructure responsible for storing and exchanging data. It is an overlooked yet critical link in the connectivity chain, between international connectivity – or “first-mile” connectivity – and “last-mile” connectivity, made of the infrastructure that connects the users, which is hence more visible and tangible. The three key components of a domestic data infrastructure ecosystem are Internet exchange points (IXPs), data centres and cloud computing.

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Kende, Michael, Sonia Livingstone, Scott Minehane, Michael Minges, Simon Molloy, and George Sciadas. "GLOBAL CONNECTIVTY REPORT 2022. CHAPTER 2. THE JOURNEY TO UNIVERSAL AND MEANINGFUL CONNECTIVITY." SYNCHROINFO JOURNAL 8, no. 3 (2022): 29–37. http://dx.doi.org/10.36724/2664-066x-2022-8-3-29-37.

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The Global Connectivity Report 2022 takes stock of the progress in digital connectivity over the past three decades. It provides a detailed assessment of the current state of connectivity and how close the world is to achieving universal and meaningful connectivity, using a unique analytical framework. It goes on to showcase solutions and good practices to accelerate progress. The second part of the report consists of seven thematic deep dives on infrastructure, affordability, financing, the pandemic, regulation, youth, and data. Chapter 2 relies on the framework for universal and meaningful connectivity and the associated targets for 2030, developed by ITU and the Office of the Secretary-General’s Envoy on Technology, to analyse the current state of digital connectivity globally and progress towards reaching the targets by 2030. The framework considers usage by various stakeholders (universal dimension of connectivity) and the five enablers of connectivity (meaningful dimension of connectivity): infrastructure, device, affordability, skills, and safety and security. The assessment reveals that the world is still far from universal and meaningful connectivity. Infrastructure needs to be rolled out or improved to bridge the coverage gap. There are still significant differences between and within countries in network availability and quality. Fixed broadband is a costly investment and is not available or is unaffordable for many. Mobile broadband offers greater flexibility and is less expensive, and most rely on this technology to go online. But in many rural areas of developing countries, only 3G is available, when meaningful connectivity requires 4G. The coverage gap, currently at 5%, is dwarfed by the usage gap: 32% of people who are within range of a mobile broadband network and could therefore connect, remain offline. Data compiled by ITU make it possible to classify the offline population based on who they are and where they live. The main reasons cited by people for not using the Internet are the lack of affordability, of awareness about the Internet, of need, as well as the inability to use the Internet. Globally, connectivity became more expensive in 2021 due to the global economic downturn triggered by the COVID-19 pandemic. After years of steady decline, the share of income spent on telecommunication and Internet services increased in 2021. The global median price of an entry-level broadband plan in the majority of countries amounts to more than 2% of the gross national income per capita, which is the affordability threshold set by the Broadband Commission for Sustainable Development. People should not be forced to use the Internet. However, evidence suggests that introducing people to the Internet usually entices them to stay online. Based on activities people reported, use of the Internet leads to an improved social life, with the use of social networks, making Internet calls and streaming video the most common activities.

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Kulli, V. R. "ATOM BOND CONNECTIVITY E-BANHATTI INDICES." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 01 (January 30, 2023): 3201–8. http://dx.doi.org/10.47191/ijmcr/v11i1.13.

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In this paper, we introduce the atom bond connectivity E-Banhatti index and the sum atom bond connectivity E-Banhatti index of a graph. Also we compute these newly defined atom bond connectivity E-Banhatti indices for wheel graphs, friendship graphs, chain silicate networks, honeycomb networks and nanotubes.

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26

Lin, Xiaoxia, Keke Wang, Meng Zhang та Hong-Jian Lai. "Bounding ℓ-edge-connectivity in edge-connectivity". Discrete Applied Mathematics 321 (листопад 2022): 350–56. http://dx.doi.org/10.1016/j.dam.2022.07.011.

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27

Vukicevic, Damir, Nenad Trinajstic, Sonja Nikolic, Bono Lucic, and Bo Zhou. "Master Connectivity Index and Master Connectivity Polynomial." Current Computer Aided-Drug Design 6, no. 4 (December 1, 2010): 235–39. http://dx.doi.org/10.2174/1573409911006040235.

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Lin, Cheng-Kuan, Lili Zhang, Jianxi Fan, and Dajin Wang. "Structure connectivity and substructure connectivity of hypercubes." Theoretical Computer Science 634 (June 2016): 97–107. http://dx.doi.org/10.1016/j.tcs.2016.04.014.

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Bonchev, Danail. "Overall connectivity — a next generation molecular connectivity." Journal of Molecular Graphics and Modelling 20, no. 1 (December 2001): 65–75. http://dx.doi.org/10.1016/s1093-3263(01)00101-2.

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Zhang, Zhao. "Extra edge connectivity and isoperimetric edge connectivity." Discrete Mathematics 308, no. 20 (October 2008): 4560–69. http://dx.doi.org/10.1016/j.disc.2007.08.066.

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31

Zhao, Shu-Li, and Jou-Ming Chang. "Connectivity, super connectivity and generalized 3-connectivity of folded divide-and-swap cubes." Information Processing Letters 182 (August 2023): 106377. http://dx.doi.org/10.1016/j.ipl.2023.106377.

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Mehmet, Şerif Aldemir, Ediz Süleyman, Çiftçi İdris, Yamaç Kerem, and Taş Ziyattin. "Domination edge connectivity of graphs." Graphs and Linear Algebra, no. 2 (September 23, 2023): 1–10. https://doi.org/10.5281/zenodo.8372637.

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Domination and connectivity are two independent subjects of graph theory which have many applications in computer and information sciences. To bring these two terms together, we first define a novel conditional connectivity measure: k-domination edge connectivity.   In this study we compute k-domination edge connectivity of paths, cycles and complete graphs.

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33

Darainy, Mohammad, Shahabeddin Vahdat, and David J. Ostry. "Neural Basis of Sensorimotor Plasticity in Speech Motor Adaptation." Cerebral Cortex 29, no. 7 (July 6, 2018): 2876–89. http://dx.doi.org/10.1093/cercor/bhy153.

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Abstract When we speak, we get correlated sensory feedback from speech sounds and from the muscles and soft tissues of the vocal tract. Here we dissociate the contributions of auditory and somatosensory feedback to identify brain networks that underlie the somatic contribution to speech motor learning. The technique uses a robotic device that selectively alters somatosensory inputs in combination with resting-state fMRI scans that reveal learning-related changes in functional connectivity. A partial correlation analysis is used to identify connectivity changes that are not explained by the time course of activity in any other learning-related areas. This analysis revealed changes related to behavioral improvements in movement and separately, to changes in auditory perception: Speech motor adaptation itself was associated with connectivity changes that were primarily in non-motor areas of brain, specifically, to a strengthening of connectivity between auditory and somatosensory cortex and between presupplementary motor area and the inferior parietal lobule. In contrast, connectively changes associated with alterations to auditory perception were restricted to speech motor areas, specifically, primary motor cortex and inferior frontal gyrus. Overall, our findings show that during adaptation, somatosensory inputs result in a broad range of changes in connectivity in areas associated with speech motor control and learning.

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Bell, Gelsey. "Profound Connectivity." TDR: The Drama Review 65, no. 1 (March 2021): 180–88. http://dx.doi.org/10.1017/s1054204320000155.

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Online musical performances in the first few months of the pandemic and lockdown in New York City bring to light the sonic and temporal challenges, unique acoustic space, and aesthetic possibilities of performing on Zoom. The social connection gained through these performance events is the key to their efficacy.

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Walsh, John, Ruth Roberts, Richard Morris, and Lutz Heinemann. "Device Connectivity." Journal of Diabetes Science and Technology 9, no. 3 (January 21, 2015): 701–5. http://dx.doi.org/10.1177/1932296814568806.

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MacNeil, Melanie, Edilma L. Yearwood, and Elizabeth Poster. "Cultural Connectivity." Journal of Child and Adolescent Psychiatric Nursing 21, no. 3 (August 2008): 123–24. http://dx.doi.org/10.1111/j.1744-6171.2008.00143.x.

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Silverajan, Bilhanan, Sari Kinnari, Antti Vekkeli, and Tuure Vartiainen. "Beyond connectivity." IEEE Vehicular Technology Magazine 4, no. 3 (September 2009): 55–61. http://dx.doi.org/10.1109/mvt.2009.933476.

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Godskesen, Jens Chr. "Connectivity Testing." Formal Methods in System Design 25, no. 1 (July 2004): 5–38. http://dx.doi.org/10.1023/b:form.0000033961.36239.68.

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Pawar, Priya S. "Village Connectivity." International Journal for Research in Applied Science and Engineering Technology 12, no. 4 (April 30, 2024): 2707–12. http://dx.doi.org/10.22214/ijraset.2024.60532.

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Abstract: The primary objective is to bridge the digital divide by ensuring access to affordable and reliable internet connectivity in rural area. The project aims to enhance economic opportunities in villages by promoting e-commerce, online education and digital services. It seeks to improve the overall quality of life in rural communities by enabling access to information, healthcare and government services. The Village Connectivity Project is a comprehensive initiative aim at improving the accessibility and connectivity of remote rural areas.

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Hirschheim, Rudy, and Dennis Adams. "Organizational Connectivity." Journal of General Management 17, no. 2 (December 1991): 65–76. http://dx.doi.org/10.1177/030630709101700206.

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Gong, Gaolang, Yong He, and Alan C. Evans. "Brain Connectivity." Neuroscientist 17, no. 5 (April 28, 2011): 575–91. http://dx.doi.org/10.1177/1073858410386492.

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Pillai, Jay J. "Functional Connectivity." Neuroimaging Clinics of North America 27, no. 4 (November 2017): i. http://dx.doi.org/10.1016/s1052-5149(17)30097-7.

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KOLB, DARL G., PAUL D. COLLINS, and E. ALLAN LIND. "Requisite Connectivity:." Organizational Dynamics 37, no. 2 (April 2008): 181–89. http://dx.doi.org/10.1016/j.orgdyn.2008.02.004.

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van Dijck, José. "After Connectivity." Social Media + Society 1, no. 1 (April 29, 2015): 205630511557887. http://dx.doi.org/10.1177/2056305115578873.

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NEHANIV, CHRYSTOPHER LEV. "ALGEBRAIC CONNECTIVITY." International Journal of Algebra and Computation 01, no. 04 (December 1991): 445–71. http://dx.doi.org/10.1142/s0218196791000316.

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Let [Formula: see text] be a type of algebra in the sense of universal algebra. By defining singular simplices in algebras and emulating singular [co] homology, we introduce for each variety, pseudo-variety, and divisional class V of type [Formula: see text], a homology and cohomology theory which measure the V-connectivity of type-[Formula: see text] algebras. Intuitively, if we were to think of an algebra as a space and subalgebras which lie in V as simplices, then V-connectivity describes the failure of subalgebras to lie in V, i.e., it describes the "holes" in this space. These [co]homologies are functorial on the class of type-[Formula: see text] algebras and are characterized by a natural topological interpretation. All these notions extend to subsets of algebras. One obtains for this algebraic connectivity, the long exact sequences, relative [co]homologies, and the analogues of the usual [co]homological notions of the algebraic topologists. In fact, we show that the [co]homologies are actually the same as the simplicial [co]homology of simplicial complexes that depend functorially on the algebras. Thus the connectivities in question have a natural geometric meaning. This allows the wholesale import into algebra of the concepts, results, and techniques of algebraic topology. In particular, functoriality implies that the [co]homology of a pair of algebras A ⊆ B is an invariant of the position of A in B. When one V contains another, we obtain relationships between the [co] homology theories in the form of long exact sequences. Furthermore for finite algebras, V-[co]homology is effectively computable if membership in V is. We obtain an analogue of the Poincaré lemma (stating that subsets of an algebra in V are V-homologically trivial), extremely general guarantees of the existence of subsets with non-trivial V-homology for algebras not in V, long exact V-homotopy sequences, as well as analogues of the powerful Eilenberg-Zilber theorems and Kunneth theorems in the setting of V-connectivity for V a variety or pseudo-variety. Also in the more general case of any divisionally closed V, we construct the long exact Mayer-Vietoris sequences for V-homology. Results for homomorphisms include an algebraic version of contiguity for homomorphisms (which implies they are V-homotopic) and a proof that V-surmorphisms are V-homotopy equivalences. If we allow the divisional classes to vary, then algebraic connectivity may be viewed as a functor from the category of pairs W ⊆ V of divisional classes of [Formula: see text]-algebras with inclusions as morphisms' to the category of functors from pairs of [Formula: see text]-algebras to pairs of simplicial complexes. Examples show the non-triviality of this theory (e.g. "associativity tori"), and two preliminary applications to semigroups are given: 1) a proof that the group connectivity of a torsion semigroup S is homotopy equivalent to a space whose points are the maximal subgroups of S, and 2) an aperiodic connectivity analogue of the fundamental lemma of complexity.

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Yakushev, Igor, Alexander Drzezga, and Christian Habeck. "Metabolic connectivity." Current Opinion in Neurology 30, no. 6 (December 2017): 677–85. http://dx.doi.org/10.1097/wco.0000000000000494.

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Pillai, Jay J. "Functional Connectivity." Neuroimaging Clinics of North America 27, no. 4 (November 2017): xvii. http://dx.doi.org/10.1016/j.nic.2017.08.001.

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Mukherji, Suresh K. "Functional Connectivity." Neuroimaging Clinics of North America 27, no. 4 (November 2017): xv. http://dx.doi.org/10.1016/j.nic.2017.08.002.

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Cieslik, D., A. Dress, K. T. Huber, and V. Moulton. "Connectivity calculus." Applied Mathematics Letters 16, no. 3 (April 2003): 395–99. http://dx.doi.org/10.1016/s0893-9659(03)80063-0.

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Zenklusen, Rico. "Connectivity interdiction." Operations Research Letters 42, no. 6-7 (September 2014): 450–54. http://dx.doi.org/10.1016/j.orl.2014.07.010.

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