Journal articles: 'Connectivity Functions'

1

Rosen. "Dense Extendable Connectivity Functions." Real Analysis Exchange 18, no. 1 (1992): 42. http://dx.doi.org/10.2307/44133042.

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Gibson and Gibson. "CONCERNING EXTENDABLE CONNECTIVITY FUNCTIONS." Real Analysis Exchange 11, no. 1 (1985): 56. http://dx.doi.org/10.2307/44151727.

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3

Oxley, James, and Geoff Whittle. "Connectivity of submodular functions." Discrete Mathematics 105, no. 1-3 (August 1992): 173–84. http://dx.doi.org/10.1016/0012-365x(92)90140-b.

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4

Jowett, Susan, Songbao Mo, and Geoff Whittle. "Connectivity functions and polymatroids." Advances in Applied Mathematics 81 (October 2016): 1–12. http://dx.doi.org/10.1016/j.aam.2016.06.004.

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5

Gibson, Richard G., and Fred Roush. "Connectivity functions defined on $I^n$." Colloquium Mathematicum 55, no. 1 (1987): 41–44. http://dx.doi.org/10.4064/cm-55-1-41-44.

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Gibson and Roush. "THE UNIFORM LIMIT OF CONNECTIVITY FUNCTIONS." Real Analysis Exchange 11, no. 1 (1985): 254. http://dx.doi.org/10.2307/44151744.

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Gibson and Roush. "CONNECTIVITY FUNCTIONS WITH A PERFECT ROAD." Real Analysis Exchange 11, no. 1 (1985): 260. http://dx.doi.org/10.2307/44151745.

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8

Gibson. "CONCERNING EXTENDABLE CONNECTIVITY FUNCTIONS, A CONTINUATION." Real Analysis Exchange 12, no. 1 (1986): 85. http://dx.doi.org/10.2307/44151773.

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Gibson and Roush. "A CHARACTERIZATION OF EXTENDABLE CONNECTIVITY FUNCTIONS." Real Analysis Exchange 13, no. 1 (1987): 214. http://dx.doi.org/10.2307/44151872.

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10

Garrett. "CONNECTED AND CONNECTIVITY FUNCTIONS ON DENDRITES." Real Analysis Exchange 14, no. 2 (1988): 440. http://dx.doi.org/10.2307/44151959.

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11

Gibson. "Concerning Two Properties of Connectivity Functions." Real Analysis Exchange 15, no. 1 (1989): 16. http://dx.doi.org/10.2307/44151979.

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12

Kellum. "COMPOSITIONS OF DARBOUX AND CONNECTIVITY FUNCTIONS." Real Analysis Exchange 24, no. 1 (1998): 67. http://dx.doi.org/10.2307/44152923.

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13

Ciesielski and Kellum. "COMPOSITIONS OF DARBOUX AND CONNECTIVITY FUNCTIONS." Real Analysis Exchange 24, no. 2 (1998): 599. http://dx.doi.org/10.2307/44152982.

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14

Bowler, Nathan, and Susan Jowett. "Recognising graphic and matroidal connectivity functions." Discrete Mathematics 343, no. 12 (December 2020): 112093. http://dx.doi.org/10.1016/j.disc.2020.112093.

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15

Baker, I. N., J. Kotus, and Lü Yinian. "Iterates of meromorphic functions III: Preperiodic domains." Ergodic Theory and Dynamical Systems 11, no. 4 (December 1991): 603–18. http://dx.doi.org/10.1017/s0143385700006386.

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AbstractThe paper discusses the connectivity of periodic and preperiodic domains in the stable set in the iteration of a meromorphic function. The connectivity of an invariant component has one of the values 1, 2, ∞. Examples are constructed to show that the connectivity of a preperiodic component may take any value.

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16

Cohen, Matthew J., Irena F. Creed, Laurie Alexander, Nandita B. Basu, Aram J. K. Calhoun, Christopher Craft, Ellen D’Amico, et al. "Do geographically isolated wetlands influence landscape functions?" Proceedings of the National Academy of Sciences 113, no. 8 (February 8, 2016): 1978–86. http://dx.doi.org/10.1073/pnas.1512650113.

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Geographically isolated wetlands (GIWs), those surrounded by uplands, exchange materials, energy, and organisms with other elements in hydrological and habitat networks, contributing to landscape functions, such as flow generation, nutrient and sediment retention, and biodiversity support. GIWs constitute most of the wetlands in many North American landscapes, provide a disproportionately large fraction of wetland edges where many functions are enhanced, and form complexes with other water bodies to create spatial and temporal heterogeneity in the timing, flow paths, and magnitude of network connectivity. These attributes signal a critical role for GIWs in sustaining a portfolio of landscape functions, but legal protections remain weak despite preferential loss from many landscapes. GIWs lack persistent surface water connections, but this condition does not imply the absence of hydrological, biogeochemical, and biological exchanges with nearby and downstream waters. Although hydrological and biogeochemical connectivity is often episodic or slow (e.g., via groundwater), hydrologic continuity and limited evaporative solute enrichment suggest both flow generation and solute and sediment retention. Similarly, whereas biological connectivity usually requires overland dispersal, numerous organisms, including many rare or threatened species, use both GIWs and downstream waters at different times or life stages, suggesting that GIWs are critical elements of landscape habitat mosaics. Indeed, weaker hydrologic connectivity with downstream waters and constrained biological connectivity with other landscape elements are precisely what enhances some GIW functions and enables others. Based on analysis of wetland geography and synthesis of wetland functions, we argue that sustaining landscape functions requires conserving the entire continuum of wetland connectivity, including GIWs.

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17

Rosen. "LIMITS AND SERIES OF EXTENDABLE CONNECTIVITY FUNCTIONS." Real Analysis Exchange 20, no. 1 (1994): 36. http://dx.doi.org/10.2307/44152450.

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18

Rosen. "LIMITS AND SUMS OF EXTENDABLE CONNECTIVITY FUNCTIONS." Real Analysis Exchange 20, no. 1 (1994): 183. http://dx.doi.org/10.2307/44152479.

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19

Ciesielski, K., and J. Wojciechowski. "Sums of Connectivity Functions on R n." Proceedings of the London Mathematical Society 76, no. 2 (March 1998): 406–26. http://dx.doi.org/10.1112/s0024611598000136.

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20

Hroudová, Jana, and Zdeněk Fišar. "Connectivity between mitochondrial functions and psychiatric disorders." Psychiatry and Clinical Neurosciences 65, no. 2 (March 2011): 130–41. http://dx.doi.org/10.1111/j.1440-1819.2010.02178.x.

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21

Boxer, Laurence, and P. Christopher Staecker. "Connectivity Preserving Multivalued Functions in Digital Topology." Journal of Mathematical Imaging and Vision 55, no. 3 (January 4, 2016): 370–77. http://dx.doi.org/10.1007/s10851-015-0625-5.

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22

Koss, L. L. "Frequency response functions for power and connectivity." Journal of Sound and Vibration 181, no. 4 (April 1995): 709–25. http://dx.doi.org/10.1006/jsvi.1995.0167.

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23

Franco, Mario, Octavio Zapata, David A. Rosenblueth, and Carlos Gershenson. "Random Networks with Quantum Boolean Functions." Mathematics 9, no. 8 (April 7, 2021): 792. http://dx.doi.org/10.3390/math9080792.

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We propose quantum Boolean networks, which can be classified as deterministic reversible asynchronous Boolean networks. This model is based on the previously developed concept of quantum Boolean functions. A quantum Boolean network is a Boolean network where the functions associated with the nodes are quantum Boolean functions. We study some properties of this novel model and, using a quantum simulator, we study how the dynamics change in function of connectivity of the network and the set of operators we allow. For some configurations, this model resembles the behavior of reversible Boolean networks, while for other configurations a more complex dynamic can emerge. For example, cycles larger than 2N were observed. Additionally, using a scheme akin to one used previously with random Boolean networks, we computed the average entropy and complexity of the networks. As opposed to classic random Boolean networks, where “complex” dynamics are restricted mainly to a connectivity close to a phase transition, quantum Boolean networks can exhibit stable, complex, and unstable dynamics independently of their connectivity.

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24

Maliszewski, A. "Connectivity of diagonal products of Baire one functions." Fundamenta Mathematicae 146, no. 1 (1994): 21–29. http://dx.doi.org/10.4064/fm-146-1-21-29.

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25

Rosen. "ON CHARACTERIZING EXTENDABLE CONNECTIVITY FUNCTIONS BY ASSOCIATED SETS." Real Analysis Exchange 22, no. 1 (1996): 279. http://dx.doi.org/10.2307/44152750.

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26

Looney, Carl G. "Fuzzy connectivity clustering with radial basis kernel functions." Fuzzy Sets and Systems 160, no. 13 (July 2009): 1868–85. http://dx.doi.org/10.1016/j.fss.2008.12.010.

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27

Harvey Rosen. "Sierpinski-Zygmund Uniform Limits of Extendable Connectivity Functions." Real Analysis Exchange 28, no. 1 (2003): 105. http://dx.doi.org/10.14321/realanalexch.28.1.0105.

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Tian, Kai, Xin-an Yin, Jie Bai, Wei Yang, and Yan-wei Zhao. "Grading Evaluation of the Structural Connectivity of River System Networks Based on Ecological Functions, and a Case Study of the Baiyangdian Wetland, China." Water 13, no. 13 (June 27, 2021): 1775. http://dx.doi.org/10.3390/w13131775.

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River system network (RSN) connectivity is important to maintain the environmental and ecological functions of wetlands. Quantitative evaluation of connectivity can provide crucial support for efforts to improve wetland connectivity and to restore and protect wetland ecosystems. Most existing evaluation methods uniformly generalise RSN to form an undifferentiated RSN of edges and nodes that is taken as a whole to evaluate the connectivity. However, actual RSNs comprise rivers, canals, ditches, lakes, and ponds, which differ substantially in their structures, morphologies, and attributes. The mix of RSN elements therefore defines grades that give RSNs distinctive characteristics. Moreover, RSNs with different grades perform different ranges of environmental and ecological functions. The existing evaluation methods, which have some limitations, do not account for these characteristics. To account for these differences, we examined the grade characteristics and their impact on environmental and ecological functions. We established a grading system of RSN elements and a grading method of RSN, and constructed the structural connectivity evaluation indicator system for RSNs at different grades. On this basis, we propose a method for grading evaluation of RSN connectivity. We used China’s Baiyangdian Wetland to demonstrate the use of the system and validate the results. The proposed method provided an objective and accurate evaluation of RSN connectivity and clarified the differences in connectivity among RSNs with different grades, thereby providing improved guidance for the development and maintenance of the environmental and ecological functions of RSNs.

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TIBĂR, MIHAI. "CONNECTIVITY VIA NONGENERIC PENCILS." International Journal of Mathematics 13, no. 02 (March 2002): 111–23. http://dx.doi.org/10.1142/s0129167x02001289.

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We use slicing by nongeneric pencils of hypersurfaces and prove a new theorem of Lefschetz type for singular non-compact spaces, at the homotopy level. As applications, we derive results on the topology of the fibres of polynomial functions or the topology of complements of hypersurfaces in [Formula: see text].

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30

ANDRES, JAN, PAVLA ŠNYRYCHOVÁ, and PIOTR SZUCA. "SHARKOVSKII'S THEOREM FOR CONNECTIVITY Gδ-RELATIONS." International Journal of Bifurcation and Chaos 16, no. 08 (August 2006): 2377–93. http://dx.doi.org/10.1142/s0218127406016136.

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A version of Sharkovskii's cycle coexistence theorem is formulated for a composition of connectivity Gδ-relations with closed values. Thus, a multivalued version in [Andres & Pastor, 2005] holding with at most two exceptions for M-maps, jointly with a single-valued version in [Szuca, 2003], for functions with a connectivity Gδ-graph, are generalized. In particular, our statement is applicable to differential inclusions as well as to some discontinuous functions.

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31

Kolomeec, N. A. "On the minimal distance graph connectivity for bent functions." Prikladnaya diskretnaya matematika. Prilozhenie, no. 8 (December 1, 2015): 33–34. http://dx.doi.org/10.17223/2226308x/8/12.

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32

Hawthorne, Frank. "Connectivity and formula-generating functions for sheet-silicate minerals." Acta Crystallographica Section A Foundations and Advances 70, a1 (August 5, 2014): C1089. http://dx.doi.org/10.1107/s2053273314089104.

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Silicate sheets may be described by two-dimensional nets in which the vertices of the net are occupied by tetrahedra, and the edges of the net represent linkages between tetrahedra. A plane net must contain 3-connected vertices, but not all vertices need to be 3-connected. Simple silicate structures may thus be generated from simple 3-connected plane nets (e.g. 63, 4.82, 4.6.8, (4.6.8)2(6.82)1, etc.). More complicated silicate nets may be generated by various "building operations": (1) Insertion: insertion of 2- and 4-connected vertices into 3-connected plane nets; (2) Repetition: generation of double (or triple) nets by topological symmetry operations that retain transitivity at the junction between the repeated elements. Diversity is also introduced within the sheets of tetrahedra by [1] adjacent apical tetrahedron vertices pointing in the same or different directions, and [2] by folding of the sheets. For simple structures, net type strongly affects the stoichiometry of the resultant structure as the unit cells of the various nets are of different sizes (and shapes), although the stoichiometry may also be affected by non-tetrahedral components. Building operations strongly affect the stoichiometry of the resultant sheet, and this effect may be quantified. We define a formula-generating function F(k,l,...) that generates the formula of a sheet with specific topological features denoted by the indices k,l,... . A simple 3-connected net results in sheets of the form (T2O5)n where n denotes the number of (T2O5)n in the unit cell of the underlying net (for 63, n = 1; for 4.82, n = 2; for (4.6.8)2(6.82)1, n = 3, etc). Plane nets with k 3-connected vertices and l inserted 2-connected vertices result in sheets of the form [T(k+l) O(2.5k+3l)], where (...) are subscripted. Single- and double-sheet structures may be generated from the function F(k,l) = T(N{k+l}) O(N{3k+2.5l}-n{N-1}) where N = 1 and 2 for single- and double-sheets, respectively, and (...) are subscripted.

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33

Hawkins, Jane, and Lorelei Koss. "Connectivity properties of Julia sets of Weierstrass elliptic functions." Topology and its Applications 152, no. 1-2 (July 2005): 107–37. http://dx.doi.org/10.1016/j.topol.2004.08.018.

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34

Chan, Kit C., Gokul R. Kadel, and Leonardo Pinheiro. "Chaotic differentiation operators on harmonic functions and simple connectivity." Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 109, no. 2 (August 26, 2014): 385–93. http://dx.doi.org/10.1007/s13398-014-0188-0.

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Zhu, Wei, Jingyu Hou, and Yi-Ping Phoebe Chen. "Semantically predicting protein functions based on protein functional connectivity." Computational Biology and Chemistry 44 (June 2013): 9–14. http://dx.doi.org/10.1016/j.compbiolchem.2013.01.002.

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36

Xiao, Ling, Li Cui, Qun’ou Jiang, Meilin Wang, Lidan Xu, and Haiming Yan. "Spatial Structure of a Potential Ecological Network in Nanping, China, Based on Ecosystem Service Functions." Land 9, no. 10 (October 7, 2020): 376. http://dx.doi.org/10.3390/land9100376.

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The increasing scale of urbanization and human activities has resulted in the fragmentation of natural habitats, leading to the reduction of ecological landscape connectivity and biodiversity. Taking Nanping as the study area, the core areas with good connectivity were extracted as ecological sources using a morphological spatial pattern analysis (MSPA) and landscape connectivity index. Then the ecosystem service functions of the ecological sources were evaluated based on the InVEST model. Finally, we extracted the potential ecological corridor based on the land type, elevation and ecosystem service functions. The results showed that the ecological source with higher landscape connectivity is distributed in the north and there are clear landscape connectivity faults in the northern and southern regions. Moreover, the areas with high habitat quality, soil retention and water production are mainly distributed in the northern ecological source areas. The 15 potential ecological corridors extracted were distributed unevenly. Among them, the important ecological corridors formed a triangle network, while the general ecological corridors were concentrated in the northwest. Therefore, it is suggested that the important core patches in the north be protected, and the effective connection between the north and south be improved. These results can provide a scientific basis for ecological construction and hierarchical management of the ecological networks.

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Beketayev, Kenes, Damir Yeliussizov, Dmitriy Morozov, Gunther H. Weber, and Bernd Hamann. "Measuring the Error in Approximating the Sub-Level Set Topology of Sampled Scalar Data." International Journal of Computational Geometry & Applications 28, no. 01 (March 2018): 57–77. http://dx.doi.org/10.1142/s0218195918500036.

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This paper studies the influence of the definition of neighborhoods and methods used for creating point connectivity on topological analysis of scalar functions. It is assumed that a scalar function is known only at a finite set of points with associated function values. In order to utilize topological approaches to analyze the scalar-valued point set, it is necessary to choose point neighborhoods and, usually, point connectivity to meaningfully determine critical-point behavior for the point set. Two distances are used to measure the difference in topology when different point neighborhoods and means to define connectivity are used: (i) the bottleneck distance for persistence diagrams and (ii) the distance between merge trees. Usually, these distances define how different scalar functions are with respect to their topology. These measures, when properly adapted to point sets coupled with a definition of neighborhood and connectivity, make it possible to understand how topological characteristics depend on connectivity. Noise is another aspect considered. Five types of neighborhoods and connectivity are discussed: (i) the Delaunay triangulation; (ii) the relative neighborhood graph; (iii) the Gabriel graph; (iv) the [Formula: see text]-nearest-neighbor (KNN) neighborhood; and (v) the Vietoris–Rips complex. It is discussed in detail how topological characterizations depend on the chosen connectivity.

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Kawagoe, Toshikazu. "Overview of (f)MRI Studies of Cognitive Aging for Non-Experts: Looking through the Lens of Neuroimaging." Life 12, no. 3 (March 12, 2022): 416. http://dx.doi.org/10.3390/life12030416.

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This special issue concerning Brain Functional and Structural Connectivity and Cognition aims to expand our understanding of brain connectivity. Herein, I review related topics including the principle and concepts of functional MRI, brain activation, and functional/structural connectivity in aging for uninitiated readers. Visuospatial attention, one of the well-studied functions in aging, is discussed from the perspective of neuroimaging.

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Pasquini, Lorenzo, Fernanda Palhano-Fontes, and Draulio B. Araujo. "Subacute effects of the psychedelic ayahuasca on the salience and default mode networks." Journal of Psychopharmacology 34, no. 6 (April 7, 2020): 623–35. http://dx.doi.org/10.1177/0269881120909409.

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Background: Neuroimaging studies have just begun to explore the acute effects of psychedelics on large-scale brain networks’ functional organization. Even less is known about the neural correlates of subacute effects taking place days after the psychedelic experience. This study explores the subacute changes of primary sensory brain networks and networks supporting higher-order affective and self-referential functions 24 hours after a single session with the psychedelic ayahuasca. Methods: We leveraged task-free functional magnetic resonance imaging data 1 day before and 1 day after a randomized placebo-controlled trial exploring the effects of ayahuasca in naïve healthy participants (21 placebo/22 ayahuasca). We derived intra- and inter-network functional connectivity of the salience, default mode, visual, and sensorimotor networks, and assessed post-session connectivity changes between the ayahuasca and placebo groups. Connectivity changes were associated with Hallucinogen Rating Scale scores assessed during the acute effects. Results: Our findings revealed increased anterior cingulate cortex connectivity within the salience network, decreased posterior cingulate cortex connectivity within the default mode network, and increased connectivity between the salience and default mode networks 1 day after the session in the ayahuasca group compared to placebo. Connectivity of primary sensory networks did not differ between groups. Salience network connectivity increases correlated with altered somesthesia scores, decreased default mode network connectivity correlated with altered volition scores, and increased salience default mode network connectivity correlated with altered affect scores. Conclusion: These findings provide preliminary evidence for subacute functional changes induced by the psychedelic ayahuasca on higher-order cognitive brain networks that support interoceptive, affective, and self-referential functions.

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40

Nadler, Sam B. "Local connectivity functions on arcwise connected spaces and certain continua." Topology and its Applications 153, no. 8 (February 2006): 1279–90. http://dx.doi.org/10.1016/j.topol.2005.03.012.

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41

KISAKA, MASASHI. "On the connectivity of Julia sets of transcendental entire functions." Ergodic Theory and Dynamical Systems 18, no. 1 (February 1998): 189–205. http://dx.doi.org/10.1017/s0143385798097570.

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42

Barański, Krzysztof, Núria Fagella, Xavier Jarque, and Bogusława Karpińska. "On the connectivity of the Julia sets of meromorphic functions." Inventiones mathematicae 198, no. 3 (February 8, 2014): 591–636. http://dx.doi.org/10.1007/s00222-014-0504-5.

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Perez, Elizabeth, Juan A. Araiza, Dreysy Pozos, Edmundo Bonilla, Jose C. Hernandez, and Jesus A. Cortes. "APPLICATION FOR FUNCTIONALITY AND REGISTRATION IN THE CLOUD OF A MICROCONTROLLER DEVELOPMENT BOARD FOR IOT IN AWS." Applied Computer Science 17, no. 2 (June 30, 2021): 14–27. http://dx.doi.org/10.35784/acs-2021-10.

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The use of the Amazon Web Services cloud enables new functionalities that are not possible with traditional solutions: low latency, local data processing and storage, and direct connectivity to other cloud services. Reimagining the way IoT connectivity services are presented by combining AWS cloud technology with mobile connectivity offers rapid prototyping to help connect devices natively over Wi-Fi. For this, the MQTT communication protocol is used to interact with the IoT device and exchange data, which allows controlling the basic functions of a sensor node. The installation is realized through a software development kit (SDK), which allows the creation of an application for Android devices. This solution gives the option to integrate together, improving the connectivity of the IoT system. The results enable board logging and network configuration, and can also be used to control the IoT device. The embedded firmware provides the required security functions.

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Jinks, Kristin I., Christopher J. Brown, Thomas A. Schlacher, Andrew D. Olds, Sarah L. Engelhard, Ryan M. Pearson, and Rod M. Connolly. "Being Well-Connected Pays in a Disturbed World: Enhanced Herbivory in Better-Linked Habitats." Diversity 12, no. 11 (November 12, 2020): 424. http://dx.doi.org/10.3390/d12110424.

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Seascapes are typically comprised of multiple components that are functionally linked by the movement of organisms and fluxes of matter. Changes to the number and spatial arrangement of these linkages affect biological connectivity that, in turn, can alter ecological functions. Herbivory is one such function, pivotal in controlling excessive algal growth when systems become disturbed. Here, we used microcosm experiments to test how the change to connectivity affects herbivory under different levels of disturbance. We applied network theory to measure types of connectivity at different scales (patch and whole system) and quantified herbivory by a crustacean mesograzer exposed to excess algae, mimicking pulse and press disturbances. We demonstrate that greater connectivity significantly enhances herbivory in Clibanarius virescens: Both the number of linkages and their spatial arrangement interact to shape the response of herbivory in systems to disturbance. Our findings highlight the value of controlled experiments for advancing theories about the potential effects of connectivity on important ecological functions, such as herbivory, and justify further investigation to measure how connectivity might affect the resilience of ecosystems. We posit that the variation in the type, and scale, of spatial linkages might have profound consequences for managing the capacity of ecosystems to respond to disturbance.

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Aarabi, Ardalan. "Brain Dynamics and Connectivity from Birth through Adolescence." Brain Sciences 12, no. 3 (March 15, 2022): 395. http://dx.doi.org/10.3390/brainsci12030395.

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Altun, Mustafa, and Marc D. Riedel. "Robust Computation through Percolation." International Journal of Nanotechnology and Molecular Computation 3, no. 2 (April 2011): 12–30. http://dx.doi.org/10.4018/jnmc.2011040102.

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This paper proposes a probabilistic framework for digital computation with lattices of nanoscale switches based on the mathematical phenomenon of percolation. With random connectivity, percolation gives rise to a sharp non-linearity in the probability of global connectivity as a function of the probability of local connectivity. This phenomenon is exploited to compute Boolean functions robustly in the presence of defects. It is shown that the margins, defined in terms of the steepness of the non-linearity, translate into the degree of defect tolerance. Achieving good margins entails a mapping problem. Given a target Boolean function, the problem is how to assign literals to regions of the lattice such that no diagonal paths of 1’s exist in any assignment that evaluates to 0. Assignments with such paths result in poor error margins due to stray, random connections that can form across the diagonal. A necessary and sufficient condition is formulated for a mapping strategy that preserves good margins: the top-to-bottom and left-to-right connectivity functions across the lattice must be dual functions. Based on lattice duality, an efficient algorithm to perform the mapping is proposed. The algorithm optimizes the lattice area while meeting prescribed worst-case margins. Its effectiveness is demonstrated on benchmark circuits.

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Baker, I. N. "Some entire functions with multiply-connected wandering domains." Ergodic Theory and Dynamical Systems 5, no. 2 (June 1985): 163–69. http://dx.doi.org/10.1017/s0143385700002832.

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AbstractA component U of the complement of the Julia set of an entire function ƒ is a wandering domain if the sets ƒn(U) are mutually disjoint, where n ∈ℕ and ƒn is the n-th iterate of ƒ. Examples are given of entire ƒ of order , which have multiply-connected wandering domains. An example is given where the connectivity is infinite.

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Gustin, Marie-Paule, Christian Z. Paultre, Jacques Randon, Giampiero Bricca, and Catherine Cerutti. "Functional meta-analysis of double connectivity in gene coexpression networks in mammals." Physiological Genomics 34, no. 1 (June 2008): 34–41. http://dx.doi.org/10.1152/physiolgenomics.00008.2008.

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In functional genomics, the high-throughput methods such as microarrays 1) allow analysis of the relationships between genes considering them as elements of a network and 2) lead to biological interpretations thanks to Gene Ontology. But up to now it has not been possible to find relationships between the functions and the connectivity of the genes in coexpression networks. To achieve this aim, we have defined a double connectivity for each gene by the numbers of its significant negative and positive correlations with the other genes within a given biological condition, or group. Here, based on the analysis of 1,260 DNA microarrays, we show that this double connectivity clearly separates two types of genes, those with a predominantly strong negative connectivity, hub− genes, and those with a predominantly strong positive connectivity, hub+ genes. Interestingly, the hub+ genes concerned transcription factors more often than by chance and, similarly, for the hub− genes concerning miRNA predicted targets. Furthermore, a meta-analysis of GO annotations carried out on 67 groups in humans and rats shows that these two types of genes correspond to a functional biological duality. The hub− genes were mainly involved in basic functions common to all eukaryote cells, whereas the hub+ genes were mainly involved in specialized functions related to cell differentiation and communication. The separation and the biological role of these hub− and hub+ genes provide a powerful new tool for a better understanding of the control and regulation of the key genes involved in cellular differentiation and physiopathological conditions.

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Shah-Basak, Priyanka, Gayatri Sivaratnam, Selina Teti, Tiffany Deschamps, Aneta Kielar, Regina Jokel, and Jed A. Meltzer. "Electrophysiological connectivity markers of preserved language functions in post-stroke aphasia." NeuroImage: Clinical 34 (2022): 103036. http://dx.doi.org/10.1016/j.nicl.2022.103036.

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Rosen. "EVERY REAL FUNCTION IS THE SUM OF TWO EXTENDABLE CONNECTIVITY FUNCTIONS." Real Analysis Exchange 21, no. 1 (1995): 299. http://dx.doi.org/10.2307/44153918.

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Journal articles on the topic 'Connectivity Functions'

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