1. Craven, B. A., Paterson, E. G. & Settles, G. S. The fluid dynamics of canine olfaction: unique nasal airflow patterns as an explanation of macrosmia. J. R. Soc. Interface 7, 933–943 (2009).

2. Grosmaitre, X., Santarelli, L. C., Tan, J., Luo, M. & Ma, M. Dual functions of mammalian olfactory sensory neurons as odor detectors and mechanical sensors. Nat. Neurosci. 10, 348–354 (2007).

3. Verhagen, J. V., Wesson, D. W., Netoff, T. I., White, J. A. & Wachowiak, M. Sniffing controls an adaptive filter of sensory input to the olfactory bulb. Nat. Neurosci. 10, 631–639 (2007).

4. Shusterman, R., Smear, M. C., Koulakov, A. A. & Rinberg, D. Precise olfactory responses tile the sniff cycle. Nat. Neurosci. 14, 1039–1044 (2011).

5. Smear, M., Shusterman, R., O’Connor, R., Bozza, T. & Rinberg, D. Perception of sniff phase in mouse olfaction. Nature 479, 397–400 (2011).

6. Sobel, N. et al. Sniffing and smelling: separate subsystems in the human olfactory cortex. Nature 392, 282–286 (1998).

7. Fontanini, A., Spano, P. & Bower, J. M. Ketamine-xylazine-induced slow (<1.5 Hz) oscillations in the rat piriform (olfactory) cortex are functionally correlated with respiration. J. Neurosci. 23, 7993–8001 (2003).

8. Kepecs, A., Uchida, N. & Mainen, Z. F. The sniff as a unit of olfactory processing. Chem. Senses 31, 167–179 (2005).

9. Mainland, J. & Sobel, N. The sniff is part of the olfactory percept. Chem. Senses 31, 181–196 (2005).

10. Strausfeld, N. J. & Hildebrand, J. G. Olfactory systems: common design, uncommon origins? Curr. Opin. Neurobiol. 9, 634–639 (1999).

11. Rowe, T. B., Macrini, T. E. & Luo, Z.-X. Fossil evidence on origin of the mammalian brain. Science 332, 955–957 (2011).

12. Rowe, T. B. & Shepherd, G. M. Role of ortho‐retronasal olfaction in mammalian cortical evolution. J. Comp. Neurol. 524, 471–495 (2016).

13. Freeman, W. J. The place of ‘codes’ in nonlinear neurodynamics. Prog. Brain Res. 165, 447–462 (2007).

14. Heck, D. H. et al. Breathing as a fundamental rhythm of brain function. Front. Neural Circuits 10, 115 (2017).

15. Fontanini, A. & Bower, J. M. Slow-waves in the olfactory system: an olfactory perspective on cortical rhythms. Trends Neurosci. 29, 429–437 (2006).

16. Tort, A., Brankačk, J. & Draguhn, A. Respiration-entrained brain rhythms are global but often overlooked. Trends Neurosci. 41, 186–197 (2018).

17. Biskamp, J., Bartos, M. & Sauer, J.-F. Organization of prefrontal network activity by respiration-related oscillations. Sci. Rep. 7, 45508 (2017).

18. Zhong, W. et al. Selective entrainment of gamma subbands by different slow network oscillations. Proc. Natl Acad. Sci. USA 114, 4519–4524 (2017).

19. Herrero, J. L., Khuvis, S., Yeagle, E., Cerf, M. & Mehta, A. D. Breathing above the brain stem: volitional control and attentional modulation in humans. J. Neurophysiol. 119, 145–159 (2017).

20. Piarulli, A. et al. Ultra-slow mechanical stimulation of olfactory epithelium modulates consciousness by slowing cerebral rhythms in humans. Sci. Rep. 8, 6581 (2018).

21. Cao, Y., Roy, S., Sachdev, R. N. & Heck, D. H. Dynamic correlation between whisking and breathing rhythms in mice. J. Neurosci. 32, 1653–1659 (2012).

22. Moore, J. D. et al. Hierarchy of orofacial rhythms revealed through whisking and breathing. Nature 497, 205–210 (2013).

23. Sirotin, Y. B., Costa, M. E. & Laplagne, D. A. Rodent ultrasonic vocalizations are bound to active sniffing behavior. Front. Behav. Neurosci. 8, 399 (2014).

24. Wong, J. & Waters, D. The synchronisation of signal emission with wingbeat during the approach phase in soprano pipistrelles (Pipistrellus pygmaeus). J. Exp. Biol. 204, 575–583 (2001).

25. Suthers, R. A., Thomas, S. P. & Suthers, B. J. Respiration, wing-beat and ultrasonic pulse emission in an echo-locating bat. J. Exp. Biol. 56, 37–48 (1972).

26. Kleinfeld, D., Deschênes, M., Wang, F. & Moore, J. D. More than a rhythm of life: breathing as a binder of orofacial sensation. Nat. Neurosci. 17, 647–651 (2014).

27. Zelano, C. et al. Nasal respiration entrains human limbic oscillations and modulates cognitive function. J. Neurosci. 36, 12448–12467 (2016).

28. Bensafi, M. et al. Olfactomotor activity during imagery mimics that during perception. Nat. Neurosci. 6, 1142–1144 (2003).

29. Arshamian, A., Iravani, B., Majid, A. & Lundström, J. N. Respiration modulates olfactory memory consolidation in humans. J. Neurosci. 38, 10286–10294 (2018).

30. Nakamura, N. H., Fukunaga, M. & Oku, Y. Respiratory modulation of cognitive performance during the retrieval process. PLoS One 13, e0204021 (2018).

31. Frost, R., Siegelman, N., Narkiss, A. & Afek, L. What predicts successful literacy acquisition in a second language? Psychol. Sci. 24, 1243–1252 (2013).

32. Uecker, A. et al. Neuroanatomical correlates of implicit and explicit memory for structurally possible and impossible visual objects. Learn. Mem. 4, 337–355 (1997).

33. Rubinson, M. et al. Hierarchy measurement for modeling network dynamics under directed attacks. Phys. Rev. E 96, 052307 (2017).

34. Barry, R. J., Clarke, A. R. & Johnstone, S. J. A review of electrophysiology in attention-deficit/hyperactivity disorder: I. Qualitative and quantitative electroencephalography. Clin. Neurophysiol. 114, 171–183 (2003).

35. Renault, B., Ragot, R., Lesevre, N. & Remond, A. Onset and offset of brain events as indices of mental chronometry. Science 215, 1413–1415 (1982).

36. Kenemans, J., Kok, A. & Smulders, F. Event-related potentials to conjunctions of spatial frequency and orientation as a function of stimulus parameters and response requirements. Electroencephalogr. Clin. Neurophysiol. 88, 51–63 (1993).

37. Pascual-Marqui, R. D., Michel, C. M. & Lehmann, D. Low resolution electromagnetic tomography: a new method for localizing electrical activity in the brain. Int. J. Psychophysiol. 18, 49–65 (1994).

38. Grech, R. et al. Review on solving the inverse problem in EEG source analysis. J. Neuroeng. Rehabil. 5, 25 (2008).

39. Pascual-Marqui, R. D. Review of methods for solving the EEG inverse problem. Int. J. Bioelectromagn. 1, 75–86 (1999).

40. Brown, R. P. & Gerbarg, P. L. Sudarshan Kriya yogic breathing in the treatment of stress, anxiety, and depression: part I—neurophysiologic model. J. Altern. Complement. Med. 11, 189–201 (2005).

41. Park, H.-J. & Friston, K. Structural and functional brain networks: from connections to cognition. Science 342, 1238411 (2013).

42. Egner, T. & Gruzelier, J. H. EEG biofeedback of low beta band components: frequency-specific effects on variables of attention and event-related brain potentials. Clin. Neurophysiol. 115, 131–139 (2004).

43. Bassett, D. S. & Bullmore, E. Small-world brain networks. Neuroscientist 12, 512–523 (2006).

44. Stam, C. J., Jones, B., Nolte, G., Breakspear, M. & Scheltens, P. Small-world networks and functional connectivity in Alzheimer’s disease. Cereb. Cortex 17, 92–99 (2006).

45. Micheloyannis, S. et al. Small-world networks and disturbed functional connectivity in schizophrenia. Schizophr. Res. 87, 60–66 (2006).

46. Naim-Feil, J. et al. Altered brain network dynamics in schizophrenia: a cognitive electroencephalography study. Biol. Psychiatry Cogn. Neurosci. Neuroimaging 3, 88–98 (2018).

47. Klimesch, W., Sauseng, P. & Hanslmayr, S. EEG alpha oscillations: the inhibition–timing hypothesis. Brain Res. Rev. 53, 63–88 (2007).

48. Ritter, P., Moosmann, M. & Villringer, A. Rolandic alpha and beta EEG rhythms’ strengths are inversely related to fMRI‐BOLD signal in primary somatosensory and motor cortex. Hum. Brain Mapp. 30, 1168–1187 (2009).

49. Janzen, G. & Weststeijn, C. G. Neural representation of object location and route direction: an event-related fMRI study. Brain Res. 1165, 116–125 (2007).

50. Del Negro, C. A., Funk, G. D. & Feldman, J. L. Breathing matters. Nat. Rev. Neurosci. 19, 351–367 (2018).

51. Dlouhy, B. J. et al. Breathing inhibited when seizures spread to the amygdala and upon amygdala stimulation. J. Neurosci. 35, 10281–10289 (2015).

52. Nobis, W. P. et al. Amygdala‐stimulation‐induced apnea is attention and nasal‐breathing dependent. Ann. Neurol. 83, 460–471 (2018).

53. Birn, R. M., Murphy, K., Handwerker, D. A. & Bandettini, P. A. fMRI in the presence of task-correlated breathing variations. Neuroimage 47, 1092–1104 (2009).

54. Simonsohn, U., Nelson, L. D. & Simmons, J. P. p-Curve and effect size: correcting for publication bias using only significant results. Perspect. Psychol. Sci. 9, 666–681 (2014).

55. Kozma, R. & Freeman, W. Analysis of visual theta rhythm—experimental and theoretical evidence of visual sniffing. In IJCNN'01. International Joint Conference on Neural Networks 1118–1121 (IEEE, 2001).

56. Faul, F., Erdfelder, E., Lang, A. G. & Buchner, A. G*Power 3: a flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behav. Res. Methods 39, 175–191 (2007).

57. Johnson, B. N., Russell, C., Khan, R. M. & Sobel, N. A comparison of methods for sniff measurement concurrent with olfactory tasks in humans. Chem. Senses 31, 795–806 (2006).

58. Homan, R. W., Herman, J. & Purdy, P. Cerebral location of international 10–20 system electrode placement. Electroencephal. Clin. Neurophysiol. 66, 376–382 (1987).

59. Gratton, G., Coles, M. G. & Donchin, E. A new method for off-line removal of ocular artifact. Electroencephal. Clin. Neurophysiol. 55, 468–484 (1983).

60. Koenig, T., Kottlow, M., Stein, M. & Melie-García, L. Ragu: a free tool for the analysis of EEG and MEG event-related scalp field data using global randomization statistics. Comput. Intell. Neurosci. 2011, 938925 (2011).

61. Bailey, N. et al. Mindfulness meditators show altered distributions of early and late neural activity markers of attention in a response inhibition task. Preprint at https://www.biorxiv.org/content/10.1101/396259v1 (2018).

62. Xia, M., Wang, J. & He, Y. BrainNet Viewer: a network visualization tool for human brain connectomics. PLoS One 8, e68910 (2013).

63. Tibshirani, R. The lasso method for variable selection in the Cox model. Stat. Med. 16, 385–395 (1997).