A Unified Approach to Quasiregular Linearization in the Plane

We generalize the classical K\"onig's and B\"ottcher's Theorems in complex dynamics to certain quasiregular mappings in the plane. Our approach to these results is unified in the sense that it does not depend on the local injectivity, or not, of the map at the fixed point. By passing to the logarithmic transform we obtain a quasiconformal mapping in either case. Certain restrictions on the quasiregular mappings are needed in order for there to be a candidate to linearize to. These are provided by requiring a simple infinitesimal space of the mapping at the fixed point and restricting to the BIP mappings introduced by the authors in prior work

Great Expectations: Recommendations for improving the methodological rigor of psychedelic clinical trials

Rationale: Psychedelic research continues to garner significant public and scientific interest with a growing number of clinical studies examining a wide range of conditions and disorders. However, expectancy effects and effective condition masking have been raised as critical limitations to the interpretability of the research. Objective: In this article, we review the many methodological challenges of conducting psychedelic clinical trials and provide recommendations for improving the rigor of future research. Results: We found that although some challenges are shared with psychotherapy and pharmacology trials more broadly, psychedelic clinical trials have to contend with several unique sources of potential bias. The subjective effects of a high-dose psychedelic are often so pronounced that it is difficult to mask participants to their treatment condition; the significant hype from positive media coverage on the clinical potential of psychedelics influences participants’ expectations for treatment benefit; and participant unmasking and treatment expectations can interact in such a way that makes psychedelic therapy highly susceptible to large placebo and nocebo effects. Specific recommendations to increase the success of masking procedures and reduce the influence of participant expectancies concern study development, participant recruitment and selection, incomplete disclosure of the study design, choice of active placebo condition, as well as the measurement of participant expectations and masking efficacy. Conclusion: Incorporating these design elements is intended to reduce the risk of bias in psychedelic clinical trials and thereby increase the ability to discern treatment-specific effects of psychedelic therap

Great Expectations: recommendations for improving the methodological rigor of psychedelic clinical trials

RationalePsychedelic research continues to garner significant public and scientific interest with a growing number of clinical studies examining a wide range of conditions and disorders. However, expectancy effects and effective condition masking have been raised as critical limitations to the interpretability of the research.ObjectiveIn this article, we review the many methodological challenges of conducting psychedelic clinical trials and provide recommendations for improving the rigor of future research.ResultsAlthough some challenges are shared with psychotherapy and pharmacology trials more broadly, psychedelic clinical trials have to contend with several unique sources of potential bias. The subjective effects of a high-dose psychedelic are often so pronounced that it is difficult to mask participants to their treatment condition; the significant hype from positive media coverage on the clinical potential of psychedelics influences participants' expectations for treatment benefit; and participant unmasking and treatment expectations can interact in such a way that makes psychedelic therapy highly susceptible to large placebo and nocebo effects. Specific recommendations to increase the success of masking procedures and reduce the influence of participant expectancies are discussed in the context of study development, participant recruitment and selection, incomplete disclosure of the study design, choice of active placebo condition, as well as the measurement of participant expectations and masking efficacy.ConclusionIncorporating the recommended design elements is intended to reduce the risk of bias in psychedelic clinical trials and thereby increases the ability to discern treatment-specific effects of psychedelic therapy