Existence and implications of a pitchfork-Hopf bifurcation in a continuous-time two-sector growth model

This paper shows that the dynamics of the Lucas (J Monet Econ, 22:3–42, 1988) endogenous growth model with flow externalities may give rise to a 2-torus, a compact three-dimensional manifold enclosed by a two-dimensional surface. The implications of this result are relevant for many fields of economic theory. It is first of all clear that if we choose to initialize the dynamics in the basin of attraction of this trapping region, a continuum of perfect foresight solutions may be observed. A simple econometric exercise, linking the physical-to-human capital ratio (state variable) to the 5-years forward variance of the growth rate of an unbalanced sample of 183 countries, seems to provide empirical backing for the phenomenon. Other important consequences, relevant from the point of view of endogenous cycles theory, are also scrutinized in the paper.

MOSAIC: a joint modeling methodology for combined circadian and non-circadian analysis of multi-omics data

Motivation Circadian rhythms are approximately 24-h endogenous cycles that control many biological functions. To identify these rhythms, biological samples are taken over circadian time and analyzed using a single omics type, such as transcriptomics or proteomics. By comparing data from these single omics approaches, it has been shown that transcriptional rhythms are not necessarily conserved at the protein level, implying extensive circadian post-transcriptional regulation. However, as proteomics methods are known to be noisier than transcriptomic methods, this suggests that previously identified arrhythmic proteins with rhythmic transcripts could have been missed due to noise and may not be due to post-transcriptional regulation. Results To determine if one can use information from less-noisy transcriptomic data to inform rhythms in more-noisy proteomic data, and thus more accurately identify rhythms in the proteome, we have created the Multi-Omics Selection with Amplitude Independent Criteria (MOSAIC) application. MOSAIC combines model selection and joint modeling of multiple omics types to recover significant circadian and non-circadian trends. Using both synthetic data and proteomic data from Neurospora crassa, we showed that MOSAIC accurately recovers circadian rhythms at higher rates in not only the proteome but the transcriptome as well, outperforming existing methods for rhythm identification. In addition, by quantifying non-circadian trends in addition to circadian trends in data, our methodology allowed for the recognition of the diversity of circadian regulation as compared to non-circadian regulation. Availability and implementation MOSAIC’s full interface is available at https://github.com/delosh653/MOSAIC. An R package for this functionality, mosaic.find, can be downloaded at https://CRAN.R-project.org/package=mosaic.find. Supplementary information Supplementary data are available at Bioinformatics online.

MOSAIC: A Joint Modeling Methodology for Combined Circadian and Non-Circadian Analysis of Multi-Omics Data

MotivationCircadian rhythms are approximately 24 hour endogenous cycles that control many biological functions. To identify these rhythms, biological samples are taken over circadian time and analyzed using a single omics type, such as transcriptomics or proteomics. By comparing data from these single omics approaches, it has been shown that transcriptional rhythms are not necessarily conserved at the protein level, implying extensive circadian post-transcriptional regulation. However, as proteomics methods are known to be noisier than transcriptomic methods, this suggests that previously identified arrhythmic proteins with rhythmic transcripts could have been missed due to noise and may not be due to post-transcriptional regulation.ResultsTo determine if one can use information from less-noisy transcriptomic data to inform rhythms in more-noisy proteomic data, and thus more accurately identify rhythms in the proteome, we have created the MOSAIC (Multi-Omics Selection with Amplitude Independent Criteria) application. MOSAIC combines model selection and joint modeling of multiple omics types to recover significant circadian and non-circadian trends. Using both synthetic data and proteomic data from Neurospora crassa, we showed that MOSAIC accurately recovers circadian rhythms at higher rates in not only the proteome but the transcriptome as well, outperforming existing methods for rhythm identification. In addition, by quantifying non-circadian trends in addition to circadian trends in data, our methodology allowed for the recognition of the diversity of circadian regulation as compared to non-circadian regulation.AvailabilityMOSAIC’s full interface is available at https://github.com/delosh653/[email protected] informationSupplementary data are available.at Bioinformatics online.

COMPLEX DYNAMICS IN LUCAS’ TREE ASSET PRICING MODEL WITH DYNAMIC SELF-CONTROL PREFERENCES

This paper studies the global equilibrium dynamics implied by a Lucas’ tree asset pricing model where the representative agent is subject to temptation in consumption choices, and displays dynamic self-control preferences, as defined by Gul and Pesendorfer [(2004) Econometrica 72, 119–158.]. It shows that endogenous cycles of period 2 and higher, as well as chaotic dynamics exist provided temptation utility is sufficiently important (with respect to standard commitment utility) and sufficiently convex. For parameterizations leading to complex deterministic dynamics, a stochastic version of the model admits rational expectations equilibria displaying excess volatility with respect to the underlying fundamentals.