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Fifty years have passed since David Marr, Masao Ito, and James Albus proposed seminal models of cerebellar functions. These models share the essential concept that parallel-fiber-Purkinje-cell synapses undergo plastic changes, guided by climbing-fiber activities during sensorimotor learning. However, they differ in several important respects, including holistic versus complementary roles of the cerebellum, pattern recognition versus control as computational objectives, potentiation versus depression of synaptic plasticity, teaching signals versus error signals transmitted by climbing-fibers, sparse expansion coding by granule cells, and cerebellar internal models. In this review, we evaluate the different features of the three models based on recent computational and experimental studies. While acknowledging that the three models have greatly advanced our understanding of cerebellar control mechanisms in eye movements and classical conditioning, we propose a new direction for computational frameworks of the cerebellum. That is, hierarchical reinforcement learning with multiple internal models.
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We present a cerebellar architecture with two main characteristics. The first one is that complex spikes respond to increases in sensory errors. The second one is that cerebellar modules associate particular contexts where errors have increased in the past with corrective commands that stop the increase in error. We analyze our architecture formally and computationally for the case of reaching in a 3D environment. In the case of motor control, we show that there are synergies of this architecture with the Equilibrium-Point hypothesis, leading to novel ways to solve the motor error problem. In particular, the presence of desired equilibrium lengths for muscles provides a way to know when the error is increasing, and which corrections to apply. In the context of Threshold Control Theory and Perceptual Control Theory we show how to extend our model so it implements anticipative corrections in cascade control systems that span from muscle contractions to cognitive operations.
I revisit two theories of cell differentiation in multicellular organisms published a half-century ago, Stuart Kauffmans global gene regulatory dynamics (GGRD) model and Roy Brittens and Eric Davidsons modular gene regulatory network (MGRN) model, in light of newer knowledge of mechanisms of gene regulation in the metazoans (animals). The two models continue to inform hypotheses and computational studies of differentiation of lineage-adjacent cell types. However, their shared notion (based on bacterial regulatory systems) of gene switches and networks built from them, have constrained progress in understanding the dynamics and evolution of differentiation. Recent work has described unique write-read-rewrite chromatin-based expression encoding in eukaryotes, as well metazoan-specific processes of gene activation and silencing in condensed-phase, enhancer-recruiting regulatory hubs, employing disordered proteins, including transcription factors, with context-dependent identities. These findings suggest an evolutionary scenario in which the origination of differentiation in animals, rather than depending exclusively on adaptive natural selection, emerged as a consequence of a type of multicellularity in which the novel metazoan gene regulatory apparatus was readily mobilized to amplify and exaggerate inherent cell functions of unicellular ancestors. The plausibility of this hypothesis is illustrated by the evolution of the developmental role of Grainyhead-like in the formation of epithelium.
The paper discusses relationships between aesthetics theory and mathematical models of mind. Mathematical theory describes abilities for concepts, emotions, instincts, imagination, adaptation, learning, cognition, language, approximate hierarchy of the mind and evolution of these abilities. The knowledge instinct is the foundation of higher mental abilities and aesthetic emotions. Aesthetic emotions are present in every act of perception and cognition, and at the top of the mind hierarchy they become emotions of the beautiful. The learning ability is essential to everyday perception and cognition as well as to the historical development of understanding of the meaning of life. I discuss a controversy surrounding this issue. Conclusions based on cognitive and mathematical models confirm that judgments of taste are at once subjective and objective, and I discuss what it means. The paper relates cognitive and mathematical concepts to those of philosophy and aesthetics, from Plato to our days, clarifies cognitive mechanisms and functions of the beautiful, and resolves many difficulties of contemporary aesthetics.
Epidemic models are useful tools in the fight against infectious diseases, as they allow policy makers to test and compare various strategies to limit disease transmission while mitigating collateral damage on the economy. Epidemic models that are more faithful to the microscopic details of disease transmission can offer more reliable projections, which in turn can lead to more reliable control strategies. For example, many epidemic models describe disease progression via a series of artificial stages or compartments (e.g. exposed, activated, infectious, etc.) but an epidemic model that explicitly tracks time since infection (TSI) can provide a more precise description. At present, epidemic models with compartments are more common than TSI models , largely due to higher computational cost and complexity typically associated with TSI models. Here, however, we show that with the right discretization scheme a TSI model is not much more difficult to solve than a comparment model with three or four stages for the infected class. We also provide a new perspective for adding stages to a TSI model in a way that decouples the disease transmission dynamics from the residence time distributions at each stage. These results are also generalized for age-structured TSI models in an appendix. Finally, as proof-of-principle for the efficiency of the proposed numerical methods, we provide calculations for optimal epidemic control by non-pharmaceutical intervention. Many of the tools described in this report are available through the software package pyross
Our understanding of the nature of interstellar grains has evolved considerably over the past half century with the present author and Fred Hoyle being intimately involved at several key stages of progress. The currently fashionable graphite-silicate-organic grain model has all its essential aspects unequivocally traceable to original peer-reviewed publications by the author and/or Fred Hoyle. The prevailing reluctance to accept these clear-cut priorities may be linked to our further work that argued for interstellar grains and organics to have a biological provenance - a position perceived as heretical. The biological model, however, continues to provide a powerful unifying hypothesis for a vast amount of otherwise disconnected and disparate astronomical data.
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