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   https://doi.org/10.3934/dcds.2023131  

   Norton, Trevor; Wayne, C. Eugene (October 2023, Discrete and Continuous Dynamical Systems)

   It is well known that the Korteweg-deVries(KdV) equation and its generalizations serve as modulation equations for traveling wave solutions to generic Fermi-Pasta-Ulam-Tsingou (FPUT) lattices. Explicit approximation estimates and other such results have been proved in this case. However, situ- ations in which the defocusing modified KdV (mKdV) equation is expected to be the modulation equation have been much less studied. As seen in numerical experiments, the kink solution of the mKdV seems essential in understanding the -FPUT recurrence. In this paper, we derive explicit approximation re- sults for solutions of the FPUT using the mKdV as a modulation equation. In contrast to previous work, our estimates allow for solutions to be non-localized as to allow approximate kink solutions. These results allow us to conclude meta-stability results of kink-like solutions of the FPUT. 

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2. Smart Tattoo Patch for Long Long-term Monitoring and Drug Delivery

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3. Long-term priors influence visual perception through recruitment of long-range feedback

   https://doi.org/10.1038/s41467-021-26544-w  

   Hardstone, Richard; Zhu, Michael; Flinker, Adeen; Melloni, Lucia; Devore, Sasha; Friedman, Daniel; Dugan, Patricia; Doyle, Werner K.; Devinsky, Orrin; He, Biyu J. (November 2021, Nature Communications)

   Abstract Perception results from the interplay of sensory input and prior knowledge. Despite behavioral evidence that long-term priors powerfully shape perception, the neural mechanisms underlying these interactions remain poorly understood. We obtained direct cortical recordings in neurosurgical patients as they viewed ambiguous images that elicit constant perceptual switching. We observe top-down influences from the temporal to occipital cortex, during the preferred percept that is congruent with the long-term prior. By contrast, stronger feedforward drive is observed during the non-preferred percept, consistent with a prediction error signal. A computational model based on hierarchical predictive coding and attractor networks reproduces all key experimental findings. These results suggest a pattern of large-scale information flow change underlying long-term priors’ influence on perception and provide constraints on theories about long-term priors’ influence on perception. 

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4. Long Memory via Networking

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   Schennach, Susanne M. (January 2018, Econometrica)
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