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1. From zero to positive entropy

   https://doi.org/https://doi.org/10.1090/noti2478  

   Sylvain Crovisier Enrique Pujals (June 2022, Notices of the American Mathematical Society)

   Daniela De Silva (Ed.)

   In the sciences in general, the phrase “route to chaos” has come to refer to a metaphor when some physical, biological, economic, or social system transitions from one exhibiting order to one displaying randomness (or chaos). Sometimes the goal is to understand which universal mechanisms explain that transition, and how one can describe systems that operate in a region between order and complete chaos. In other words, the goal is to understand the mathematical processes by which a system evolves from one whose recurrent set is finite towards another one exhibiting chaotic behavior as parameters governing the behavior of the system are varied. This has only been understood for one-dimensional dynamics. The present note exposes new approaches that allow one to move away from those limitations. A tentative global framework toward describing a large class of two-dimensional dynamics, inspired partially by the developments in the one-dimensional theory of interval maps is discussed. More precisely, we present a class of intermediate smooth dynamics between one and higher dimensions. In this setting, it could be possible to develop a similar one-dimensional type approach and in particular to understand the transition from zero entropy to positive entropy. 

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2. Text2Video-Zero: Text-to-Image Diffusion Models are Zero-Shot Video Generators

   https://doi.org/10.1109/ICCV51070.2023.01462  

   Khachatryan, Levon; Movsisyan, Andranik; Tadevosyan, Vahram; Henschel, Roberto; Wang, Zhangyang; Navasardyan, Shant; Shi, Humphrey (October 2023, 2023 IEEE/CVF International Conference on Computer Vision (ICCV))
3. Scaling Zero-Knowledge to Verifiable Databases

   https://doi.org/10.1145/3595647.3595648  

   Derei, Tal; Aulenbach, Benjamin; Carolino, Victor; Geren, Caleb; Kaufman, Michael; Klein, Jonathan; Islam_Shanto, Rishad; Korth, Henry F (June 2023, ACM)

   Zero-Knowledge proofs are a cryptographic technique to reveal knowledge of information without revealing the information it- self, thus enabling systems optimally to mix privacy and trans- parency, and, where needed, regulatability. Application domains include health and other enterprise data, financial systems such as central-bank digital currencies, and performance enhancement in blockchain systems. The challenge of zero-knowledge proofs is that, although they are computationally easy to verify, they are computationally hard to produce. This paper examines the scala- bility limits of leading zero-knowledge algorithms and addresses the use of parallel architectures to meet performance demands of applications. 

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4. Linear Optimal Regulation to Zero Dynamics

   https://doi.org/10.1109/TAC.2024.3389736  

   Ludeke, Taylor; Iwasaki, Tetsuya (October 2024, IEEE Transactions on Automatic Control)

   A general problem encompassing output regulation and pattern generation can be formulated as the design of controllers to achieve convergence to a persistent trajectory within the zero dynamics on which an output vanishes. We develop an optimal control theory for such design by adding the requirement to minimize the H2 norm of a closed-loop transfer function. Within the framework of eigenstructure assignment, the optimal control is proven identical to the standard H2 control in form. However, the solution to the Riccati equation for the linear quadratic regulator is not stabilizing. Instead it partially stabilizes the closed-loop dynamics excluding the zero dynamics. The optimal control architecture is shown to have the feedback of the deviation from the subspace of the zero dynamics and the feedforward of the control input to remain in the subspace. 

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5. Pathways to net-zero emissions from aviation

   https://doi.org/10.1038/s41893-022-01046-9  

   Bergero, Candelaria; Gosnell, Greer; Gielen, Dolf; Kang, Seungwoo; Bazilian, Morgan; Davis, Steven J. (April 2023, Nature Sustainability)