Bowen's equations for invariance pressure of control systems

We aim to establish Bowen's equations for upper capacity invariance pressure and Pesin-Pitskel invariance pressure of discrete-time control systems. We first introduce a new invariance pressure called induced invariance pressure on partitions that specializes the upper capacity invariance pressure on partitions, and then show that the two types of invariance pressures are related by a Bowen's equation. Besides, to establish Bowen's equation for Pesin-Pitskel invariance pressure on partitions we also introduce a new notion called BS invariance dimension on subsets. Moreover, a variational principle for BS invariance dimension on subsets is established.Comment: 23page

RePAST: A ReRAM-based PIM Accelerator for Second-order Training of DNN

The second-order training methods can converge much faster than first-order optimizers in DNN training. This is because the second-order training utilizes the inversion of the second-order information (SOI) matrix to find a more accurate descent direction and step size. However, the huge SOI matrices bring significant computational and memory overheads in the traditional architectures like GPU and CPU. On the other side, the ReRAM-based process-in-memory (PIM) technology is suitable for the second-order training because of the following three reasons: First, PIM's computation happens in memory, which reduces data movement overheads; Second, ReRAM crossbars can compute SOI's inversion in $O\left(1\right)$ time; Third, if architected properly, ReRAM crossbars can perform matrix inversion and vector-matrix multiplications which are important to the second-order training algorithms. Nevertheless, current ReRAM-based PIM techniques still face a key challenge for accelerating the second-order training. The existing ReRAM-based matrix inversion circuitry can only support 8-bit accuracy matrix inversion and the computational precision is not sufficient for the second-order training that needs at least 16-bit accurate matrix inversion. In this work, we propose a method to achieve high-precision matrix inversion based on a proven 8-bit matrix inversion (INV) circuitry and vector-matrix multiplication (VMM) circuitry. We design \archname{}, a ReRAM-based PIM accelerator architecture for the second-order training. Moreover, we propose a software mapping scheme for \archname{} to further optimize the performance by fusing VMM and INV crossbar. Experiment shows that \archname{} can achieve an average of 115.8$\times$/11.4$\times$ speedup and 41.9$\times$/12.8$\times$energy saving compared to a GPU counterpart and PipeLayer on large-scale DNNs.Comment: 13pages, 13 figure

Improving "color rendering" of LED lighting for the growth of lettuce

Light plays a vital role on the growth and development of plant. On the base of white light with high color rendering to the benefit of human survival and life, we proposed to improve “color rendering” of LED lighting for accelerating the growth of lettuce. Seven spectral LED lights were adopted to irradiate the lettuces under 150 μmol·m−2·s−1 for a 16 hd−1 photoperiod. The leaf area and number profiles, plant biomass, and photosynthetic rate under the as-prepared LED light treatments were investigated. We let the absorption spectrum of fresh leaf be the emission spectrum of ideal light and then evaluate the “color rendering” of as-prepared LED lights by the Pearson product-moment correlation coefficient and CIE chromaticity coordinates. Under the irradiation of red-yellow-blue light with high correlation coefficient of 0.587, the dry weights and leaf growth rate are 2-3 times as high as the sharp red-blue light. The optimized LED light for lettuce growth can be presumed to be limited to the angle (about 75°) between the vectors passed through the ideal light in the CIE chromaticity coordinates. These findings open up a new idea to assess and find the optimized LED light for plant growth

DHAV-1 2A1 Peptide – A Newly Discovered Co-expression Tool That Mediates the Ribosomal “Skipping” Function

Duck hepatitis A virus 1 (DHAV-1) belongs to the genus Avihepatovirus in the family Picornaviridae. Little research has been carried out on the non-structural proteins of this virus. This study reports that 2A1 protein, the first non-structural protein on the DHAV-1 genome, has a ribosomal “skipping” function mediated by a “-GxExNPGP-” motif. In addition, we prove that when the sequence is extended 10aa to VP1 from the N-terminal of 2A1, the ribosome “skips” completely. However, as the N-terminus of 2A is shortened, the efficiency of ribosomal “skipping” reduces. When 2A1 is shortened to 10aa, it does not function. In addition, we demonstrate that N18, P19 G20, and P21 have vital roles in this function. We find that the expression of upstream and downstream proteins linked by 2A1 is different, and the expression of the upstream protein is much greater than that of the downstream protein. In addition, we demonstrate that it is the nature of 2A1 that is responsible for the expression imbalance. We also shows that the protein “cleavage” is not due to RNA “cleavage” or RNA transcription abnormalities, and the expressed protein level is independent of RNA transcriptional level. This study provides a systematic analysis of the activity of the DHAV-1 2A1 sequence and, therefore, adds to the “tool-box” that can be deployed for the co-expression applications. It provides a reference for how to apply 2A1 as a co-expression tool

PSR J1926-0652: A Pulsar with Interesting Emission Properties Discovered at FAST

We describe PSR J1926-0652, a pulsar recently discovered with the Five-hundred-meter Aperture Spherical radio Telescope (FAST). Using sensitive single-pulse detections from FAST and long-term timing observations from the Parkes 64-m radio telescope, we probed phenomena on both long and short time scales. The FAST observations covered a wide frequency range from 270 to 800 MHz, enabling individual pulses to be studied in detail. The pulsar exhibits at least four profile components, short-term nulling lasting from 4 to 450 pulses, complex subpulse drifting behaviours and intermittency on scales of tens of minutes. While the average band spacing P3 is relatively constant across different bursts and components, significant variations in the separation of adjacent bands are seen, especially near the beginning and end of a burst. Band shapes and slopes are quite variable, especially for the trailing components and for the shorter bursts. We show that for each burst the last detectable pulse prior to emission ceasing has different properties compared to other pulses. These complexities pose challenges for the classic carousel-type models.Comment: 13pages with 12 figure

Roadmap for Sustainable Mixed Ionic‐Electronic Conducting Membranes

Mixed ionic‐electronic conducting (MIEC) membranes have gained growing interest recently for various promising environmental and energy applications, such as H₂ and O₂ production, CO₂ reduction, O₂ and H₂ separation, CO₂ separation, membrane reactors for production of chemicals, cathode development for solid oxide fuel cells, solar‐driven evaporation and energy‐saving regeneration as well as electrolyzer cells for power‐to‐X technologies. The purpose of this roadmap, written by international specialists in their fields, is to present a snapshot of the state‐of‐the‐art, and provide opinions on the future challenges and opportunities in this complex multidisciplinary research field. As the fundamentals of using MIEC membranes for various applications become increasingly challenging tasks, particularly in view of the growing interdisciplinary nature of this field, a better understanding of the underlying physical and chemical processes is also crucial to enable the career advancement of the next generation of researchers. As an integrated and combined article, it is hoped that this roadmap, covering all these aspects, will be informative to support further progress in academics as well as in the industry‐oriented research toward commercialization of MIEC membranes for different applications

Metric mean dimension of flows

The present paper aims to investigate the metric mean dimension theory of continuous flows. We introduce the notion of metric mean dimension for continuous flows to characterize the complexity of flows with infinite topological entropy. For continuous flows, we establish variational principles for metric mean dimension in terms of local $\epsilon$-entropy function and Brin-Katok $\epsilon$-entropy; For a class of special flow, called uniformly Lipschitz flow, we establish variational principles for metric mean dimension in terms of Kolmogorov-Sinai $\epsilon$-entropy, Brin-Katok's $\epsilon$-entropy and Katok's $\epsilon$-entropy.Comment: 17 page

Bowen's equations for upper metric mean dimension with potential

Firstly, we introduce a new notion called induced upper metric mean dimension with potential, which naturally generalizes the definition of upper metric mean dimension with potential given by Tsukamoto to more general cases, then we establish variational principles for it in terms of upper and lower rate distortion dimensions and show there exists a Bowen's equation between induced upper metric mean dimension with potential and upper metric mean dimension with potential. Secondly, we continue to introduce two new notions, called BS metric mean dimension and Packing BS metric mean dimension on arbitrary subsets, to establish Bowen's equations for Bowen upper metric mean dimension and Packing upper metric mean dimension with potential on subsets. Besides, we also obtain two variational principles for BS metric mean dimension and Packing BS metric mean dimension on subsets. Finally, the special interest about the Bowen upper metric mean dimension of the set of generic points of ergodic measures are also involved.Comment: many typos and mistakes are correcte

On integral formulas of metric mean dimension for random dynamical systems

The present paper contributes to develop metric mean dimension theory of continuous bundle random dynamical systems, which is driven by [\emph{Adv. Math.} \textbf{361} (2020), 106935, 53 pp.] Tsukamoto's problem: For Brody curves of complex dynamical systems, why is the mean dimension connected to the certain integral? To demonstrate the deeper ergodic theoretic phenomena hidden behind this integral, inspired by the Walter's idea of topological pressure determining measure-theoretical entropy in topological dynamical systems we first introduce the concepts of metric mean dimension with potential and measure-theoretical metric mean dimension of probability measures. Secondly, some tools including outer measure theory, geometric version of Hahn-Banach theorem and Stone vector lattice, are introduced. Finally, with the help of these tools we establish an integral formula for upper metric mean dimension by using functional analysis method and Von Neumann's ergodic theorem. Furthermore, an abstract integral formula for a class of pressure function is established and some applications are also exhibited in both random systems and deterministic systems.Comment: 33 pages, the compactness of $\Omega$ is remove