Existence of φ\varphi-attractor and estimate of their attractive velocity for infinite-dimensional dynamical systems

This paper is devoted to the quantitative study of the attractive velocity of generalized attractors for infinite-dimensional dynamical systems. We introduce the notion of~$\varphi$-attractor whose attractive speed is characterized by a general non-negative decay function~$\varphi$, and prove that~$\varphi$-decay with respect to noncompactness measure is a sufficient condition for a dissipitive system to have a~$\varphi$-attractor. Furthermore, several criteria for~$\varphi$-decay with respect to noncompactness measure are provided. Finally, as an application, we establish the existence of a generalized exponential attractor and the specific estimate of its attractive velocity for a semilinear wave equation with a critical nonlinearity.Comment: arXiv admin note: substantial text overlap with arXiv:2108.0741

On the spectrum of operators concerned with the reduced singular Cauchy integral

We investigate spectrums of the reduced singular Cauchy operator and its real and imaginary components

Defect-related luminescent nanostructured hydroxyapatite promotes mineralization through both intracellular and extracellular pathways

Hydroxyapatite (HAP) is a widely used biomaterial for bone tissue substitution due to its chemical similarity with the natural bone. Defect-related luminescent HAP materials have the same chemical composition as normal HAP and excellent biocompatibility. However, only few works have focused on the defect-related luminescent HAP materials on bone regeneration. In this work, we systematically investigated the bone regeneration pathway induced by nanostructured particles using defect-related luminescent hydroxyapatite (S2) materials. We monitored the subcellular distribution and location of S2 during osteoblast differentiation with the property of defect-related luminescence. Nano-scale S2 could be internalized by osteoblasts (OBs) via caveolae-mediated endocytosis and macropinocytosis. S2 incorporated into the lysosomes dissolved and released calcium ions for the formation of mineralized nodules. Extracellular S2 also promoted bone regeneration as a nucleation site. Taken together, the physical properties of hydroxyapatite control the bone regeneration pathway in osteoblasts

Information Bottleneck-Inspired Type Based Multiple Access for Remote Estimation in IoT Systems

Type-based multiple access (TBMA) is a semantics-aware multiple access protocol for remote inference. In TBMA, codewords are reused across transmitting sensors, with each codeword being assigned to a different observation value. Existing TBMA protocols are based on fixed shared codebooks and on conventional maximum-likelihood or Bayesian decoders, which require knowledge of the distributions of observations and channels. In this letter, we propose a novel design principle for TBMA based on the information bottleneck (IB). In the proposed IB-TBMA protocol, the shared codebook is jointly optimized with a decoder based on artificial neural networks (ANNs), so as to adapt to source, observations, and channel statistics based on data only. We also introduce the Compressed IB-TBMA (CIB-TBMA) protocol, which improves IB-TBMA by enabling a reduction in the number of codewords via an IB-inspired clustering phase. Numerical results demonstrate the importance of a joint design of codebook and neural decoder, and validate the benefits of codebook compression.Comment: 5 pages, 3 figures, accepted by IEEE Signal Processing Letters (SPL