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In this note, we give a motivic characterization of the integral cohomology of dual boundary complexes of smooth quasi-projective complex algebraic varieties. As a corollary, the dual boundary complex of any stably affine space (of positive dimension) is contractible. In a separate paper [Su23], this corollary has been used by the author in his proof of the weak geometric P=W conjecture for very generic $GL_n(\mathbb{C})$-character varieties over any punctured Riemann surfaces., Comment: 8 pages; Following the anonymous referee's suggestion, the original paper arXiv:2307.16657 (v3) has been separated into two: v4 of that paper keeps the main result; this one deals with the motivic part

This article focuses on the trajectory tracking problem of mobile manipulators (MMs). Firstly, we construct a position and orientation model predictive tracking control (POMPTC) scheme for mobile manipulators. The proposed POMPTC scheme can simultaneously minimize the tracking error, joint velocity, and joint acceleration. Moreover, it can achieve synchronous control for the position and orientation of the end-effector. Secondly, a finite-time convergent neural dynamics (FTCND) model is constructed to find the optimal solution of the POMPTC scheme. Then, based on the proposed POMPTC scheme, a non-singular fast terminal sliding model (NFTSM) control method is presented, which considers the disturbances caused by the base motion on the manipulator at the dynamic level. It can achieve finite-time tracking performance and improve the anti-disturbances ability. Finally, simulation and experiments show that the proposed control method has the advantages of strong robustness, fast convergence, and high control accuracy., Comment: This article consists of 13 pages, including the text and the proof process

The weak geometric P=W conjecture of L. Katzarkov, A. Noll, P. Pandit, and C. Simpson asserts that for any smooth Betti moduli space $\mathcal{M}_B$ of complex dimension $d$ over a punctured Riemann surface, the dual boundary complex $\mathbb{D}\partial\mathcal{M}_B$ is homotopy equivalent to a $(d-1)$-dimensional sphere. Here, we consider $\mathcal{M}_B$ as a generic $GL_n(\mathbb{C})$-character variety defined on a Riemann surface of genus $g$, with local monodromies specified by generic semisimple conjugacy classes at $k$ punctures. In this article, we establish the weak geometric P=W conjecture for all \emph{very generic} $\mathcal{M}_B$ in the sense that at least one conjugacy class is regular semisimple. A crucial step is to establish a stronger form of A. Mellit's cell decomposition theorem, i.e. we decompose $\mathcal{M}_B$ (without passing to a vector bundle) into locally closed subvarieties of the form $(\mathbb{C}^{\times})^{d-2b}\times\mathcal{A}$, where $\mathcal{A}$ is stably isomorphic to $\mathbb{C}^b$. A second ingredient involves a motivic characterization of the integral cohomology of dual boundary complexes developed in a subsequent article [Su24]. Following C. Simpson's strategy, the proof is now an inductive computation of the dual boundary complexes from such a cell decomposition., Comment: v4: 39 pages; Following the anonymous referee's suggestion, the previous version of this paper has be separated into two: the current one keeps the main result, and the second one, entitled "Integral cohomology of dual boundary complexes is motivic", deals with the motivic part

Joint radar and communications (JRC) can realize two radio frequency (RF) functions using one set of resources, greatly saving hardware, energy and spectrum for wireless systems needing both functions. Frequency-hopping (FH) MIMO radar is a popular candidate for JRC, as the achieved communication symbol rate can greatly exceed radar pulse repetition frequency. However, practical transceiver imperfections can fail many existing theoretical designs. In this work, we unveil for the first time the non-trivial impact of hardware imperfections on FH-MIMO JRC and analytically model the impact. We also design new waveforms and, accordingly, develop a low-complexity algorithm to jointly estimate the hardware imperfections of unsynchronized receiver. Moreover, employing low-cost software-defined radios and commercial off-the-shelf (COTS) products, we build the first FH-MIMO JRC experiment platform with radar and communications simultaneously validated over the air. Corroborated by simulation and experiment results, the proposed designs achieves high performances for both radar and communications., Comment: 11 pages; 12 figures

The development of artificial intelligence (AI) and robotics are both based on the tenet of "science and technology are people-oriented", and both need to achieve efficient communication with the human brain. Based on multi-disciplinary research in systems neuroscience, computer architecture, and functional organic materials, we proposed the concept of using AI to simulate the operating principles and materials of the brain in hardware to develop brain-inspired intelligence technology, and realized the preparation of neuromorphic computing devices and basic materials. We simulated neurons and neural networks in terms of material and morphology, using a variety of organic polymers as the base materials for neuroelectronic devices, for building neural interfaces as well as organic neural devices and silicon neural computational modules. We assemble organic artificial synapses with simulated neurons from silicon-based Field-Programmable Gate Array (FPGA) into organic artificial neurons, the basic components of neural networks, and later construct biological neural network models based on the interpreted neural circuits. Finally, we also discuss how to further build neuromorphic devices based on these organic artificial neurons, which have both a neural interface friendly to nervous tissue and interact with information from real biological neural networks., Comment: This article need to update the corrected figure and data

The weak geometric P=W conjecture of L. Katzarkov, A. Noll, P. Pandit, and C. Simpson states that, a smooth Betti moduli space of complex dimension $d$ over a punctured Riemann surface has the dual boundary complex homotopy equivalent to a sphere of dimension $d-1$. Via a microlocal geometric perspective, we verify this conjecture for a class of rank $n$ wild character varieties over the two-sphere with one puncture, associated with any Stokes Legendrian link defined by an $n$-strand positive braid., Comment: Revised version: 34 pages, 10 figures; The revised version has undergone significant changes: A more general result, devoid of connected braid closures, has been proven. The proof is now simpler and more natural, utilizing braid varieties in place of augmentation varieties