arXiv subjects

Chenxi Wu

Publications and source records attributed to Chenxi Wu.

At least 37 records · Page 2Linked to original sources

arXiv2025

Towards spiking analog hardware implementation of a trajectory interpolation mechanism for smooth closed-loop control of a spiking robot arm

Neuromorphic engineering aims to incorporate the computational principles found in animal brains, into modern technological systems. Following this approach, in this work we propose a closed-loop neuromorphic control system for an event-based robotic arm. The proposed system consists of a shifted Winner-Take-All spiking network for interpolating a reference trajectory and a spiking comparator network responsible for controlling the flow continuity of the trajectory, which is fed back to the actual position of the robot. The comparator model is based on a differential position comparison neural network, which governs the execution of the next trajectory points to close the control loop between both components of the system. To evaluate the system, we implemented and deployed the model on a mixed-signal analog-digital neuromorphic platform, the DYNAP-SE2, to facilitate integration and communication with the ED-Scorbot robotic arm platform. Experimental results on one joint of the robot validate the use of this architecture and pave the way for future neuro-inspired control of the entire robot.

cs.NE↗

arXiv2024

Basmajian's identity over non-Archimedean local fields

Let $Σ$ be a connected compact oriented surface with boundary and negative Euler characteristic. Let $k$ be a non-Archimedean local field. In this paper, we prove Basmajian's identity for projective Anosov representations $ρ\colon π_1Σ\to {\rm PSL}(d,k), d\ge 2$. Our series identity exhibits a drastic difference from all the Basmajian-type identities over the Archimedean fields $\mathbb{R}$ and $\mathbb{C}$. In particular, the series is a signed finite sum. When $d=2$, we give a geometric proof of the identity using Berkovich hyperbolic geometry.

math.GT↗

arXiv2024

Master Teapots and Entropy Algorithms for the Mandelbrot Set

We construct an analogue of W. Thurston's "Master teapot" for each principal vein in the Mandelbrot set, and generalize geometric properties known for the corresponding object for real maps. In particular, we show that eigenvalues outside the unit circle move continuously, while we show "persistence" for roots inside the unit circle. As an application, this shows that the outside part of the corresponding "Thurston set" is path connected. In order to do this, we define a version of kneading theory for principal veins, and we prove the equivalence of several algorithms that compute the core entropy.

math.DS↗

arXiv2024

On the asymptotic translation lengths on the sphere complexes and the generalized fibered cone

In this paper, we study the asymptotic translation lengths on the sphere complexes of monodromies of a manifold fibered over the circle. Given a compact mapping torus, we define a cone in the first cohomology which we call the generalized fibered cone, and show that every primitive integral element gives a fibration over the circle. Moreover, we prove that the generalized fibered cone is a rational slice of Fried's cone, which is defined as the dual of homological directions, an analogue of Thurston's fibered cone. As a consequence of our description of the generalized fibered cone, we provide each proper subcone of the generalized fibered cone with a uniform upper bound for asymptotic translation lengths of monodromies on sphere complexes of fibers in the proper subcone. Our upper bound is purely in terms of the dimension of the proper subcone. We also deduce similar estimates for asymptotic translation lengths of some mapping classes on finite graphs constructed in the works of Dowdall--Kapovich--Leininger, measured on associated free-splitting complexes and free-factor complexes. Moreover, as an application of our result, we prove that the asymptote for the minimal asymptotic translation length of the genus $g$ handlebody group on the disk complex is $1/g^2$, the same as the one on the curve complex.

math.GT↗

arXiv2024

From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning

Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and partial differential equations using sparse measurements. Over the past few years, significant advancements have been made in the training and optimization of PINNs, covering aspects such as network architectures, adaptive refinement, domain decomposition, and the use of adaptive weights and activation functions. A notable recent development is the Physics-Informed Kolmogorov-Arnold Networks (PIKANS), which leverage a representation model originally proposed by Kolmogorov in 1957, offering a promising alternative to traditional PINNs. In this review, we provide a comprehensive overview of the latest advancements in PINNs, focusing on improvements in network design, feature expansion, optimization techniques, uncertainty quantification, and theoretical insights. We also survey key applications across a range of fields, including biomedicine, fluid and solid mechanics, geophysics, dynamical systems, heat transfer, chemical engineering, and beyond. Finally, we review computational frameworks and software tools developed by both academia and industry to support PINN research and applications.

cs.LG↗

arXiv2024

Reconstruction of Anosov flows from infinity

Every pseudo-Anosov flow $ϕ$ in a closed $3$-manifold $M$ gives rise to an action of $π_1(M)$ on a circle $S^{1}_{\infty}(ϕ)$ from infinity \cite{Fen12}, with a pair of invariant \emph{almost} laminations. From certain actions on $S^{1}$ with invariant almost laminations, we reconstruct flows and manifolds realizing these actions, including all orientable transitive pseudo-Anosov flows in closed $3$-manifolds. Our construction provides a geometry model for such flows and manifolds induced from $\mathcal{D} \times \mathcal{D}$, where $\mathcal{D}$ is the Poincaré disk with $\partial \mathcal{D}$ identified with $S^{1}_{\infty}(ϕ)$. In addition, our result applies to Cannon conjecture under the assumption that certain group-equivariant sphere-filling Peano curve exists, which offers a description of orientable quasigeodesic pseudo-Anosov flows in hyperbolic $3$-manifolds in terms of group actions on $\partial \mathbb{H}^{3} \times \partial \mathbb{H}^{3} \times \partial \mathbb{H}^{3}$.

math.GT↗

arXiv2024

Gradient-descent hardware-aware training and deployment for mixed-signal Neuromorphic processors

Mixed-signal neuromorphic processors provide extremely low-power operation for edge inference workloads, taking advantage of sparse asynchronous computation within Spiking Neural Networks (SNNs). However, deploying robust applications to these devices is complicated by limited controllability over analog hardware parameters, as well as unintended parameter and dynamical variations of analog circuits due to fabrication non-idealities. Here we demonstrate a novel methodology for ofDine training and deployment of spiking neural networks (SNNs) to the mixed-signal neuromorphic processor DYNAP-SE2. The methodology utilizes gradient-based training using a differentiable simulation of the mixed-signal device, coupled with an unsupervised weight quantization method to optimize the network's parameters. Parameter noise injection during training provides robustness to the effects of quantization and device mismatch, making the method a promising candidate for real-world applications under hardware constraints and non-idealities. This work extends Rockpool, an open-source deep-learning library for SNNs, with support for accurate simulation of mixed-signal SNN dynamics. Our approach simplifies the development and deployment process for the neuromorphic community, making mixed-signal neuromorphic processors more accessible to researchers and developers.

cs.ET↗

arXiv2023

GPT vs Human for Scientific Reviews: A Dual Source Review on Applications of ChatGPT in Science

The new polymath Large Language Models (LLMs) can speed-up greatly scientific reviews, possibly using more unbiased quantitative metrics, facilitating cross-disciplinary connections, and identifying emerging trends and research gaps by analyzing large volumes of data. However, at the present time, they lack the required deep understanding of complex methodologies, they have difficulty in evaluating innovative claims, and they are unable to assess ethical issues and conflicts of interest. Herein, we consider 13 GPT-related papers across different scientific domains, reviewed by a human reviewer and SciSpace, a large language model, with the reviews evaluated by three distinct types of evaluators, namely GPT-3.5, a crowd panel, and GPT-4. We found that 50% of SciSpace's responses to objective questions align with those of a human reviewer, with GPT-4 (informed evaluator) often rating the human reviewer higher in accuracy, and SciSpace higher in structure, clarity, and completeness. In subjective questions, the uninformed evaluators (GPT-3.5 and crowd panel) showed varying preferences between SciSpace and human responses, with the crowd panel showing a preference for the human responses. However, GPT-4 rated them equally in accuracy and structure but favored SciSpace for completeness.

cs.CL↗

arXiv2023

DYNAP-SE2: a scalable multi-core dynamic neuromorphic asynchronous spiking neural network processor

With the remarkable progress that technology has made, the need for processing data near the sensors at the edge has increased dramatically. The electronic systems used in these applications must process data continuously, in real-time, and extract relevant information using the smallest possible energy budgets. A promising approach for implementing always-on processing of sensory signals that supports on-demand, sparse, and edge-computing is to take inspiration from biological nervous system. Following this approach, we present a brain-inspired platform for prototyping real-time event-based Spiking Neural Networks (SNNs). The system proposed supports the direct emulation of dynamic and realistic neural processing phenomena such as short-term plasticity, NMDA gating, AMPA diffusion, homeostasis, spike frequency adaptation, conductance-based dendritic compartments and spike transmission delays. The analog circuits that implement such primitives are paired with a low latency asynchronous digital circuits for routing and mapping events. This asynchronous infrastructure enables the definition of different network architectures, and provides direct event-based interfaces to convert and encode data from event-based and continuous-signal sensors. Here we describe the overall system architecture, we characterize the mixed signal analog-digital circuits that emulate neural dynamics, demonstrate their features with experimental measurements, and present a low- and high-level software ecosystem that can be used for configuring the system. The flexibility to emulate different biologically plausible neural networks, and the chip's ability to monitor both population and single neuron signals in real-time, allow to develop and validate complex models of neural processing for both basic research and edge-computing applications.

cs.NE↗

arXiv2023

Minimal asymptotic translation lengths on curve complexes and homology of mapping tori

Let $S_g$ be a closed orientable surface of genus $g > 1$. Consider the minimal asymptotic translation length $L_{\mathcal{T}}(k, g)$ on the Teichmüller space of $S_g$, among pseudo-Anosov mapping classes of $S_g$ acting trivially on a $k$-dimensional subspace of $H_1(S_g)$, $0 \le k \le 2g$. The asymptotics of $L_{\mathcal{T}}(k, g)$ for extreme cases $k = 0, 2g$ have been shown by several authors. Jordan Ellenberg asked whether there is a lower bound for $L_{\mathcal{T}}(k, g)$ interpolating the known results on $L_{\mathcal{T}}(0, g)$ and $L_{\mathcal{T}}(2g, g)$, which was affirmatively answered by Agol, Leininger, and Margalit. In this paper, we study an analogue of Ellenberg's question, replacing Teichmüller spaces with curve complexes. We provide lower and upper bound on the minimal asymptotic translation length $L_{\mathcal{C}}(k, g)$ on the curve complex, whose lower bound interpolates the known results on $L_{\mathcal{C}}(0, g)$ and $L_{\mathcal{C}}(2g, g)$. Finally, for each $g$, we construct a non-Torelli pseudo-Anosov $f_g \in \operatorname{Mod}(S_g)$ which does not normally generates $\operatorname{Mod}(S_g)$ and so that the asymptotic translation length of $f_g$ on curve complexes decays more quickly than a constant multiple of $1/g$ as $g \to \infty$. From this, we provide a restriction on how small the asymptotic translation lengths on curve complexes should be if the similar phenomenon as in the work of Lanier and Margalit on Teichmüller spaces holds for curve complexes.

math.GT↗

arXiv2023

Reducible normal generators for mapping class groups are abundant

In this article, we study the normal generation of the mapping class group. We first show that a mapping class is a normal generator if its restriction on the invariant subsurface normally generates the (pure) mapping class group of the subsurface. As an application, we provided a criterion for reducible mapping classes to normally generate the mapping class groups in terms of its asymptotic translation lengths on Teichmüller spaces. This is an analogue to the work of Lanier-Margalit dealing with pseudo-Anosov normal generators.

math.GT↗

arXiv2023

Artificial to Spiking Neural Networks Conversion for Scientific Machine Learning

We introduce a method to convert Physics-Informed Neural Networks (PINNs), commonly used in scientific machine learning, to Spiking Neural Networks (SNNs), which are expected to have higher energy efficiency compared to traditional Artificial Neural Networks (ANNs). We first extend the calibration technique of SNNs to arbitrary activation functions beyond ReLU, making it more versatile, and we prove a theorem that ensures the effectiveness of the calibration. We successfully convert PINNs to SNNs, enabling computational efficiency for diverse regression tasks in solving multiple differential equations, including the unsteady Navier-Stokes equations. We demonstrate great gains in terms of overall efficiency, including Separable PINNs (SPINNs), which accelerate the training process. Overall, this is the first work of this kind and the proposed method achieves relatively good accuracy with low spike rates.

cs.NE↗

arXiv2023

Counting two-forests and random cut size via potential theory

We prove a lower bound on the number of spanning two-forests in a graph, in terms of the number of vertices, edges, and spanning trees. This implies an upper bound on the average cut size of a random two-forest. The main tool is an identity relating the number of spanning trees and two-forests to pairwise effective resistances in a graph. Along the way, we make connections to potential theoretic invariants on metric graphs.

math.CO↗

arXiv2022

A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks

Physics-informed neural networks (PINNs) have shown to be an effective tool for solving forward and inverse problems of partial differential equations (PDEs). PINNs embed the PDEs into the loss of the neural network, and this PDE loss is evaluated at a set of scattered residual points. The distribution of these points are highly important to the performance of PINNs. However, in the existing studies on PINNs, only a few simple residual point sampling methods have mainly been used. Here, we present a comprehensive study of two categories of sampling: non-adaptive uniform sampling and adaptive nonuniform sampling. We consider six uniform sampling, including (1) equispaced uniform grid, (2) uniformly random sampling, (3) Latin hypercube sampling, (4) Halton sequence, (5) Hammersley sequence, and (6) Sobol sequence. We also consider a resampling strategy for uniform sampling. To improve the sampling efficiency and the accuracy of PINNs, we propose two new residual-based adaptive sampling methods: residual-based adaptive distribution (RAD) and residual-based adaptive refinement with distribution (RAR-D), which dynamically improve the distribution of residual points based on the PDE residuals during training. Hence, we have considered a total of 10 different sampling methods, including six non-adaptive uniform sampling, uniform sampling with resampling, two proposed adaptive sampling, and an existing adaptive sampling. We extensively tested the performance of these sampling methods for four forward problems and two inverse problems in many setups. Our numerical results presented in this study are summarized from more than 6000 simulations of PINNs. We show that the proposed adaptive sampling methods of RAD and RAR-D significantly improve the accuracy of PINNs with fewer residual points. The results obtained in this study can also be used as a practical guideline in choosing sampling methods.

physics.comp-ph↗

arXiv2022

Towards hardware Implementation of WTA for CPG-based control of a Spiking Robotic Arm

Biological nervous systems typically perform the control of numerous degrees of freedom for example in animal limbs. Neuromorphic engineers study these systems by emulating them in hardware for a deeper understanding and its possible application to solve complex problems in engineering and robotics. Central-Pattern-Generators (CPGs) are part of neuro-controllers, typically used at their last steps to produce rhythmic patterns for limbs movement. Different patterns and gaits typically compete through winner-take-all (WTA) circuits to produce the right movements. In this work we present a WTA circuit implemented in a Spiking-Neural-Network (SNN) processor to produce such patterns for controlling a robotic arm in real-time. The robot uses spike-based proportional-integrativederivative (SPID) controllers to keep a commanded joint position from the winner population of neurons of the WTA circuit. Experiments demonstrate the feasibility of robotic control with spiking circuits following brain-inspiration.

cs.RO↗

arXiv2021

Foliations from left orders

We describe a construction which takes as an input a left order of the fundamental group of a manifold, and outputs a (singular) foliation of this manifold which is analogous to a taut foliation. We investigate this construction in detail in dimension $2$, and exhibit connections to various problems in dimension $3$.

math.GT↗

arXiv2021

Identification of mental fatigue in language comprehension tasks based on EEG and deep learning

Mental fatigue increases the risk of operator error in language comprehension tasks. In order to prevent operator performance degradation, we used EEG signals to assess the mental fatigue of operators in human-computer systems. This study presents an experimental design for fatigue detection in language comprehension tasks. We obtained EEG signals from a 14-channel wireless EEG detector in 15 healthy participants. Each participant was given a cognitive test of a language comprehension task, in the form of multiple choice questions, in which pronoun references were selected between nominal and surrogate sentences. In this paper, the 2400 EEG fragments collected are divided into three data sets according to different utilization rates, namely 1200s data set with 50% utilization rate, 1500s data set with 62.5% utilization rate, and 1800s data set with 75% utilization rate. In the aspect of feature extraction, different EEG features were extracted, including time domain features, frequency domain features and entropy features, and the effects of different features and feature combinations on classification accuracy were explored. In terms of classification, we introduced the Convolutional Neural Network (CNN) method as the preferred method, It was compared with Least Squares Support Vector Machines(LSSVM),Support Vector Machines(SVM),Logistic Regression (LR), Random Forest(RF), Naive Bayes (NB), K-Nearest Neighbor (KNN) and Decision Tree(DT).According to the results, the classification accuracy of convolutional neural network (CNN) is higher than that of other classification methods. The classification results show that the classification accuracy of 1200S dataset is higher than the other two datasets. The combination of Frequency and entropy feature and CNN has the highest classification accuracy, which is 85.34%.

cs.AI↗

arXiv2021

Robust neuromorphic coupled oscillators for adaptive pacemakers

Neural coupled oscillators are a useful building block in numerous models and applications. They were analyzed extensively in theoretical studies and more recently, in biologically realistic simulations of spiking neural networks. The advent of mixed-signal analog/digital neuromorphic electronic circuits provides new means for implementing neural coupled oscillators on compact low-power spiking neural network hardware platforms. However, their implementation on this noisy, low-precision and inhomogeneous computing substrate raises new challenges with regards to stability and controllability. In this work, we present a robust, spiking neural network model of neural coupled oscillators and validate it with an implementation on a mixed-signal neuromorphic processor. We demonstrate its robustness showing how to reliably control and modulate the oscillator's frequency and phase shift, despite the variability of the silicon synapse and neuron properties. We show how this ultra-low power neural processing system can be used to build an adaptive cardiac pacemaker modulating the heart rate with respect to the respiration phases and compare it with surface ECG and respiratory signal recordings of dogs at rest. The implementation of our model in neuromorphic electronic hardware shows its robustness on a highly variable substrate and extends the toolbox for applications requiring rhythmic outputs such as pacemakers.

cs.ET↗