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arXiv 2025年

作者： Hao, Jiaxiong Huang, Yunqing Yi, Nianyu Yin, Peimeng Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China National Center for Applied Mathematics in Hunan Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education Xiangtan University Hunan Xiangtan411105 China Department of Mathematical Sciences University of Texas at El Paso El PasoTX79968 United States

In this paper, we present a novel enhancement to the conventional hr-adaptive finite element methods for parabolic equations, integrating traditional h-adaptive and r-adaptive methods via neural networks. A major challenge in hr-adaptive finite element methods lies in projecting the previous step’s finite element solution onto the updated mesh. This projection depends on the new mesh and must be recomputed for each adaptive iteration. To address this, we introduce a neural network to construct a mesh-free surrogate of the previous step finite element solution. Since the neural network is mesh-free, it only requires training once per time step, with its parameters initialized using the optimizer from the previous time step. This approach effectively overcomes the interpolation challenges associated with non-nested meshes in computation, making node insertion and movement more convenient and efficient. The new algorithm also emphasizes SIZING and GENERATE, allowing each refinement to roughly double the number of mesh nodes of the previous iteration and then redistribute them to form a new mesh that effectively captures the singularities. It significantly reduces the time required for repeated refinement and achieves the desired accuracy in no more than seven space-adaptive iterations per time step. Numerical experiments confirm the efficiency of the proposed algorithm in capturing dynamic changes of *** Codes 92B20, 65M60, 35K57 © 2025, CC BY.

关键词： Interpolation

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On the Importance of Error Mitigation for Quantum Computation

arXiv

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arXiv 2025年

作者： Aharonov, Dorit Alberton, Ori Arad, Itai Atia, Yosi Bairey, Eyal Brakerski, Zvika Cohen, Itsik Golan, Omri Gurwich, Ilya Kenneth, Oded Leviatan, Eyal Lindner, Netanel H. Melcer, Ron Aharon Meyer, Adiel Schul, Gili Shutman, Maor Qedma Quantum Computing Tel Aviv Israel The Benin School of Computer Science and Engineering Hebrew University Jerusalem Israel Centre for Quantum Technologies National University of Singapore Singapore Faculty of Mathematics and Computer Science Weizmann Institute of Science Israel Department of Physics Technion Haifa Israel

Quantum error mitigation (EM) is a family of hybrid quantum-classical methods for eliminating or reducing the effect of noise and decoherence on quantum algorithms run on quantum hardware, without applying quantum error correction (EC). While EM has many benefits compared to EC, specifically that it requires no (or little) qubit overhead, this benefit comes with a painful price: EM seems to necessitate an overhead in quantum run time which grows as a (mild) exponent [1–4]. Accordingly, recent results show that EM alone cannot enable exponential quantum advantages (QAs), for an average variant of the expectation value estimation problem [5]. These works raised concerns regarding the role of EM in the road map towards QAs. We aim to demystify the discussion, and provide a clear picture of the role of EM in achieving QAs, both in the near and long term. We first propose a clear distinction between finite QA and asymptotic QA, which is crucial to the understanding of the question, and present the notion of circuit volume boost, which we claim is an adequate way to quantify the benefits of EM. Using these notions we can argue straightforwardly that EM is expected to have a significant role in achieving QAs. Specifically, that EM is likely to be the first error reduction method for useful finite QAs, before EC;that the first such QAs are expected to be achieved using EM in the very near future;and that EM is expected to maintain its important role in quantum computation even when EC will be routinely used – for as long as high-quality qubits remain a scarce resource. © 2025, CC BY.

关键词： Qubits

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A Two-Stage Solution to Quantum Process Tomography: Error Analysis and Optimal Design

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IEEE Transactions on Information Theory 2025年第3期71卷 1803-1823页

作者： Xiao, Shuixin Wang, Yuanlong Zhang, Jun Dong, Daoyi Mooney, Gary J. Petersen, Ian R. Yonezawa, Hidehiro University of New South Wales School of Engineering and Technology CanberraACT2600 Australia University of Michigan-Shanghai Jiao Tong University Joint Institute Shanghai Jiao Tong University Shanghai200240 China The Australian National University School of Engineering CanberraACT2601 Australia Chinese Academy of Sciences Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Beijing100190 China The Australian National University CIICADA Laboratory School of Engineering CanberraACT2601 Australia The University of Melbourne School of Physics ParkvilleVIC3010 Australia RIKEN Center for Quantum Computing Saitama351-0198 Japan Centre for Quantum Computation and Communication Technology Australian Research Council CanberraACT2600 Australia

Quantum process tomography is a critical task for characterizing the dynamics of quantum systems and achieving precise quantum control. In this paper, we propose a two-stage solution for both trace-preserving and non-trace-preserving quantum process tomography. Utilizing a tensor structure, our algorithm exhibits a computational complexity of O(MLd2) where d is the dimension of the quantum system and M, L(M≥ d2, L≥ d2) represent the numbers of different input states and measurement operators, respectively. We establish an analytical error upper bound and then design the optimal input states and the optimal measurement operators, which are both based on minimizing the error upper bound and maximizing the robustness characterized by the condition number. Numerical examples and testing on IBM quantum devices are presented to demonstrate the performance and efficiency of our algorithm. © 1963-2012 IEEE.

关键词： Error analysis

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Sensing With Communication Signals: From Information Theory to Signal Processing

arXiv

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arXiv 2025年

作者： Liu, Fan Liu, Ya-Feng Cui, Yuanhao Masouros, Christos Xu, Jie Han, Tony Xiao Buzzi, Stefano Eldar, Yonina C. Jin, Shi National Mobile Communications Research Laboratory School of Information Science and Engineering Southeast University Nanjing210096 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematicsand Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Communication Engineering Beijing University of Posts and Telecommunications Beijing100876 China Department of Electronic and Electrical Engineering University College London LondonWC1E 7JE United Kingdom Guangdong518172 China Huawei Technologies Co. Ltd China Department of Electrical and Information Engineering University of Cassino and Southern Lazio CassinoI-03043 Italy Department of Electronics Information and Bioengineering Politecnico di Milano MilanoI-20133 Italy ParmaI-43124 Italy Faculty of Mathematics and Computer Science Weizmann Institute of Science Rehovot Israel

The Integrated Sensing and Communications (ISAC) paradigm is anticipated to be a cornerstone of the upcoming 6G networks. In order to optimize the use of wireless resources, 6G ISAC systems need to harness the communication data payload signals, which are inherently random, for both sensing and communication (S&C) purposes. This tutorial paper provides a comprehensive technical overview of the fundamental theory and signal processing methodologies for ISAC transmission with random communication signals. We begin by introducing the deterministic-random tradeoff (DRT) between S&C from an information-theoretic perspective, emphasizing the need for specialized signal processing techniques tailored to random ISAC signals. Building on this foundation, we review the core signal models and processing pipelines for communication-centric ISAC systems, and analyze the average squared auto-correlation function (ACF) of random ISAC signals, which serves as a fundamental performance metric for multi-target ranging tasks. Drawing insights from these theoretical results, we outline the design principles for the three key components of communication-centric ISAC systems: modulation schemes, constellation design, and pulse shaping filters. The goal is to either enhance sensing performance without compromising communication efficiency or to establish a scalable tradeoff between the two. We then extend our analysis from a single-antenna ISAC system to its multi-antenna counterpart, discussing recent advancements in multiinput multi-output (MIMO) precoding techniques specifically designed for random ISAC signals. We conclude by highlighting several open challenges and future research directions in the field of sensing with communication signals. Copyright © 2025, The Authors. All rights reserved.

关键词： Signal modulation

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Agentic End-to-End De Novo Protein Design for Tailored Dynamics Using a Language Diffusion Model

arXiv

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arXiv 2025年

作者： Ni, Bo Buehler, Markus J. Massachusetts Institute of Technology 77 Massachusetts Ave. CambridgeMA02139 United States Department of Materials Science and Engineering Carnegie Mellon University 5000 Forbes Avenue PittsburghPA15213 United States Center for Computational Science and Engineering Schwarzman College of Computing Massachusetts Institute of Technology 77 Massachusetts Ave. CambridgeMA02139 United States

Proteins are dynamic molecular machines whose biological functions, spanning enzymatic catalysis, signal transduction, and structural adaptation, are intrinsically linked to their motions. Designing proteins with targeted dynamic properties, however, remains a challenge due to the complex, degenerate relationships between sequence, structure, and molecular motion. Here, we introduce VibeGen, a generative AI framework that enables end-to-end de novo protein design conditioned on normal mode vibrations. VibeGen employs an agentic dual-model architecture, comprising a protein designer that generates sequence candidates based on specified vibrational modes and a protein predictor that evaluates their dynamic accuracy. This approach synergizes diversity, accuracy, and novelty during the design process. Via full-atom molecular simulations as direct validation, we demonstrate that the designed proteins accurately reproduce the prescribed normal mode amplitudes across the backbone while adopting various stable, functionally relevant structures. Notably, generated sequences are de novo, exhibiting no significant similarity to natural proteins, thereby expanding the accessible protein space beyond evolutionary constraints. Our work integrates protein dynamics into generative protein design, and establishes a direct, bidirectional link between sequence and vibrational behavior, unlocking new pathways for engineering biomolecules with tailored dynamical and functional properties. This framework holds broad implications for the rational design of flexible enzymes, dynamic scaffolds, and biomaterials, paving the way toward dynamics-informed AI-driven protein engineering. © 2025, CC BY-NC-ND.

关键词： Signal transduction

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Renormalization group analysis of noisy neural field

arXiv

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arXiv 2025年

作者： Zang, Jie Helson, Pascal Liu, Shenquan Kumar, Arvind Mitra, Dhrubaditya School of Mathematics South China University of Technology Guangdong China Division of Computational Science and Technology School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm Sweden Science for Life Laboratory Sweden Nordita KTH Royal Institute of Technology Stockholm University Hannes Alfvéns väg 12 Stockholm10691 Sweden

Neurons in the brain show great diversity in their individual properties and their connections to other neurons. To develop an understanding of how neuronal diversity contributes to brain dynamics and function at large scales we borrow from the framework of replica methods, that has been successfully applied to a large class of problems with quenched noise in equilibrium statistical mechanics. We analyze two linearized versions of Wilson-Cowan model with random coefficients which are correlated in space. In particular: (A) a model where the properties of the neurons themselves are heterogeneous and (B) where their connectivities are anisotropic. In both of these models, the averaging over the quenched randomness gives rise to additional nonlinearities. These nonlinearities are analyzed within the framework of Wilsonian renormalization group. We find that for Model A, if the spatial correlation of noise decays with distance with an exponent smaller than −2, at large spatial scales the effect of the noise vanishes. By contrast, for model B, the effect of noise in neuronal connectivity vanishes only if the spatial correlations decay with an exponent smaller than −1. Our calculations also suggest that the presence of noise, under certain conditions, can give rise to travelling wave like behavior at large scales, although it remains to be seen whether this result remains valid at higher orders in perturbation theory. Copyright © 2025, The Authors. All rights reserved.

关键词： Neurons

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Air Pollution Monitoring By Integrating Local and Global Information in Self-Adaptive Multiscale Transform Domain

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IEEE Transactions on Multimedia 2025年

作者： Gu, Ke Liu, Yuchen Liu, Hongyan Liu, Bo Qiao, Junfei Lin, Weisi Zhang, Wenjun Beijing University of Technology School of Information Science and Technology Engineering Research Center of Intelligent Perception and Autonomous Control of Ministry of Education Beijing Laboratory of Smart Environmental Protection Beijing Key Laboratory of Computational Intelligence and Intelligent System Beijing Artificial Intelligence Institute Beijing100124 China Massey University School of Mathematical and Computational Sciences New Zealand Nanyang Technological University College of Computing and Data Science Singapore Shanghai Jiao Tong University Institute of Image Communication and Information Processing Shanghai China

As the deadliest form of pollution, air pollution had a prolonged severe damage to the human health and life safety of nearly 99% of the world's population. Facing to the problem that billions of tons of pollutants discharged into the air per year by industrial activities, this paper proposed a novel image-based air pollution monitor (IAPM) by incorporating local and global information in the self-adaptive multiscale transform domain, so as to achieve the timely and effective leakage detection of typical air pollutants from a single image. To be specific, this paper first developed a screen-shaped module according to two significant findings in visual neuroscience, which include the high sensitivity of human eyes to horizontal and vertical stimuli and the center-surround inhibition, by designing and fusing the square module, horizontal strip module and vertical strip module parallelly for simulating the behaviour of human eyes to extract local features. Second, the learnable weights and proportional mapping were applied to incorporate the screen-shaped module and lightweight vision transformer as backbone, towards more richly exploiting and fusing local and global information just as the way a brain perceives external stimuli. Third, a new self-adaptive multiscale transform domain method was devised based on two motivations from the visual characteristics of multiscale perception and the brain characteristics of self-adaptive domain transform to modify the backbone by using the operations of pooling and pointwise convolution. Extensive experiments implemented on the datasets of carbon particulate matters and ethylene leakage confirmed the superior monitoring performance of the proposed IAPM model beyond the state-of-the-art (SOTA) peers by an accuracy gain of about 4%. Furthermore, the proposed IAPM model only required 0.089 GFLOPs and 0.15 million model parameters, remarkably outperforming SOTA competitors in computational efficiency and storage resources. © 1999-2

关键词： Information leakage

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Regulation of Shock Response in Cage-Like High-Energy-Density Materials: Competition between Strain Energy and Structural Symmetry

SSRN

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SSRN 2025年

作者： Song, Qingguan Meng, Li Jiang, Shengli Zhang, Lei Mo, Zeyao Institute of Applied Physics and Computational Mathematics Beijing100088 China CAEP Software Center for High Performance Numerical Simulation Beijing100088 China Institute of Chemical Materials China Academy of Engineering Physics Mianyang621999 China School of Materials Science & Engineering Beijing Institute of Technology Beijing100081 China State Key Laboratory of Explosion Science and Safety Protection Beijing Institute of Technology Beijing100081 China

The cage-like structures provide a unique combination of strain energy for enhanced energy storage and hyperstatic constraints to stabilize the system, positioning them as promising pioneers in advancing high-energy-density materials (HEDMs). However, the shock response of cage-like HEDMs is highly complex and exhibits significant variability, posing a grand challenge in the underlying mechanisms. This study reveals that the shock response of cage-like HEDMs is regulated by the interplay between strain energy and structural symmetry, and introduces a physical model to quantitatively describe how they determine shock stability. The investigated systems include a comprehensive series of cage-like polynitrocubane HEDMs, with each carbon atom in the backbone progressively functionalized with nitro groups. Ab initio molecular dynamics (AIMD) simulations were employed to simulate dynamic and kinetic responses at shock velocities ranging from 8 km/s to 11 km/s, with validation provided by consistent Hugoniot curves that align with reported experimental data. Nitro substituents at the carbon-based cage structure, recognized as explosion functional groups, were found to substantially increase the system's strain energy. However, an increasing number of nitro substituents also intensified electrostatic repulsion among oxygen lone pairs, which weakens structural integrity and renders the material more susceptible to disassembly under shock conditions. Conversely, structural symmetry—including both the cage-like molecular conformation and spatial packing within the crystal lattice—was found to mitigate these destabilizing effects, effectively balancing the trade-off between energy storage and structural stability. Based on these findings, we propose a physical model that captures the essential factors driving shock initiation in cage-like HEDMs, offering new insights to inform the design and application of novel advanced HEDMs. © 2025, The Authors. All rights reserved.

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Addressing Non-stationarity with Stochastic Trend in the Context of Limited Time Series Data: An Experimental Survey

Research Square

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Research Square 2025年

作者： Batoure Bamana, Apollinaire Sokdou Bila Lamou, Yannick Fotsa-Mbogne, David Jaures Shafiee Kamalabad, Mahdi Department of Computer Engineering University Institute of Technology The University of Ngaoundere Cameroon Department of Robotic and Industrial Computing School of Chemical Engineering and Mineral Industries The University of Ngaoundere Cameroon Department of Mathematics and Computer Science Faculty of Science The University of Ngaoundere Cameroon Laboratory of Mathematics Computer Science and Applications Department of Mathematics and Computer Science National Higher School of Agro-Industrial Sciences The University of Ngaoundéré Cameroon Laboratory of Mathematics and Computer Science Department of Mathematics Statistics and Computer Science Faculty of Science The University of Bertoua Cameroon Department of Methodology and Statistics Faculty of Social and Behavioural Sciences Utrecht University Utrecht Netherlands Centre for Complex Systems Studies Utrecht University Utrecht Netherlands

Stationarity in time series is a key property for practical data analysis, inferences, and predictions particularly in biosciences. Stationarity can be either deterministic or stochastic. If a time series data is not stationary, it can be rendered stationary through detrending or differentiation techniques. Differentiation can be performed in either an integer or fractional form. This paper investigates non-stationarity in time series data, focusing specifically on stochastic trends characterised by a unit root. It hypothesises that fractional differentiation can enhance forecast accuracy for datasets with limited volume. For experiments, 24 series corresponding to weekly Malaria and Typhoid Fever from Adamawa Region (Cameroon) are analysed and forecasted. Each series comprises 156 observations covering January 2021 to December 2023. After collecting, checking and classifying the data, four forecasting models, Auto Regressive Integrated Moving Average (ARIMA), Fractional ARIMA (ARFIMA), Long Short-Term Memory (LSTM), and the proposed Fractional Differencing and LSTM (FD-LSTM), are implemented. The models' performances are evaluated using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Coefficient of determination (R2) metrics, which inform further analysis and recommendations. Results reveal that ARFIMA outperformed the ARIMA by 93% in training and 100% in testing. Similarly, FD-LSTM achieved a 100% improvement over LSTM in training and testing. These findings underscore the value of achieving stationarity through fractional differentiation, enhancing model performance and providing a robust framework for forecasting in datasets with limited observations. © 2025, CC BY.

关键词： Time series

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Geometry engineering of tunneling transistors in transition metal dichalcogenide nanoribbon heterojunctions

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Communications Physics 2025年第1期8卷 1-9页

作者： Jiang, Ye Dan, Minjiang Fan, Shuaiwei Hu, Gongwei Huang, Fobao Wang, Wei-Yang Chen, Qiao School of Computational Science and Electronics The lnnovation Institute of Advanced Functional Materials Hunan Institute of Engineering Xiangtan China Joint Laboratory for Extreme Conditions Matter Properties School of Mathematics and Physics Southwest University of Science and Technology Mianyang China Hubei Engineering Research Center of Weak Magnetic-field Detection College of Science China Three Gorges University Yichang China School of Microelectronics Northwestern Polytechnical University Xi’an China Shangrao Open University Jiangxi Shangrao China

Graphene nanoribbon heterojunctions are promising one-dimensional materials for quantum electronics due to their tunable bandgap and sizable quantum confinement. However, their band alignment is significantly influenced by dimensional fluctuations, impeding the development of stable and reliable devices. Here, we engineer geometry edges of transition metal dichalcogenide (TMD) nanoribbons to design versatile nanoribbon heterojunctions by combining metallic zigzag and semiconducting armchair edges. T- and H-shaped nanoribbons exhibit robust edge-state transport for tunneling and resonant tunneling, respectively. The quantized subbands confined within H-shaped nanoribbon are modulated by zigzag edges. In contrast, T-shaped configuration shows different tunneling for electrons and holes, which are tunable via armchair edges. Moreover, the device characteristics suggest that tunneling transistors display moderate current dependence on the barrier width, while resonant tunneling transistors exhibit negative differential resistance with peak-valley ratio improved by lengthening armchair edge. This study proposes using geometry edge as a degree of freedom to engineer two-dimensional material nanoribbon heterojunctions, with broad potential for quantum electronic and optoelectronic applications. (Figure presented.) © The Author(s) 2025.

关键词： Quantum electronics

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