Showing 1–18 of 18 results for author: Quan, P

TS-Skill: A Benchmark for Evaluating Analytical Skills in Time-Series Question Answering

Authors: Liying Han, Kang Yang, Oliver Wang, Jason Wu, Pengrui Quan, Gaofeng Dong, Ozan Baris Mulayim, Sizhe Ma, Yuyang Yuan, Dezhi Hong, Mario Berges, Mani Srivastava

Abstract: Large language models (LLMs) and time-series language models (TSLMs) are increasingly applied to time-series question answering (TSQA). Unlike text-only QA, TSQA requires models to ground answers in temporal signals whose patterns may occur at different scales, specific time locations, or across separated intervals. However, existing benchmarks are typically organized by task types or high-level r… ▽ More Large language models (LLMs) and time-series language models (TSLMs) are increasingly applied to time-series question answering (TSQA). Unlike text-only QA, TSQA requires models to ground answers in temporal signals whose patterns may occur at different scales, specific time locations, or across separated intervals. However, existing benchmarks are typically organized by task types or high-level reasoning categories, making it difficult to diagnose the underlying signal-level capabilities driving model performance. We introduce TS-Skill, a controlled benchmark for evaluating three composable analytical skills in TSQA: temporal scale selection (SK1), temporal localization (SK2), and cross-interval integration (SK3). TS-Skill provides timestamp-aware questions, broad domain coverage, and human-validated QA quality. To construct the benchmark at scale, we develop SKEvol, a skill-guided agentic framework that combines domain-aware time-series seed generation, skill-controlled question generation, metadata- and code-assisted answer construction, multi-phase signal-grounded verification, and human-in-the-loop curation. Experiments on ten state-of-the-art LLMs and TSLMs reveal substantial and uneven capability gaps across SK1-SK3. In particular, SK3 remains consistently challenging for non-agent models, whereas tool-augmented agents show a selective advantage on standalone SK3. These findings demonstrate that skill-level evaluation can uncover temporal reasoning failures that are obscured by aggregate TSQA scores. △ Less

Submitted 23 May, 2026; originally announced May 2026.

Spectral Predictability as a Fast Reliability Indicator for Time Series Forecasting Model Selection

Authors: Oliver Wang, Pengrui Quan, Kang Yang, Mani Srivastava

Abstract: Practitioners deploying time series forecasting models face a dilemma: exhaustively validating dozens of models is computationally prohibitive, yet choosing the wrong model risks poor performance. We show that spectral predictability~$Ω$ -- a simple signal processing metric -- systematically stratifies model family performance, enabling fast model selection. We conduct controlled experiments in fo… ▽ More Practitioners deploying time series forecasting models face a dilemma: exhaustively validating dozens of models is computationally prohibitive, yet choosing the wrong model risks poor performance. We show that spectral predictability~$Ω$ -- a simple signal processing metric -- systematically stratifies model family performance, enabling fast model selection. We conduct controlled experiments in four different domains, then further expand our analysis to 51 models and 28 datasets from the GIFT-Eval benchmark. We find that large time series foundation models (TSFMs) systematically outperform lightweight task-trained baselines when $Ω$ is high, while their advantage vanishes as $Ω$ drops. Computing $Ω$ takes seconds per dataset, enabling practitioners to quickly assess whether their data suits TSFM approaches or whether simpler, cheaper models suffice. We demonstrate that $Ω$ stratifies model performance predictably, offering a practical first-pass filter that reduces validation costs while highlighting the need for models that excel on genuinely difficult (low-$Ω$) problems rather than merely optimizing easy ones. △ Less

Submitted 11 November, 2025; originally announced November 2025.

GAS-MIL: Group-Aggregative Selection Multi-Instance Learning for Ensemble of Foundation Models in Digital Pathology Image Analysis

Authors: Peiran Quan, Zifan Gu, Zhuo Zhao, Qin Zhou, Donghan M. Yang, Ruichen Rong, Yang Xie, Guanghua Xiao

Abstract: Foundation models (FMs) have transformed computational pathology by providing powerful, general-purpose feature extractors. However, adapting and benchmarking individual FMs for specific diagnostic tasks is often time-consuming and resource-intensive, especially given their scale and diversity. To address this challenge, we introduce Group-Aggregative Selection Multi-Instance Learning (GAS-MIL), a… ▽ More Foundation models (FMs) have transformed computational pathology by providing powerful, general-purpose feature extractors. However, adapting and benchmarking individual FMs for specific diagnostic tasks is often time-consuming and resource-intensive, especially given their scale and diversity. To address this challenge, we introduce Group-Aggregative Selection Multi-Instance Learning (GAS-MIL), a flexible ensemble framework that seamlessly integrates features from multiple FMs, preserving their complementary strengths without requiring manual feature selection or extensive task-specific fine-tuning. Across classification tasks in three cancer datasets-prostate (PANDA), ovarian (UBC-OCEAN), and breast (TCGA-BrCa)-GAS-MIL consistently achieves superior or on-par performance relative to individual FMs and established MIL methods, demonstrating its robustness and generalizability. By enabling efficient integration of heterogeneous FMs, GAS-MIL streamlines model deployment for pathology and provides a scalable foundation for future multimodal and precision oncology applications. △ Less

Submitted 3 October, 2025; originally announced October 2025.

E2ATST: A Temporal-Spatial Optimized Energy-Efficient Architecture for Training Spiking Transformer

Authors: Yunhao Ma, Yanyu Lin, Mingjing Li, Puli Quan, Chenlin Zhou, Wenyue Zhang, Zhiwei Zhong, Wanyi Jia, Xueke Zhu, Qingyan Meng, Huihui Zhou, Fengwei An

Abstract: (1) Pengcheng Laboratory, (2) Southern University of Science and Technology, (3) Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, (4) University of Chinese Academy of Sciences (1) Pengcheng Laboratory, (2) Southern University of Science and Technology, (3) Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, (4) University of Chinese Academy of Sciences △ Less

Submitted 1 August, 2025; originally announced August 2025.

Can Time-Series Foundation Models Perform Building Energy Management Tasks?

Authors: Ozan Baris Mulayim, Pengrui Quan, Liying Han, Xiaomin Ouyang, Dezhi Hong, Mario Bergés, Mani Srivastava

Abstract: Building energy management (BEM) tasks require processing and learning from a variety of time-series data. Existing solutions rely on bespoke task- and data-specific models to perform these tasks, limiting their broader applicability. Inspired by the transformative success of Large Language Models (LLMs), Time-Series Foundation Models (TSFMs), trained on diverse datasets, have the potential to cha… ▽ More Building energy management (BEM) tasks require processing and learning from a variety of time-series data. Existing solutions rely on bespoke task- and data-specific models to perform these tasks, limiting their broader applicability. Inspired by the transformative success of Large Language Models (LLMs), Time-Series Foundation Models (TSFMs), trained on diverse datasets, have the potential to change this. Were TSFMs to achieve a level of generalizability across tasks and contexts akin to LLMs, they could fundamentally address the scalability challenges pervasive in BEM. To understand where they stand today, we evaluate TSFMs across four dimensions: (1) generalizability in zero-shot univariate forecasting, (2) forecasting with covariates for thermal behavior modeling, (3) zero-shot representation learning for classification tasks, and (4) robustness to performance metrics and varying operational conditions. Our results reveal that TSFMs exhibit \emph{limited} generalizability, performing only marginally better than statistical models on unseen datasets and modalities for univariate forecasting. Similarly, inclusion of covariates in TSFMs does not yield performance improvements, and their performance remains inferior to conventional models that utilize covariates. While TSFMs generate effective zero-shot representations for downstream classification tasks, they may remain inferior to statistical models in forecasting when statistical models perform test-time fitting. Moreover, TSFMs forecasting performance is sensitive to evaluation metrics, and they struggle in more complex building environments compared to statistical models. These findings underscore the need for targeted advancements in TSFM design, particularly their handling of covariates and incorporating context and temporal dynamics into prediction mechanisms, to develop more adaptable and scalable solutions for BEM. △ Less

Submitted 12 June, 2025; originally announced June 2025.

Comments: 30 pages, 5 tables, 8 figures. Under review for Data-Centric Engineering journal

Benchmarking Spatiotemporal Reasoning in LLMs and Reasoning Models: Capabilities and Challenges

Authors: Pengrui Quan, Brian Wang, Kang Yang, Liying Han, Mani Srivastava

Abstract: Spatiotemporal reasoning plays a key role in Cyber-Physical Systems (CPS). Despite advances in Large Language Models (LLMs) and Large Reasoning Models (LRMs), their capacity to reason about complex spatiotemporal signals remains underexplored. This paper proposes a hierarchical SpatioTemporal reAsoning benchmaRK, STARK, to systematically evaluate LLMs across three levels of reasoning complexity: s… ▽ More Spatiotemporal reasoning plays a key role in Cyber-Physical Systems (CPS). Despite advances in Large Language Models (LLMs) and Large Reasoning Models (LRMs), their capacity to reason about complex spatiotemporal signals remains underexplored. This paper proposes a hierarchical SpatioTemporal reAsoning benchmaRK, STARK, to systematically evaluate LLMs across three levels of reasoning complexity: state estimation (e.g., predicting field variables, localizing and tracking events in space and time), spatiotemporal reasoning over states (e.g., inferring spatial-temporal relationships), and world-knowledge-aware reasoning that integrates contextual and domain knowledge (e.g., intent prediction, landmark-aware navigation). We curate 26 distinct spatiotemporal tasks with diverse sensor modalities, comprising 14,552 challenges where models answer directly or by Python Code Interpreter. Evaluating 3 LRMs and 8 LLMs, we find LLMs achieve limited success in tasks requiring geometric reasoning (e.g., multilateration or triangulation), particularly as complexity increases. Surprisingly, LRMs show robust performance across tasks with various levels of difficulty, often competing or surpassing traditional first-principle-based methods. Our results show that in reasoning tasks requiring world knowledge, the performance gap between LLMs and LRMs narrows, with some LLMs even surpassing LRMs. However, the LRM o3 model continues to achieve leading performance across all evaluated tasks, a result attributed primarily to the larger size of the reasoning models. STARK motivates future innovations in model architectures and reasoning paradigms for intelligent CPS by providing a structured framework to identify limitations in the spatiotemporal reasoning of LLMs and LRMs. △ Less

Submitted 9 January, 2026; v1 submitted 16 May, 2025; originally announced May 2025.

Foundation Models for CPS-IoT: Opportunities and Challenges

Authors: Ozan Baris, Yizhuo Chen, Gaofeng Dong, Liying Han, Tomoyoshi Kimura, Pengrui Quan, Ruijie Wang, Tianchen Wang, Tarek Abdelzaher, Mario Bergés, Paul Pu Liang, Mani Srivastava

Abstract: Methods from machine learning (ML) have transformed the implementation of Perception-Cognition-Communication-Action loops in Cyber-Physical Systems (CPS) and the Internet of Things (IoT), replacing mechanistic and basic statistical models with those derived from data. However, the first generation of ML approaches, which depend on supervised learning with annotated data to create task-specific mod… ▽ More Methods from machine learning (ML) have transformed the implementation of Perception-Cognition-Communication-Action loops in Cyber-Physical Systems (CPS) and the Internet of Things (IoT), replacing mechanistic and basic statistical models with those derived from data. However, the first generation of ML approaches, which depend on supervised learning with annotated data to create task-specific models, faces significant limitations in scaling to the diverse sensor modalities, deployment configurations, application tasks, and operating dynamics characterizing real-world CPS-IoT systems. The success of task-agnostic foundation models (FMs), including multimodal large language models (LLMs), in addressing similar challenges across natural language, computer vision, and human speech has generated considerable enthusiasm for and exploration of FMs and LLMs as flexible building blocks in CPS-IoT analytics pipelines, promising to reduce the need for costly task-specific engineering. Nonetheless, a significant gap persists between the current capabilities of FMs and LLMs in the CPS-IoT domain and the requirements they must meet to be viable for CPS-IoT applications. In this paper, we analyze and characterize this gap through a thorough examination of the state of the art and our research, which extends beyond it in various dimensions. Based on the results of our analysis and research, we identify essential desiderata that CPS-IoT domain-specific FMs and LLMs must satisfy to bridge this gap. We also propose actions by CPS-IoT researchers to collaborate in developing key community resources necessary for establishing FMs and LLMs as foundational tools for the next generation of CPS-IoT systems. △ Less

Submitted 4 February, 2025; v1 submitted 22 January, 2025; originally announced January 2025.

A High Energy-Efficiency Multi-core Neuromorphic Architecture for Deep SNN Training

Authors: Mingjing Li, Huihui Zhou, Xiaofeng Xu, Zhiwei Zhong, Puli Quan, Xueke Zhu, Yanyu Lin, Wenjie Lin, Hongyu Guo, Junchao Zhang, Yunhao Ma, Wei Wang, Qingyan Meng, Zhengyu Ma, Guoqi Li, Xiaoxin Cui, Yonghong Tian

Abstract: There is a growing necessity for edge training to adapt to dynamically changing environment. Neuromorphic computing represents a significant pathway for high-efficiency intelligent computation in energy-constrained edges, but existing neuromorphic architectures lack the ability of directly training spiking neural networks (SNNs) based on backpropagation. We develop a multi-core neuromorphic archit… ▽ More There is a growing necessity for edge training to adapt to dynamically changing environment. Neuromorphic computing represents a significant pathway for high-efficiency intelligent computation in energy-constrained edges, but existing neuromorphic architectures lack the ability of directly training spiking neural networks (SNNs) based on backpropagation. We develop a multi-core neuromorphic architecture with Feedforward-Propagation, Back-Propagation, and Weight-Gradient engines in each core, supporting high efficient parallel computing at both the engine and core levels. It combines various data flows and sparse computation optimization by fully leveraging the sparsity in SNN training, obtaining a high energy efficiency of 1.05TFLOPS/W@ FP16 @ 28nm, 55 ~ 85% reduction of DRAM access compared to A100 GPU in SNN trainings, and a 20-core deep SNN training and a 5-worker federated learning on FPGAs. Our study develops the first multi-core neuromorphic architecture supporting the direct SNN training, facilitating the neuromorphic computing in edge-learnable applications. △ Less

Submitted 29 December, 2024; v1 submitted 26 November, 2024; originally announced December 2024.

SensorBench: Benchmarking LLMs in Coding-Based Sensor Processing

Authors: Pengrui Quan, Xiaomin Ouyang, Jeya Vikranth Jeyakumar, Ziqi Wang, Yang Xing, Mani Srivastava

Abstract: Effective processing, interpretation, and management of sensor data have emerged as a critical component of cyber-physical systems. Traditionally, processing sensor data requires profound theoretical knowledge and proficiency in signal-processing tools. However, recent works show that Large Language Models (LLMs) have promising capabilities in processing sensory data, suggesting their potential as… ▽ More Effective processing, interpretation, and management of sensor data have emerged as a critical component of cyber-physical systems. Traditionally, processing sensor data requires profound theoretical knowledge and proficiency in signal-processing tools. However, recent works show that Large Language Models (LLMs) have promising capabilities in processing sensory data, suggesting their potential as copilots for developing sensing systems. To explore this potential, we construct a comprehensive benchmark, SensorBench, to establish a quantifiable objective. The benchmark incorporates diverse real-world sensor datasets for various tasks. The results show that while LLMs exhibit considerable proficiency in simpler tasks, they face inherent challenges in processing compositional tasks with parameter selections compared to engineering experts. Additionally, we investigate four prompting strategies for sensor processing and show that self-verification can outperform all other baselines in 48% of tasks. Our study provides a comprehensive benchmark and prompting analysis for future developments, paving the way toward an LLM-based sensor processing copilot. △ Less

Submitted 28 March, 2025; v1 submitted 14 October, 2024; originally announced October 2024.

Efficient relaxation scheme for the SIR and related compartmental models

Authors: Vo Anh Khoa, Pham Minh Quan, Ja'Niyah Allen, Kbenesh W. Blayneh

Abstract: In this paper, we introduce a novel numerical approach for approximating the SIR model in epidemiology. Our method enhances the existing linearization procedure by incorporating a suitable relaxation term to tackle the transcendental equation of nonlinear type. Developed within the continuous framework, our relaxation method is explicit and easy to implement, relying on a sequence of linear differ… ▽ More In this paper, we introduce a novel numerical approach for approximating the SIR model in epidemiology. Our method enhances the existing linearization procedure by incorporating a suitable relaxation term to tackle the transcendental equation of nonlinear type. Developed within the continuous framework, our relaxation method is explicit and easy to implement, relying on a sequence of linear differential equations. This approach yields accurate approximations in both discrete and analytical forms. Through rigorous analysis, we prove that, with an appropriate choice of the relaxation parameter, our numerical scheme is non-negativity-preserving and globally strongly convergent towards the true solution. These theoretical findings have not received sufficient attention in various existing SIR solvers. We also extend the applicability of our relaxation method to handle some variations of the traditional SIR model. Finally, we present numerical examples using simulated data to demonstrate the effectiveness of our proposed method. △ Less

Submitted 15 August, 2023; originally announced August 2023.

Comments: 17 pages, 21 figures, 2 tables

MSC Class: 65L05; 65L70; 65Z05

On the amplification of security and privacy risks by post-hoc explanations in machine learning models

Authors: Pengrui Quan, Supriyo Chakraborty, Jeya Vikranth Jeyakumar, Mani Srivastava

Abstract: A variety of explanation methods have been proposed in recent years to help users gain insights into the results returned by neural networks, which are otherwise complex and opaque black-boxes. However, explanations give rise to potential side-channels that can be leveraged by an adversary for mounting attacks on the system. In particular, post-hoc explanation methods that highlight input dimensio… ▽ More A variety of explanation methods have been proposed in recent years to help users gain insights into the results returned by neural networks, which are otherwise complex and opaque black-boxes. However, explanations give rise to potential side-channels that can be leveraged by an adversary for mounting attacks on the system. In particular, post-hoc explanation methods that highlight input dimensions according to their importance or relevance to the result also leak information that weakens security and privacy. In this work, we perform the first systematic characterization of the privacy and security risks arising from various popular explanation techniques. First, we propose novel explanation-guided black-box evasion attacks that lead to 10 times reduction in query count for the same success rate. We show that the adversarial advantage from explanations can be quantified as a reduction in the total variance of the estimated gradient. Second, we revisit the membership information leaked by common explanations. Contrary to observations in prior studies, via our modified attacks we show significant leakage of membership information (above 100% improvement over prior results), even in a much stricter black-box setting. Finally, we study explanation-guided model extraction attacks and demonstrate adversarial gains through a large reduction in query count. △ Less

Submitted 28 June, 2022; originally announced June 2022.

Comments: 9 pages, appendix: 2 pages

Towards Imperceptible Query-limited Adversarial Attacks with Perceptual Feature Fidelity Loss

Authors: Pengrui Quan, Ruiming Guo, Mani Srivastava

Abstract: Recently, there has been a large amount of work towards fooling deep-learning-based classifiers, particularly for images, via adversarial inputs that are visually similar to the benign examples. However, researchers usually use Lp-norm minimization as a proxy for imperceptibility, which oversimplifies the diversity and richness of real-world images and human visual perception. In this work, we pro… ▽ More Recently, there has been a large amount of work towards fooling deep-learning-based classifiers, particularly for images, via adversarial inputs that are visually similar to the benign examples. However, researchers usually use Lp-norm minimization as a proxy for imperceptibility, which oversimplifies the diversity and richness of real-world images and human visual perception. In this work, we propose a novel perceptual metric utilizing the well-established connection between the low-level image feature fidelity and human visual sensitivity, where we call it Perceptual Feature Fidelity Loss. We show that our metric can robustly reflect and describe the imperceptibility of the generated adversarial images validated in various conditions. Moreover, we demonstrate that this metric is highly flexible, which can be conveniently integrated into different existing optimization frameworks to guide the noise distribution for better imperceptibility. The metric is particularly useful in the challenging black-box attack with limited queries, where the imperceptibility is hard to achieve due to the non-trivial perturbation power. △ Less

Submitted 31 January, 2021; originally announced February 2021.

Instrument for in situ hard x-ray nanobeam characterization during epitaxial crystallization and materials transformations

Authors: Samuel D. Marks, Peiyu Quan, Rui Liu, Matthew J. Highland, Hua Zhou, Thomas F. Keuch, G. Brian Stephenson, Paul G. Evans

Abstract: Solid-phase epitaxy (SPE) and other three-dimensional epitaxial crystallization processes pose challenging structural and chemical characterization problems. The concentration of defects, the spatial distribution of elastic strain, and the chemical state of ions each vary with nanoscale characteristic length scales and depend sensitively on the gas environment and elastic boundary conditions durin… ▽ More Solid-phase epitaxy (SPE) and other three-dimensional epitaxial crystallization processes pose challenging structural and chemical characterization problems. The concentration of defects, the spatial distribution of elastic strain, and the chemical state of ions each vary with nanoscale characteristic length scales and depend sensitively on the gas environment and elastic boundary conditions during growth. The lateral or three-dimensional propagation of crystalline interfaces in SPE has nanoscale or submicron characteristic distances during typical crystallization times. An in situ synchrotron hard x-ray instrument allows these features to be studied during deposition and crystallization using diffraction, resonant scattering, nanobeam and coherent diffraction imaging, and reflectivity. The instrument incorporates a compact deposition system allowing the use of short-working-distance x-ray focusing optics. Layers are deposited using radio-frequency magnetron sputtering and evaporation sources. The deposition system provides control of the gas atmosphere and sample temperature. The sample is positioned using a stable mechanical design to minimize vibration and drift and employs precise translation stages to enable nanobeam experiments. Results of in situ x-ray characterization of the amorphous thin film deposition process for a SrTiO3/BaTiO3 multilayer illustrate implementation of this instrument. △ Less

Submitted 1 December, 2020; originally announced December 2020.

Comments: 28 pages, 6 figures

Efficient Optimization Methods for Extreme Similarity Learning with Nonlinear Embeddings

Authors: Bowen Yuan, Yu-Sheng Li, Pengrui Quan, Chih-Jen Lin

Abstract: We study the problem of learning similarity by using nonlinear embedding models (e.g., neural networks) from all possible pairs. This problem is well-known for its difficulty of training with the extreme number of pairs. For the special case of using linear embeddings, many studies have addressed this issue of handling all pairs by considering certain loss functions and developing efficient optimi… ▽ More We study the problem of learning similarity by using nonlinear embedding models (e.g., neural networks) from all possible pairs. This problem is well-known for its difficulty of training with the extreme number of pairs. For the special case of using linear embeddings, many studies have addressed this issue of handling all pairs by considering certain loss functions and developing efficient optimization algorithms. This paper aims to extend results for general nonlinear embeddings. First, we finish detailed derivations and provide clean formulations for efficiently calculating some building blocks of optimization algorithms such as function, gradient evaluation, and Hessian-vector product. The result enables the use of many optimization methods for extreme similarity learning with nonlinear embeddings. Second, we study some optimization methods in detail. Due to the use of nonlinear embeddings, implementation issues different from linear cases are addressed. In the end, some methods are shown to be highly efficient for extreme similarity learning with nonlinear embeddings. △ Less

Submitted 15 June, 2021; v1 submitted 26 October, 2020; originally announced October 2020.

Comments: Published as a conference paper at KDD 2021

A new stability results for the backward heat equation

Authors: Alain Pham Ngoc Dinh, Dang Duc Trong, Pham Hoang Quan, Nguyen Huy Tuan

Abstract: In this paper, we regularize the nonlinear inverse time heat problem in the unbounded region by Fourier method. Some new convergence rates are obtained. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. Especially, the optimal convergence of the approximate solution at t = 0 is also proved. This work extends to many earlier results in (… ▽ More In this paper, we regularize the nonlinear inverse time heat problem in the unbounded region by Fourier method. Some new convergence rates are obtained. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. Especially, the optimal convergence of the approximate solution at t = 0 is also proved. This work extends to many earlier results in (f2,f3, hao1,Quan,tau1, tau2, Trong3,x1). △ Less

Submitted 13 November, 2009; originally announced November 2009.

Comments: 13 pages

MSC Class: 35K05; 35K99; 47J06; 47H10.

Ice formation in the Arctic during summer: false-bottoms

Authors: Phan Thanh Nam, Alain Pham Ngoc Dinh, Pham Hoang Quan, Dang Duc Trong

Abstract: The only source of ice formation in the Arctic during summer is a layer of ice called false-bottoms between an under-ice melt pond and the underlying ocean. Of interest is to give a mathematical model in order to determine the simultaneous growth and ablation of false-bottoms, which is governed by both of heat fluxes and salt fluxes. In one dimension, this problem may be considered mathematically… ▽ More The only source of ice formation in the Arctic during summer is a layer of ice called false-bottoms between an under-ice melt pond and the underlying ocean. Of interest is to give a mathematical model in order to determine the simultaneous growth and ablation of false-bottoms, which is governed by both of heat fluxes and salt fluxes. In one dimension, this problem may be considered mathematically as a two-phase Stefan problem with two free boundaries. Our main result is to prove the existence and uniqueness of the solution from the initial condition. △ Less

Submitted 24 November, 2011; v1 submitted 15 July, 2008; originally announced July 2008.

Comments: 22 pages

Journal ref: Applied Mathematics and Computation 227 (2014) 857-870

A nonlinearly ill-posed problem of reconstructing the temperature from interior data

Authors: Alain Pham Ngoc Dinh, Pham Hoang Quan, Dang Duc Trong

Abstract: We consider the problem of reconstructing, from the interior data $u(x,1)$, a function $u$ satisfying a nonlinear elliptic equation $$ Δu = f(x,y,u(x,y)), x \in \RR, y > 0. $$ We consider the problem of reconstructing, from the interior data $u(x,1)$, a function $u$ satisfying a nonlinear elliptic equation $$ Δu = f(x,y,u(x,y)), x \in \RR, y > 0. $$ △ Less

Submitted 23 May, 2007; originally announced May 2007.

Comments: 24 pages

MSC Class: 47J06; 35J60; 42A38; 47H10

Journal ref: Numerical Functional Analysis and Optimization / Numerical Functional Analysis and Optimization An International Journal 29, 3-4 (2008) 445-469

Sinc Approximation of the Heat Distribution on the Boundary of a Two-Dimensional Finite Slab

Authors: Alain Pham Ngoc Dinh, Pham Hoang Quan, Dang Duc Trong

Abstract: We consider the two-dimensional problem of recovering globally in time the heat distribution on the surface of a layer inside of a heat conducting body from two interior temperature measurements. The problem is ill-posed. The approximation function is represented by a two-dimensional Sinc series and the error estimate is given. We consider the two-dimensional problem of recovering globally in time the heat distribution on the surface of a layer inside of a heat conducting body from two interior temperature measurements. The problem is ill-posed. The approximation function is represented by a two-dimensional Sinc series and the error estimate is given. △ Less

Submitted 19 May, 2007; originally announced May 2007.

Comments: 10 pages

MSC Class: 35K05; 31A25; 44A35

Journal ref: Nonlinear Analysis Real World Applications, 9 (2008) 1103-1111