arXiv subjects

Jingye Xu

Publications and source records attributed to Jingye Xu.

12 recordsLinked to original sources

arXiv2026

Probabilistic analysis of dual decomposition on two-stage stochastic integer programs

Two-stage stochastic integer programs provide a powerful framework for modeling decision-making under uncertainty, but they are notoriously difficult to solve at scale due to their high dimensionality and intrinsic nonconvexity. Decomposition-based algorithms such as Benders methods and Branch-and-Price (related dual decomposition methods) have become standard computational approaches for such problems and demonstrate excellent empirical performance in practice. Despite their widespread use, however, existing theoretical guarantees are almost exclusively based on worst-case analyses, which predict exponential convergence behavior in the problem dimension and fail to explain the strong performance observed in practice. In this paper, we present the first average-case analysis of Branch-and-Price for a broad class of two-stage stochastic binary integer programs. We study a stochastic-input model in which objective coefficients and constraint matrices are drawn at random and right-hand-side vectors scale with the decision dimension, while the number of constraints per scenario is fixed. Under this model, we prove that, with high probability, Branch-and-Price explores at most n^O(log s)nodes, yielding a quasi-polynomial bound on the size of the search tree in typical instances, where n denotes the decision dimension and s the number of scenarios. A key ingredient of our analysis is an average-case bound on the integrality gap of the natural linear programming (LP) relaxation. We show that this gap shrinks at rate O((logs log^2 n)/n)with high probability. This result is of independent interest, as it implies that the integrality gap grows only logarithmically with the number of scenarios on average.

math.OC↗

arXiv2026

FeynmanBench: Benchmarking Multimodal LLMs on Diagrammatic Physics Reasoning

Current multimodal benchmarks for scientific reasoning primarily evaluate local information extraction -- models recognize symbols and values and then perform textual inference. They do not assess whether models can reason over the global structural properties of formal diagrams, such as topology, conservation constraints, and the consistent mapping between visual patterns and algebraic expressions. We introduce FeynmanBench, a benchmark of over 2,000 tasks centered on Feynman diagrams spanning the electromagnetic, weak, and strong interactions of the Standard Model. Each instance couples a diagram image with minimal textual conventions and requires models to recover the full physical content -- vertex inventory, propagator types, topological connectivity, momentum routing, and the complete scattering amplitude. An automated generation and verification pipeline produces the diagrams, annotations, and reference answers under standardized rules. Evaluating 19 state-of-the-art multimodal LLMs, we find a consistent failure pattern: models achieve 70--95\% on local recognition (vertex and propagator identification) but collapse to 13--17\% on topological reconstruction (CP3), and near zero on full algebraic derivation (CP5). FeynmanBench offers a controlled testbed for multimodal reasoning over formal scientific diagrams and highlights fundamental limitations of current architectures in topology-sensitive scientific reasoning.

cs.AI↗

arXiv2026

Asymptotically tight Lagrangian dual of smooth nonconvex problems via improved error bound of Shapley-Folkman Lemma

In convex geometry, the Shapley-Folkman Lemma asserts that the nonconvexity of a Minkowski sum of $n$ dimensional bounded nonconvex sets does not accumulate once the number of summands exceeds the dimension $n$, and thus the sum becomes approximately convex. Originally published by Starr in the context of quasi-equilibrium in nonconvex market models in economics, the lemma has since found widespread use in optimization, particularly for estimating the duality gap of the Lagrangian dual of separable nonconvex problems. Given its foundational nature, we pose the following geometric question: Is it possible for the nonconvexity of the Minkowski sum of $n$-dimensional nonconvex sets to even diminish instead of just not accumulating as the number of summands increases, under some general conditions? We answer this affirmatively. First, we provide an elementary geometric proof of the Shapley-Folkman Lemma based on the facial structure of the convex hull of each set. This leads to refinement of the classical error bound derived from the lemma. Building on this new geometric perspective, we further show that when most of the sets satisfy a certain local smoothness condition which naturally arises in the epigraphs of smooth functions, their Minkowski sum converges directly to a convex set, with a vanishing nonconvexity measure. In optimization, this implies that the Lagrangian dual of block-structured smooth nonconvex problems with potentially additional sparsity constraints is asymptotically tight under mild assumptions, which contracts nonvanishing duality gap obtained via classical Shapley-Folkman Lemma.

math.OC↗

arXiv2026

AERO: Adaptive and Efficient Runtime-Aware OTA Updates for Energy-Harvesting IoT

Energy-harvesting (EH) Internet of Things (IoT) devices operate under intermittent energy availability, which disrupts task execution and makes energy-intensive over-the-air (OTA) updates particularly challenging. Conventional OTA update mechanisms rely on reboots and incur significant overhead, rendering them unsuitable for intermittently powered systems. Recent live OTA update techniques reduce reboot overhead but still lack mechanisms to ensure consistency when updates interact with runtime execution. This paper presents AERO, an Adaptive and Efficient Runtime-Aware OTA update mechanism that integrates update tasks into the device's Directed Acyclic Graph (DAG) and schedules them alongside routine tasks under energy and timing constraints. By identifying update-affected execution regions and dynamically adjusting dependencies, AERO ensures consistent up date integration while adapting to intermittent energy availability. Experiments on representative workloads demonstrate improved update reliability and efficiency compared to existing live update approaches.

cs.AR↗

arXiv2025

A Comprehensive PPG-based Dataset for HR/HRV Studies

Heart rate (HR) and heart rate variability (HRV) are important vital signs for human physical and mental health. Recent research has demonstrated that photoplethysmography (PPG) sensors can infer HR and HRV. However, it is difficult to find a comprehensive PPG-based dataset for HR/HRV studies, especially for various study needs: multiple scenes, long-term monitoring, and multimodality (multiple PPG channels and extra acceleration data). In this study, we collected a comprehensive multimodal long-term dataset to address the gap of missing an all-in-one HR/HRV dataset (denoted as UTSA-PPG). We began by reviewing state-of-the-art datasets, emphasizing their strengths and limitations. Following this, we developed a custom data acquisition system and then collected the UTSA-PPG dataset and compared its key features with those of existing datasets. Additionally, five case studies were conducted, including comparisons with state-of-the-art datasets. The outcomes highlight the value of our dataset, demonstrating its utility for HR/HRV estimation exploration and its potential to aid researchers in creating generalized models for targeted research challenges.

eess.SP↗

arXiv2024

Lagrangian dual with zero duality gap that admits decomposition

For mixed integer programs (MIPs) with block structures and coupling constraints, on dualizing the coupling constraints the resulting Lagrangian relaxation becomes decomposable into blocks which allows for the use of parallel computing. However, the resulting Lagrangian dual can have non-zero duality gap due to the inherent non-convexity of MIPs. In this paper, we propose two reformulations of such MIPs by adding redundant constraints, such that the Lagrangian dual obtained by dualizing the coupling constraints and the redundant constraints have zero duality gap while still remaining decomposable. One of these reformulations is similar, although not the same as the RLT hierarchy. In this case, we present multiplicative bounds on the quality of the dual bound at each level of the hierarchy for packing and covering MIPs. We show our results are applicable to general sparse MIPs, where decomposability is revealed via the tree-decomposition of the intersection graph of the constraint matrix. In preliminary experiments, we observe that the proposed Lagrangian duals give better dual bounds than classical Lagrangian dual and Gurobi in equal time, where Gurobi is not exploiting decomposability.

math.OC↗

arXiv2024

Branching with a pre-specified finite list of $k$-sparse split sets for binary MILPs

When branching for binary mixed integer linear programs with disjunctions of sparsity level $2$, we observe that there exists a finite list of $2$-sparse disjunctions, such that any other $2$-sparse disjunction is dominated by one disjunction in this finite list. For sparsity level greater than $2$, we show that a finite list of disjunctions with this property cannot exist. This leads to the definition of covering number for a list of splits disjunctions. Given a finite list of split sets $\mathcal{F}$ of $k$-sparsity, and a given $k$-sparse split set $S$, let $\mathcal{F}(S)$ be the minimum number of split sets from the list $\mathcal{F}$, whose union contains $S \cap [0, \ 1]^n$. Let the covering number of $\mathcal{F}$ be the maximum value of $\mathcal{F}(S)$ over all $k$-sparse split sets $S$. We show that the covering number for any finite list of $k$-sparse split sets is at least $\lfloor k/2\rfloor $ for $k \geq 4$. We also show that the covering number of the family of $k$-sparse split sets with coefficients in $\{-1, 0, 1\}$ is upper bounded by $k-1$ for $k \leq 4$.

math.OC↗

arXiv2024

Data Distribution Dynamics in Real-World WiFi-Based Patient Activity Monitoring for Home Healthcare

This paper examines the application of WiFi signals for real-world monitoring of daily activities in home healthcare scenarios. While the state-of-the-art of WiFi-based activity recognition is promising in lab environments, challenges arise in real-world settings due to environmental, subject, and system configuration variables, affecting accuracy and adaptability. The research involved deploying systems in various settings and analyzing data shifts. It aims to guide realistic development of robust, context-aware WiFi sensing systems for elderly care. The findings suggest a shift in WiFi-based activity sensing, bridging the gap between academic research and practical applications, enhancing life quality through technology.

eess.SP↗

arXiv2023

Sensitivity analysis for mixed binary quadratic programming

We consider sensitivity analysis for Mixed Binary Quadratic Programs (MBQPs) with respect to changing right-hand-sides (rhs). We show that even if the optimal solution of a given MBQP is known, it is NP-hard to approximate the change in objective function value with respect to changes in rhs. Next, we study algorithmic approaches to obtaining dual bounds for MBQP with changing rhs. We leverage Burer's completely-positive (CPP) reformulation of MBQPs. Its dual is an instance of co-positive programming (COP), and can be used to obtain sensitivity bounds. We prove that strong duality between the CPP and COP problems holds if the feasible region is bounded or if the objective function is convex, while the duality gap can be strictly positive if neither condition is met. We also show that the COP dual has multiple optimal solutions, and the choice of the dual solution affects the quality of the bounds with rhs changes. We finally provide a method for finding good nearly optimal dual solutions, and we present preliminary computational results on sensitivity analysis for MBQPs.

math.OC↗

arXiv2023

Computational complexity of decomposing a symmetric matrix as a sum of positive semidefinite and diagonal matrices

We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades. On the one hand, we prove that when the rank of the positive semidefinite matrix in the decomposition is bounded above by an absolute constant, the problem can be solved in polynomial time. On the other hand, we prove that, in general, these problems as well as their certain approximation versions are all NP-hard. Finally, we prove that many of these low-rank decomposition problems are complete in the first-order theory of the reals; i.e., given any system of polynomial equations, we can write down a low-rank decomposition problem in polynomial time so that the original system has a solution iff our corresponding decomposition problem has a feasible solution of certain (lowest) rank.

math.OC↗

arXiv2023

PPG-based Heart Rate Estimation with Efficient Sensor Sampling and Learning Models

Recent studies showed that Photoplethysmography (PPG) sensors embedded in wearable devices can estimate heart rate (HR) with high accuracy. However, despite of prior research efforts, applying PPG sensor based HR estimation to embedded devices still faces challenges due to the energy-intensive high-frequency PPG sampling and the resource-intensive machine-learning models. In this work, we aim to explore HR estimation techniques that are more suitable for lower-power and resource-constrained embedded devices. More specifically, we seek to design techniques that could provide high-accuracy HR estimation with low-frequency PPG sampling, small model size, and fast inference time. First, we show that by combining signal processing and ML, it is possible to reduce the PPG sampling frequency from 125 Hz to only 25 Hz while providing higher HR estimation accuracy. This combination also helps to reduce the ML model feature size, leading to smaller models. Additionally, we present a comprehensive analysis on different ML models and feature sizes to compare their accuracy, model size, and inference time. The models explored include Decision Tree (DT), Random Forest (RF), K-nearest neighbor (KNN), Support vector machines (SVM), and Multi-layer perceptron (MLP). Experiments were conducted using both a widely-utilized dataset and our self-collected dataset. The experimental results show that our method by combining signal processing and ML had only 5% error for HR estimation using low-frequency PPG data. Moreover, our analysis showed that DT models with 10 to 20 input features usually have good accuracy, while are several magnitude smaller in model sizes and faster in inference time.

cs.LG↗

arXiv2023

Efficient and Direct Inference of Heart Rate Variability using Both Signal Processing and Machine Learning

Heart Rate Variability (HRV) measures the variation of the time between consecutive heartbeats and is a major indicator of physical and mental health. Recent research has demonstrated that photoplethysmography (PPG) sensors can be used to infer HRV. However, many prior studies had high errors because they only employed signal processing or machine learning (ML), or because they indirectly inferred HRV, or because there lacks large training datasets. Many prior studies may also require large ML models. The low accuracy and large model sizes limit their applications to small embedded devices and potential future use in healthcare. To address the above issues, we first collected a large dataset of PPG signals and HRV ground truth. With this dataset, we developed HRV models that combine signal processing and ML to directly infer HRV. Evaluation results show that our method had errors between 3.5% to 25.7% and outperformed signal-processing-only and ML-only methods. We also explored different ML models, which showed that Decision Trees and Multi-level Perceptrons have 13.0% and 9.1% errors on average with models at most hundreds of KB and inference time less than 1ms. Hence, they are more suitable for small embedded devices and potentially enable the future use of PPG-based HRV monitoring in healthcare.

cs.LG↗