arXiv subjects

Jie Han

Publications and source records attributed to Jie Han.

At least 37 records · Page 2Linked to original sources

arXiv2026

Driving Condition-Aware Multi-Agent Integrated Power and Thermal Management for Hybrid Electric Vehicles

Effective co-optimization of energy management strategy (EMS) and thermal management (TM) is crucial for optimizing fuel efficiency in hybrid electric vehicles (HEVs). Driving conditions significantly influence the performance of both EMS and TM in HEVs. This study presents a novel driving condition-aware integrated thermal and energy management (ITEM) framework. In this context, after analyzing and segmenting driving data into micro-trips, two primary features (average speed and maximum acceleration) are measured. Using the K-means approach, the micro-trips are clustered into three main groups. Finally, a deep neural network is employed to develop a real-time driving recognition model. An ITEM is then developed based on multi-agent deep reinforcement learning (DRL), leveraging the proposed real-time driving recognition model. The primary objectives are to improve the fuel economy and reduce TM power consumption while maintaining a pleasant cabin temperature for passengers. Our simulation results illustrate the effectiveness of the suggested framework and the positive impact of recognizing driving conditions on ITEM, improving fuel economy by 16.14% and reducing TM power consumption by 8.22% compared to the benchmark strategy.

eess.SY↗

arXiv2026

On the Keevash-Knox-Mycroft Conjecture

Given $1\le \ell 1-(1-1/k)^{k-\ell}$ and verified the case $\ell=k-1$. In this paper we show that this problem can be reduced to the study of the minimum $\ell$-degree condition forcing the existence of fractional perfect matchings. Together with existing results on fractional perfect matchings, this solves the conjecture of Keevash, Knox and Mycroft for $\ell\ge 0.4k$. Moreover, we also supply an algorithm that outputs a perfect matching, provided that one exists.

math.CO↗

arXiv2026

Extrapolative Quantum Error Mitigation in Continuous-Variable Systems beyond the Training Horizon

Continuous-variable (CV) quantum systems provide a versatile platform for quantum information processing, in which quantum states can be represented in the quadrature phase space. In realistic implementations, environmental noise, primarily photon loss and dephasing, progressively degrades these states. Machine-learning-based quantum error mitigation (QEM) has recently emerged as a promising approach to suppress such noise; however, existing methods are typically limited to the training horizon and require training data that cover the entire evolution, which is experimentally demanding. Here we introduce a framework for extrapolative quantum error mitigation based on a time-conditioned Swin Transformer. By explicitly embedding the evolution time via adaptive layer normalization, the model learns a correction map that accounts for the continuous accumulation of noise while capturing nonlocal phase-space correlations. Numerical simulations under both Markovian and non-Markovian noise demonstrate accurate state recovery in the long-time regime, where existing approaches deteriorate. Our results establish extrapolative QEM as a practical route to mitigating noise in CV quantum systems without exhaustive training data.

quant-ph↗

arXiv2026

Temperature-Aware Scheduling of LLM Inference in Large-Scale Geo-Distributed Edge Data Centers with Distributed Optimization

The environmental impact of Large Language Models (LLMs) on data centers hosting these models is becoming a significant concern. While many efforts have focused on reducing the substantial training overhead of LLMs, carbon and water consumption during the inference phase can often surpass the costs associated with their training. The cooling systems of data centers are crucial in this context, but they are frequently modeled with a location-independent efficiency term. However, their energy efficiency is highly influenced by ambient temperature, which can vary significantly across different geographical locations. Leveraging this temperature diversity can help reduce total cooling energy costs and improve the performance of edge data centers. To address these critical sustainability issues related to LLMs, this study proposes a temperature-aware approach that co-optimizes LLM energy costs, carbon emissions, time-to-first token, and water consumption. The approach employs a distributed optimization algorithm based on an alternating direction method of multipliers, aimed at enhancing the sustainability of LLM hosting across geo-distributed edge data centers in Australia. Our method demonstrates reductions in cooling energy consumption and improves overall cost efficiency for geo-distributed cloud environments.

eess.SY↗

arXiv2026

Leveraging Quantum Annealing for Large-Scale Household Energy Scheduling with Hydrogen Storage

Hydrogen integration into microgrids facilitates the absorption of intermittencies from renewable energy resources. However, significant challenges remain due to complex optimization problems, particularly in large-scale applications involving multiple fuel cells (FCs) and electrolyzers (ELs) with numerous binary decision variables. This paper presents a hierarchical quantum annealing (QA) model predictive control-based power allocation framework aimed at accelerating these optimization problems. First, in a day-ahead stage, the framework determines the startup and shutdown of the FCs and ELs. The short-term stage then refines the output power of the FCs and the hydrogen generation rate of the ELs. The feasibility is evaluated through a case study consisting of multiple households in Australia. Our findings demonstrate that while the traditional optimization approach performs satisfactorily in scenarios with a small number of households, the QA approach becomes more appropriate and effectively solves the problem within an acceptable range as the number of connected households increases.

eess.SY↗

arXiv2026

A parameterized algorithm for $K_r$-factors in graphs of high minimum degree

A $K_r$-factor of a graph $G$ is a collection of vertex-disjoint $r$-cliques covering $V(G)$. We prove the following algorithmic version of the classical Hajnal--Szemerédi Theorem in graph theory, when $r$ is considered as a constant. Given $r, c, n\in \mathbb{N}$ such that $n\in r\mathbb N$, let $G$ be an $n$-vertex graph with minimum degree at least $(1-1/r)n - c$. Then there is an algorithm with running time $2^{c^{O(1)}} n^{O(1)}$ that outputs either a $K_r$-factor of $G$ or a certificate showing that none exists, namely, this problem is fixed-parameter tractable in $c$. On the other hand, it is known that if $c = n^{\varepsilon}$ for fixed $\varepsilon \in (0,1)$, the problem is \texttt{NP-C}. By taking the complement, our result yields a similar result on the equitable $Δ$-colorings of graphs of maximum degree $Δ+c$, for $Δ\in [n/r, n/(r-1)]$. We indeed establish characterization theorems for this problem, showing that the existence of a $K_r$-factor is equivalent to the existence of certain class of $K_r$-tilings of size $o(n)$, whose existence can be searched by the color-coding technique developed by Alon--Yuster--Zwick.

math.CO↗

arXiv2026

The perturbation threshold of degenerate graphs

We show that for any $d\ge 2$ and $Δ>0$ there exists $η>0$ such that the following holds: Let $G$ be an $n$-vertex graph with at least $Ω(n^2)$ edges and let $H$ be an $n$-vertex $d$-degenerate graph with maximum degree at most $Δ$. Then with high probability, $G \cup G(n, n^{-1/d - η})$ contains a copy of $H$. We also prove that the same conclusion extends to $d$-regular graphs with $d\ge 4$ satisfying a certain edge expansion property, with the threshold improved to $n^{-2/d - η}$. Such a property is satisfied by almost all $d$-regular graphs and for even $d$, by the $(d/2)$-th power of a Hamilton cycle.

math.CO↗

arXiv2026

Traffic-aware Hierarchical Integrated Thermal and Energy Management for Connected HEVs

The energy and thermal management systems of hybrid electric vehicles (HEVs) are inherently interdependent. With the ongoing deployment of intelligent transportation systems (ITSs) and increasing vehicle connectivity, the integration of traffic information has become crucial for improving both energy efficiency and thermal comfort in modern vehicles. To enhance fuel economy, this paper proposes a novel traffic-aware hierarchical integrated thermal and energy management (TA-ITEM) strategy for connected HEVs. In the upper layer, global reference trajectories for battery state of charge (SOC) and cabin temperature are planned using traffic flow speed information obtained from ITSs. In the lower layer, a real-time model predictive control (MPC)-based ITEM controller is developed, which incorporates a novel Transformer-based speed predictor with driving condition recognition (TF-DCR) to enable anticipatory tracking of the reference trajectories. Numerical simulations are conducted under various driving cycles and ambient temperature conditions. The results demonstrate that the proposed TA-ITEM approach outperforms conventional rule-based and MPC-SP approaches, with average fuel consumption reductions of 56.36\% and 5.84\%, respectively, while maintaining superior thermal regulation and cabin comfort. These findings confirm the effectiveness and strong generalization capability of TA-ITEM and underscore the advantages of incorporating traffic information.

eess.SY↗

arXiv2026

Exact minimum co-degree conditions for $\ell$-Hamiltonicity in hypergraphs

Suppose $1\le \ell <k$ such that $(k-\ell)\nmid k$. Given an $n$-vertex $k$-uniform hypergraph $\mathcal H$, for all $k/2<\ell< 3k/4$ and sufficiently large $n\in (k-\ell)\mathbb N$, we prove that if $\mathcal H$ has minimum co-degree at least $\frac{n}{\lceil \frac{k}{k-\ell}\rceil (k-\ell)}$, then $\mathcal H$ contains a Hamilton $\ell$-cycle, which partially verifies a conjecture of Han and Zhao and (partially) resolves a problem of Rödl and Ruciński. Moreover, we show that assuming minimum co-degree $\frac{n}{\lceil \frac{k}{k-\ell}\rceil (k-\ell)}+\frac{k^2}2$ is enough for all $\ell$.

math.CO↗

arXiv2025

High Torque Density PCB Axial Flux Permanent Magnet Motor for Micro Robots

Quasi-direct-drive (QDD) actuation is transforming legged and manipulator robots by eliminating high-ratio gearboxes, yet it demands motors that deliver very high torque at low speed within a thin, disc-shaped joint envelope. Axial-flux permanent-magnet (AFPM) machines meet these geometric and torque requirements, but scaling them below a 20mm outer diameter is hampered by poor copper fill in conventional wound stators, inflating resistance and throttling continuous torque. This paper introduces a micro-scale AFPM motor that overcomes these limitations through printed-circuit-board (PCB) windings fabricated with advanced IC-substrate high-density interconnect (HDI) technology. The resulting 48-layer stator-formed by stacking four 12-layer HDI modules-achieves a record 45\% copper fill in a package only 5mm thick and 19mm in diameter. We perform comprehensive electromagnetic and thermal analyses to inform the motor design, then fabricate a prototype whose performance characteristics are experimentally verified.

cs.RO↗

arXiv2025

Robustness for expander graphs

We study robust versions of properties of $(n,d,λ)$-graphs, namely, the property of a random sparsification of an $(n,d,λ)$-graph, where each edge is retained with probability $p$ independently. We prove such results for the containment problem of perfect matchings, Hamiltonian cycles, and triangle factors. These results address a series of problems posed by Frieze and Krivelevich. First we prove that given $γ>0$, for sufficient large $n$, any $(n,d,λ)$-graph $G$ with $λ=o(d)$, $d=Ω(\log n)$ and $p\ge\frac{(1+γ)\log n}{d}$, $G\cap G(n,p)$ contains a Hamiltonian cycle (and thus a perfect matching if $n$ is even) with high probability. This result is asymptotically optimal. Moreover, we show that for sufficient large $n$, any $(n,d,λ)$-graph $G$ with $λ=o(\frac{d^2}{n})$, $d=Ω(n^{\frac{5}{6}}\log^{\frac{1}{2}}n)$ and $p\gg d^{-1}n^{\frac{1}{3}}\log^{\frac{1}{3}} n$, $G\cap G(n,p)$ contains a triangle factor with high probability. Here, the restrictions on $p$ and $λ$ are asymptotically optimal. Our proof for the triangle factor problem uses the iterative absorption approach to build a spread measure on the triangle factors, and we also prove and use a coupling result for triangles in the random subgraph of an expander $G$ and the hyperedges in the random subgraph of the triangle-hypergraph of $G$.

math.CO↗

arXiv2025

Powers of Hamilton cycles in oriented and directed graphs

The Pósa--Seymour conjecture determines the minimum degree threshold for forcing the $k$th power of a Hamilton cycle in a graph. After numerous partial results, Komlós, Sárközy and Szemerédi proved the conjecture for sufficiently large graphs. In this paper we focus on the analogous problem for digraphs and for oriented graphs. We asymptotically determine the minimum total degree threshold for forcing the square of a Hamilton cycle in a digraph. We also give a conjecture on the corresponding threshold for $k$th powers of a Hamilton cycle more generally. For oriented graphs, we provide a minimum semi-degree condition that forces the $k$th power of a Hamilton cycle; although this minimum semi-degree condition is not tight, it does provide the correct order of magnitude of the threshold. Turán-type problems for oriented graphs are also discussed.

math.CO↗

arXiv2025

Clique-factors in graphs with low $K_{\ell}$-independence number

Given $r\in \mathbb{N}$ with $r\geq 4$, we show that there exists $n_0\in \mathbb{N}$ such that for every $n\geq n_0$, every $n$-vertex graph $G$ with $δ(G)\geq (\frac{1}{2}+o(1))n$ and $α_{r-2}(G)=o(n)$ contains a $K_{r}$-factor. This resolves the first open case of a question proposed by Nenadov and Pehova, and reiterated by Knierm and Su. We further introduce two lower bound constructions that, along with some known results, fully resolve a question presented by Balogh, Molla, and Sharifzadeh.

math.CO↗

arXiv2025

Perturbation of dense graphs

In the past two decades, various properties of randomly perturbed/augmented (hyper)graphs have been intensively studied, since the model was introduced by Bohman, Frieze and Martin in 2003. The model usually considers a deterministic graph $G$ with minimum degree condition, perturbed/augmented by a binomial random graph $G(n,p)$ on the same vertex set. In this paper, we show that for many problems of finding spanning subgraphs, one can indeed relax the minimum degree condition to a density condition. This includes the embedding problem for $F$-factors when $F$ is not a forest, graphs with bounded maximum degree, $r$-th power of $k$-uniform tight Hamilton cycles for $r,k\ge 2$, and $k$-uniform Hamilton $\ell$-cycles for $\ell\in[2,k-1]$. These results strengthen the results of Balogh, Treglown, and Wagner, of Böttcher, Montgomery, Parczyk, and Person, and of Chang, Han and Thoma.

math.CO↗

arXiv2025

Transversal packings in families of percolated hypergraphs

Let $F$ be a strictly $1$-balanced $k$-graph on $s$ vertices with $t$ edges and $δ_{F,d}^T$ be the infimum of $δ>0$ such that for every $α>0$ and sufficiently large $n\in \mathbb{N}$, every $k$-graph system $\mathbf H=\{H_{1}, H_{2}, \dots ,H_{tn}\}$ on the same $sn$ vertices with $δ_d(H_i)\ge (δ+α)\binom{sn-d}{k-d}$, $i\in [tn]$ contains a transversal $F$-factor, that is, an $F$-factor consisting of exactly one edge from each $H_i$. In this paper we prove the following result. Let $\mathbf{H} =\{H_{1}, H_{2}, \dots ,H_{tn}\}$ be a $k$-graph system where each $H_{i}$ is an $sn$-vertex $k$-graph with $δ_d(H_i)\ge (δ_{F,d}^T+α)\binom{sn-d}{k-d}$. Then with high probability $\mathbf{H}(p) :=\{H_{1}(p), H_{2}(p), \dots ,H_{tn}(p)\}$ contains a transversal $F$-factor, where $H_i(p)$ is a random subhypergraph of $H_i$ and $p=Ω(n^{-1/d_1(F)-1}(\log n)^{1/t})$. This extends a recent result by Kelly, Müyesser and Pokrovskiy, and independently by Joos, Lang and Sanhueza-Matamala. Moreover, the assumption on $p$ is best possible up to a constant. Along the way, we also obtain a spread version of a result of Pikhurko on perfect matchings in $k$-partite $k$-graphs.

math.CO↗

arXiv2025

Turán number of complete multipartite graphs in multipartite graphs

In this paper we study a multi-partite version of the Erdős--Stone theorem. Given integers $r<k$ and $t\ge 1$, let $\text{ex}_k(n, K_{r+1}(t))$ be the maximum number of edges of $K_{r+1}(t)$-free $k$-partite graphs with $n$ vertices in each part, where $K_{r+1}(t)$ is the complete $(r+1)$-partite graph with $t$ vertices in each part. We determine the exact value of $\text{ex}_k(n, K_{r+1}(t))$ for $t\le 3$, $r<k\le 2r$ and sufficiently large $n$. We also characterize all extremal graphs for $r, k$ such that $r$ divides $k$, analogous to a result of Erd\H os and Simonovits on forbidding $K_{r+1}(t)$ in general graphs.

math.CO↗

arXiv2025

Supersaturation of odd linear cycles

An $r$-uniform linear cycle of length $\ell$, denoted by $C^r_{\ell}$, is an $r$-graph with $\ell$ edges $e_1,e_2,\dots,e_{\ell}$ where $e_i=\{v_{(r-1)(i-1)},v_{(r-1)(i-1)+1},\dots,v_{(r-1)i}\}$ (here $v_0=v_{(r-1)\ell}$). For $0<δ<1$ and $n$ sufficiently large, we show that every $n$-vertex $r$-graph $G$ with $n^{r-δ}$ edges contains at least $n^{(r-1)(2\ell+1)-δ(2\ell+1+\frac{4\ell-1}{(r-1)(2\ell+1)-3})-o(1)}$ copies of $C^r_{2\ell+1}$. Further, conditioning on the existence of dense high-girth hypergraphs, we show that there exists $n$-vertex $r$-graphs with $n^{r-δ}$ edges and at most $n^{(r-1)(2\ell+1)-δ(2\ell+1+\frac{1}{(r-1)\ell-1})+o(1)}$ copies of $C^r_{2\ell+1}$.

math.CO↗

arXiv2025

TempoGPT: Enhancing Time Series Reasoning via Quantizing Embedding

Multi-modal language model has made advanced progress in vision and audio, but still faces significant challenges in dealing with complex reasoning tasks in the time series domain. The reasons are twofold. First, labels for multi-modal time series data are coarse and devoid of analysis or reasoning processes. Training with these data cannot improve the model's reasoning capabilities. Second, due to the lack of precise tokenization in processing time series, the representation patterns for temporal and textual information are inconsistent, which hampers the effectiveness of multi-modal alignment. To address these challenges, we propose a multi-modal time series data construction approach and a multi-modal time series language model (TLM), TempoGPT. Specially, we construct multi-modal data for complex reasoning tasks by analyzing the variable-system relationships within a white-box system. Additionally, proposed TempoGPT achieves consistent representation between temporal and textual information by quantizing temporal embeddings, where temporal embeddings are quantized into a series of discrete tokens using a predefined codebook; subsequently, a shared embedding layer processes both temporal and textual tokens. Extensive experiments demonstrate that TempoGPT accurately perceives temporal information, logically infers conclusions, and achieves state-of-the-art in the constructed complex time series reasoning tasks. Moreover, we quantitatively demonstrate the effectiveness of quantizing temporal embeddings in enhancing multi-modal alignment and the reasoning capabilities of TLMs. Code and data are available at https://github.com/zhanghaochuan20/TempoGPT.

cs.LG↗