arXiv subjects

Haoran Qi

Publications and source records attributed to Haoran Qi.

6 recordsLinked to original sources

arXiv2026

Analytical properties of the principal clamped transmission eigenpair for a planar region

This paper investigates the analytical properties of the principal eigenpair for the clamped transmission eigenvalue problem, which arises in the context of biharmonic (i.e. flexural wave) scattering by a clamped planar obstacle. By deriving a suitable Rayleigh quotient, we provide rigorous proofs for several fundamental properties that were previously only observed through numerical experiments. One of the results we have shown here is that the first eigenvalue is monotone decreasing with respect to the domain. Furthermore, we prove that the corresponding eigenfunction is of a single sign, a property analogous to the principal eigenfunction of the Dirichlet eigenvalues of the Laplacian. Another key result is a Faber--Krahn type inequality, establishing that the disk minimizes the principal eigenvalue among all domains of a given measure. The theoretical results are supported by a comprehensive numerical investigation.

math.AP↗

arXiv2026

Faster Algorithms for Disjoint Paths in DAGs and Two Disjoint Shortest Paths

For $k$ vertex-disjoint paths with prescribed endpoints in a directed acyclic graph (DAG), the $O(mn^{k-1})$-time pebbling algorithm of Fortune, Hopcroft, and Wyllie [TCS 1980] has remained the fastest for every $k\geq3$ for over four decades, even when the paths must be shortest. We break this bound for every $k\geq3$ with randomized algorithms running in expected $O_k(m+n^{k-3+ω+\varepsilon})$ time for every $\varepsilon>0$, where $ω<2.372$ is the matrix multiplication exponent; this is $O_k(m+n^{k-0.62})$. For two disjoint shortest paths, we find the paths as fast as we detect them: in expected linear time on DAGs and on undirected graphs with polynomially bounded integer weights, and in expected $O(\min\{mn,n^{ω+\varepsilon}\})$ time on directed graphs whose cycles have positive weight, which on dense graphs is $o(mn)$ even for detection. All algorithms evaluate a polynomial whose monomials are the solutions: a new first-collision circuit speeds up the evaluation in DAGs, and a correlated extraction step at cuts crossed once by every path finds a solution at the cost of a constant number of evaluations.

cs.DS↗

arXiv2026

$\ell_p$-Norm Maximization over Zonotopes Is W[1]-Hard

We study $\ell_p$-norm maximization over zonotopes given by rational generators, with input length $L$. For fixed $p=a/b>1$, the exact Turing baseline runs in $n^{O(d)}b^{O(d)}\mathrm{poly}(L)$ time, but fixed-parameter tractability in the ambient dimension $d$ was open [FGHS25]. We prove W[1]-hardness and, under the Exponential Time Hypothesis (ETH), exclude $ρ_p(d)L^{o(d)}$ time, even for $5$-sparse generators, by encoding binary CSP constraints with normalized positive cap generators. We also give a deterministic $(1-\varepsilon)$-approximation with $\varepsilon^{-(d-1)/2}$ dependence and, among algorithms with fixed-degree polynomial dependence on $L$, rule out $(1/\varepsilon)^{o(d)}$ dependence under ETH. Support-function duality transfers the results to positive-output two-layer ReLU networks.

cs.CC↗

arXiv2026

A Sc2C2@C88 cluster based ultra-compact multi-level probabilistic bit for matrix multiplication

Information units are progressively approaching the fundamental physical limits of the integration density, including in terms of extremely small sizes, multistates and probabilistic traversal. However, simultaneously encompassing all of these characteristics in a unit remains elusive. Here, via real-time in situ electrical monitoring, we clearly observed stochastic alterations of multiple conductance states in Sc2C2@C88. The true random bit sequence generated exhibited an autocorrelation function whose confidence interval fell within \pm 0.02, demonstrating high-quality randomness. The alterations of multiple conductance states are controllable, that is, whose probability distributions could traverse from 0 to 1, enabling us to factorize 551 into its prime factors. Furthermore, we proposed a matrix-chain multiplication scheme and experimentally verified the multiplication of two 4 \times 4 state-transition matrices with a small maximum error < 0.05. Combined with theoretical calculations, the stochastic but controllable multistates are probably attributed to the rich energy landscape, which could be stepwise changed by the electric field. Our findings reveal extremely small multi-level probabilistic bit for matrix multiplication, which pave the way for ultracompact intelligent electronic devices.

cond-mat.mtrl-sci↗

arXiv2025

Distributed Incast Detection in Data Center Networks

Incast traffic in data centers can lead to severe performance degradation, such as packet loss and increased latency. Effectively addressing incast requires prompt and accurate detection. Existing solutions, including MA-ECN, BurstRadar and Pulser, typically rely on fixed thresholds of switch port egress queue lengths or their gradients to identify microburst caused by incast flows. However, these queue length related methods often suffer from delayed detection and high error rates. In this study, we propose a distributed incast detection method for data center networks at the switch-level, leveraging a probabilistic hypothesis test with an optimal detection threshold. By analyzing the arrival intervals of new flows, our algorithm can immediately determine if a flow is part of an incast traffic from its initial packet. The experimental results demonstrate that our method offers significant improvements over existing approaches in both detection speed and inference accuracy.

cs.NI↗

arXiv2025

Active biphasic heat transfer enhancement in vertical natural convection

Vertical natural convection (VC), often cannot meet the high heat transfer demands due to the inherent misalignment of the direction of buoyancy (vertical) with the direction of the heat transfer (horizontal). Here we applied a novel strategy on a water based VC system to enhance the heat transfer. By adding 2% of the total volume with a low-boiling-temperature liquid (HFE-7000) and introducing a gas-liquid layer on top of the VC cell, we create a self-sustained state of pseudo-turbulence with evaporating, circulating and condensing biphasic bubbles. The system achieves 246% heat transfer enhancement at constant superheat $T_{sup}\approx6.4 \text{K}$ when the liquid in the full nucleate boiling state. Using shadowgraphy and Laser Doppler Anemometry (LDA) methods, we validate that the bubbles and biphasic particles induced agitation enhances the heat flux and modifies the temperature field of the heat transfer.

physics.flu-dyn↗