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Jiajie Chen

Publications and source records attributed to Jiajie Chen.

At least 19 recordsLinked to original sources

MeRoPE: Metric Rotary Position Embedding for Camera-Controlled Video Generation

In camera-controlled video generation, geometry-aware positional encodings condition tokens on camera extrinsics and per-token viewing rays. Existing schemes, however, have a scale-dependent failure mode on real-world metric camera trajectories: homogeneous projective encodings cause attention logits and feature norms to grow unbounded with physical translation baselines. We propose MeRoPE (Metric Rotary Position Embedding), a norm-preserving relative camera encoding for attention. MeRoPE encodes relative orientations between calibrated viewing rays with orthogonal rotation blocks, maps raw metric displacements into multi-frequency rotary phases, and adds a disparity-anchored correspondence prior along the epipolar arc. This design strictly preserves feature norms, bounds pre-softmax attention logits regardless of the physical translation scale, and maintains exact invariance to global rigid coordinate changes. Across nuScenes and PanShot, which cover large-baseline trajectories and diverse camera optics, respectively, MeRoPE achieves stronger camera control than prior encodings, with the best consistency between generated camera motion and conditioning poses in both rotation and translation. Code will be made publicly available.

cs.CV

Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data I: Analysis

Inspired by numerical evidence of a potential 3D Euler singularity \cite{luo2014potentially,luo2013potentially-2}, we prove finite-time, nearly self-similar blowup of the 2D Boussinesq and 3D axisymmetric Euler equations with smooth initial data of finite energy and boundary. The proof encounters several essential difficulties. One of the essential difficulties is to control a number of nonlocal terms that do not seem to offer any damping effect. Another essential difficulty is that the strong advection normal to the boundary introduces a large growth factor for the perturbation when using weighted $L^2$ or $H^k$ estimates. We overcome these difficulties by combining weighted $L^\infty$ estimates and weighted $C^{1/2}$ estimates, and by developing sharp functional inequalities using the symmetry properties of the kernels and some techniques from optimal transport. Moreover, we decompose the linearized operator into a leading order operator and a finite-rank operator. We design the leading order operator to obtain sharp stability estimates. The contribution from the finite-rank operator to linear stability is estimated by constructing approximate space-time solutions. These ingredients enable us to establish the nonlinear stability of the approximate self-similar profile and to prove stable nearly self-similar blowup.

math.AP

Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data II: Rigorous Numerics

This is Part II of our paper in which we prove finite time blowup of the 2D Boussinesq and 3D axisymmetric Euler equations with smooth initial data of finite energy and boundary. In Part I of our paper \cite{ChenHou2023a}, we establish an analytic framework to prove nonlinear stability of an approximate self-similar blowup profile using a combination of weighted $L^\infty$ and weighted $C^{1/2}$ energy estimates. We reduce proving nonlinear stability to verifying several inequalities for the constants in the energy estimate which depend on the approximate steady state and the weights in the energy functional only. In Part II of our paper, we construct approximate space-time solutions with rigorous error control, which are used to obtain sharp stability estimates of the linearized operator in Part I. We also obtain sharp estimates of the regular part of the velocity using numerical integration with computer assistance. These results enable us to verify that the constants in the energy estimate obtained in Part I \cite{ChenHou2023a} indeed satisfy the inequalities for nonlinear stability. The nonlinear stability further implies the finite time singularity of the axisymmetric 3D Euler equations with smooth initial data and boundary.

math.AP

A clarification on the distinction between nonlocal error and profile residual error in a computer-assisted proof of 3D Euler singularity

In \cite{zhang2025dimension}, the author discusses the applicability of a nonexistence result for self-similar profiles to the Hou--Luo scenario and raises questions about the approximate self-similar profile constructed in \cite{ChenHou2023a,ChenHou2023b}. In this note, we clarify two main points. First, the far-field discrepancy identified in \cite{zhang2025dimension} is the raw nonlocal Poisson error, not the profile residual error used in the stability proof of \cite{ChenHou2023a,ChenHou2023b}. The relevant nonlocal contribution to the profile residual contains the nonlocal velocity error multiplied by additional decaying factors, which provide crucial smallness in the far field estimates. Second, we examine the figure-based evidence used in \cite[Remark 2.4]{zhang2025dimension} to support the applicability of the assumption in \cite[Proposition 2.3(i)]{zhang2025dimension}, and show that the same grid-point data do not support that interpretation. Thus the comparisons and figure-based evidence in \cite{zhang2025dimension} neither invalidate the residual estimates in \cite{ChenHou2023a,ChenHou2023b} nor justify the claimed applicability of the angular-increase assumption to the Hou--Luo scenario.

math.AP

The Note-Chord-Voice Framework: Structured Source Separation and Causal Inference for EV Charging Data

Real-world EV charging data exhibit three interlocking pathologies: hardware fragmentation (network timeouts and billing resets split sessions), physical violations (independent energy/duration models produce impossible states like 50 kWh in 10 min on a 7 kW charger), and collider bias (clustering on post-treatment outcomes opens backdoor paths for price elasticity). We propose the Note-Chord-Voice framework, a music-inspired, axiom-driven pipeline that separates data cleaning (Repair Chords), structural pattern discovery (Harmonic Chords), descriptive source separation (NMF Voices), and causal inference into distinct, falsifiable stages. Key innovations: (i) falsification gates (A1-A5, G3, G10) that test data suitability before modeling; (ii) Gamma-initialized NMF with input rescaling for convergence stability from STL decomposition; (iii) tag-based coupon grading (A/B/C/D) to isolate quasi-random treatment from night-time confounders and targeted promotions; (iv) separate per-voice OLS to avoid simplex collinearity; (v) Foote novelty curves for structural regime detection. Applied to the Jiangmen dataset (495,707 sessions, 20 stations, from July 2024 to March 2025), all core axioms pass except G3 (no strong 168 h cycle). NMF achieves R^2=0.9921; the physically constrained duration model yields aggregate R^2=0.5409. Two voices are price-sensitive (beta = -11 to -14 min, p<0.001), of which one is stable (Voice 3, beta=-14.16) and one treatment-driven (Voice 1, beta=-11.10); only the stable voice supports causal claims. Counterfactual simulation shows targeting discounts to price-sensitive voices recovers 52.8% of discount expenditures (~0.85M CNY/year); restricting to the single stable price-sensitive voice yields a more conservative estimate.

eess.SP

Analytic finite-rank corrections for singularly weighted estimates in a computer-assisted proof of 3D Euler singularity

Computer-assisted proofs of self-similar singularity formation for fluid equations often rely on numerically constructed approximate profiles. One effective approach to establishing stability of perturbations around a numerically constructed profile is to perform weighted energy estimates with singular weights near the singularity. However, the weighted norms require exact local vanishing conditions that are not automatically preserved by the equations nor the numerical construction. In this paper, we review an analytic low-rank correction method first developed in [ChenHou2023a,ChenHou2023b] to overcome this difficulty. The numerical step determines coefficients, rigorous bounds, and low-order defect modes in explicit global basis representations, while the required vanishing conditions are enforced analytically through low-rank corrections derived from Taylor expansions of the relevant quantities represented in a smooth basis. For completeness, we briefly review the singularly weighted estimates and a quantitative finite-rank perturbation method in the 2D Boussinesq / 3D Euler stability argument, where singular weights and the required vanishing order arise. Against this background, we formulate the local correction principle in a simplified setting, explain the correction of the residual error in numerical constructions of approximate space-time solutions and the stream function, and discuss its broader applicability to computer-assisted stability analysis for nonlocal PDEs.

math.AP

A new class of Euler explosions

We study the global-in-time continuation, past the singularity, of the smooth, non-isentropic, radially symmetric imploding solutions of the compressible Euler equations recently constructed by Chen, Shkoller, and Vicol. In three space dimensions, for all physically relevant adiabatic exponents $γ>1$, we consider the Euler solution that evolves smoothly until an implosion singularity forms at the origin at time $t=0$. We then prove that this solution can be uniquely continued for $t>0$ as a reflected outward-propagating shock, sometimes called a reflected blast wave. For $t>0$, the continuation is a globally forward self-similar weak solution of the Euler equations, selected by the Rankine--Hugoniot conditions and the Lax entropy inequality; it is smooth away from the expanding shock sphere and the spatial origin. The structure at the center of symmetry distinguishes these explosions from the classical Guderley reflected shock. In Guderley's continuation, the reflected blast wave leaves a point vacuum at the origin, where the density vanishes. The solutions constructed here exhibit the opposite behavior: for every fixed $t>0$ the density is unbounded at $r=0$ (though it remains locally integrable), while the pressure stays bounded and the temperature vanishes there.

math.AP

Asymptotically Self-Similar Blowup for 3D Incompressible Euler with $C^{1, 1/3-}$ Velocity II: 3D Profiles, Blowup, and Limiting behavior

For any $α\in (0,1/3)$, we construct exact $C^α$ self-similar blowup profiles for the vorticity of the 3D incompressible Euler equation without swirl, and build on them to prove asymptotically self-similar blowup from $C_c^α$ initial vorticity and $C^{1,α}\cap L^2$ initial velocity. Moreover, we provide a complete characterization of the limiting behavior of the $C^α$ vorticity profiles and the associated blowup solutions as $α\to(1/3)^-$. Specifically, as $α\to(1/3)^-$, the spatial blowup rate $\mathsf{c}_{\mathsf{x},α}$ diverges to $\infty$, while the $C^α$ vorticity profile $Ω_{*,α}^θ$ asymptotically factorizes and converges strongly in a weighted $L^\infty$ norm to a nonzero constant multiple of $r^{1/3}\bar W_{1/3}(z)$, where $\bar W_{1/3}$ is a $C^\infty$ 1D blowup profile. Our construction is inspired by the Hou--Zhang blowup scenario. Using a fixed-point argument, we lift the $C^\infty$ blowup profiles for a 1D model constructed in the companion work [11] to exact 3D blowup profiles. To overcome the lack of $r$-directional decay in the approximate profile and capture the anisotropic structure, we develop a family of anisotropic weighted estimates and introduce a crucial integration-by-parts method along trajectories that exploits the equation twice. We then develop a finite codimension stability argument in a low-regularity setting to prove stability of the 3D profiles and establish asymptotically self-similar blowup. This blowup result is sharp in view of the global regularity theory for axisymmetric Euler without swirl with $ C_c^α$ initial vorticity for all $α\geq 1/3$. To the best of our knowledge, our results provide the first example in which a singularity from a 1D nonlocal fluid model is lifted to construct blowup for incompressible fluid equations in $\mathbb{R}^2$ or $\mathbb{R}^3$.

math.AP

Asymptotically Self-Similar Blowup for 3D Incompressible Euler with $C^{1, 1/3-}$ Velocity I: $C^{\infty}$ 1D Limiting Profiles

We consider a one-parameter family of 1D models for the 3D axisymmetric incompressible Euler equation with $C^α$ vorticity and without swirl near the symmetry axis. For $α= \frac13$, we impose a crucial normalization and construct a $C^{\infty}$ self-similar blowup profile with unbounded 1D stream function and infinite spatial blowup rate, using a fixed-point argument around a numerically constructed approximate profile. For $α< \frac13$ sufficiently close to $\frac13$, we perturb the $\frac13$-profile and analytically construct exact smooth 1D profiles with bounded stream function and finite spatial blowup rate. In the companion work~\cite{chen2026eulerII}, for any $α\in (0,\frac13)$, we lift these 1D blowup profiles to construct exact $C^{1,α}$ self-similar blowup profiles for 3D Euler, and build on them to prove sharp asymptotically self-similar blowup for 3D axisymmetric Euler without swirl from $C_c^α$ initial vorticity and $C^{1,α} \cap L^2$ initial velocity.

math.AP

Smooth and stable Euler implosions

We construct a new class of self-similar implosion profiles for the multi-dimensional compressible Euler equations. These profiles are smooth, genuinely non-isentropic, radially/spherically symmetric, and have explicit (closed-form) similarity exponents. We prove that the exact Euler solution corresponding to the ground state implosion profile is stable to radially symmetric perturbations, as a solution to the full nonlinear compressible Euler equations, modulo a one-dimensional compatibility condition on the initial data. For perturbations of the Euler solution corresponding to the ground state implosion profile of a monatomic or diatomic gas, that do not obey any symmetry assumptions, we provide a complete characterization of the set of initial data that yield nonlinear stability.

math.AP

Finite time singularities in the Landau equation with very hard potentials

We consider the inhomogeneous Landau equation with $γ\in (\sqrt{3},2]$ and construct smooth, strictly positive initial data that develop a finite time singularity. The $C^α$-norm of the distribution function blows up for every $α>0$, whereas its $L^{\infty}$-norm remains uniformly bounded. In self-similar variables, the solution becomes asymptotically hydrodynamic - the distribution function converges to a local Maxwellian, while the hydrodynamic fields develop an asymptotically self-similar implosion whose profile coincides with a smooth imploding profile of the compressible Euler equations. To our knowledge, this provides the first example of a collisional kinetic model which is globally well-posed in the homogeneous setting, but admits finite time singularities for inhomogeneous data.

math.AP

The Fast Stochastic Matching Pursuit for Neutrino and Dark Matter Experiments

Photomultiplier tubes (PMTs) are widely deployed at neutrino and dark matter experiments for photon counting. When multiple photons hit a PMT consecutively, their photo-electron (PE) pulses pile up to hinder the precise measurements of the count and timings. We introduce Fast Stochastic Matching Pursuit (FSMP) to analyze the PMT signal waveforms into individual PEs with the strategy of reversible-jump Markov-chain Monte Carlo. We demonstrate that FSMP improves the energy and time resolution of PMT-based experiments and gains acceleration on GPUs. It is suitable for dynode PMTs, and is extensible to microchannel-plate (MCP) PMTs. In the condition of our laboratory characterization of 8-inch MCP-PMTs, FSMP improves the energy resolution by up to 10% from the conventional method of waveform integration.

hep-ex

The Impact of Aortic Valve Stenosis on Pulse Wave Morphology: An in silico study with 16,038 virtual subjects

Aortic valve stenosis (AVS) presents challenges in asymptomatic detection, resulting in delayed intervention. This study aims to understand how AVS affects pulse wave (PW) morphology. A PW database of 16,038 virtual subjects aged 50 to 75 was created, representing normal physiology and varying AVS degrees. All subjects were simulated using a closed-loop one-dimensional/zero-dimensional blood flow model of the entire cardiovascular system, incorporating a four-chamber heart model capable of simulating different levels of AVS by reducing the orifice area of the aortic valve. Even in cases below clinical significance, distinct PW morphology changes were observed, suggesting potential for early AVS detection using peripheral PWs from non-invasive at-home devices.

physics.med-ph

DynSUP: Dynamic Gaussian Splatting from An Unposed Image Pair

Recent advances in 3D Gaussian Splatting have shown promising results. Existing methods typically assume static scenes and/or multiple images with prior poses. Dynamics, sparse views, and unknown poses significantly increase the problem complexity due to insufficient geometric constraints. To overcome this challenge, we propose a method that can use only two images without prior poses to fit Gaussians in dynamic environments. To achieve this, we introduce two technical contributions. First, we propose an object-level two-view bundle adjustment. This strategy decomposes dynamic scenes into piece-wise rigid components, and jointly estimates the camera pose and motions of dynamic objects. Second, we design an SE(3) field-driven Gaussian training method. It enables fine-grained motion modeling through learnable per-Gaussian transformations. Our method leads to high-fidelity novel view synthesis of dynamic scenes while accurately preserving temporal consistency and object motion. Experiments on both synthetic and real-world datasets demonstrate that our method significantly outperforms state-of-the-art approaches designed for the cases of static environments, multiple images, and/or known poses. Our project page is available at https://colin-de.github.io/DynSUP/.

cs.CV

Dissecting Conditional Branch Predictors of Apple Firestorm and Qualcomm Oryon for Software Optimization and Architectural Analysis

Branch predictor (BP) is a critical component of modern processors, and its accurate modeling is essential for compilers and applications. However, processor vendors have disclosed limited details about their BP implementations. Recent advancements in reverse engineering the BP of general-purpose processors have enabled the creation of more accurate BP models. Nonetheless, we have identified critical deficiencies in the existing methods. For instance, they impose strong assumptions on the branch history update function and the index/tag functions of key BP components, limiting their applicability to a broader range of processors, including those from Apple and Qualcomm. In this paper, we design a more general branch prediction reverse engineering pipeline that can additionally recover the conditional branch predictors (CBPs) of Apple Firestorm and Qualcomm Oryon microarchitectures, and subsequently build accurate CBP models. Leveraging these models, we uncover two previously undisclosed effects that impair branch prediction accuracy and propose related solutions, resulting in up to 14% MPKI reduction and 7% performance improvement in representative applications. Furthermore, we conduct a comprehensive comparison of the known Intel/Apple/Qualcomm CBPs using a unified standalone branch predictor simulator, which facilitates a deeper understanding of CBP behavior.

cs.AR

Blowup for the defocusing septic complex-valued nonlinear wave equation in $\mathbb{R}^{4+1}$

In this paper, we prove blowup for the defocusing septic complex-valued nonlinear wave equation in $\mathbb{R}^{4+1}$. This work builds on the earlier results of Shao, Wei, and Zhang [SWZ2024a,SWZ2024b], reducing the order of the nonlinearity from $29$ to $7$ in $\mathbb{R}^{4+1}$. As in [SWZ2024a,SWZ2024b], the proof hinges on a connection between solutions to the nonlinear wave equation and the relativistic Euler equations via a front compression blowup mechanism. More specifically, the problem is reduced to constructing smooth, radially symmetric, self-similar imploding profiles for the relativistic Euler equations. As with implosion for the compressible Euler equations, the relativistic analogue admits a countable family of smooth imploding profiles. The result in [SWZ2024a] represents the construction of the first profile in this family. In this paper, we construct a sequence of solutions corresponding to the higher-order profiles in the family. This allows us to saturate the inequalities necessary to show blowup for the defocusing complex-valued nonlinear wave equation with an integer order of nonlinearity and radial symmetry via this mechanism.

math.AP

Vorticity blowup in compressible Euler equations in $\mathbb{R}^d, d \geq 3$

We prove finite-time vorticity blowup in the compressible Euler equations in $\mathbb{R}^d$ for any $d \geq 3$, starting from smooth, localized, and non-vacuous initial data. This is achieved by lifting the vorticity blowup result from [CCSV24] in $\mathbb{R}^2$ to $\mathbb{R}^d$ and utilizing the axisymmetry in $\mathbb{R}^d$. At the time of the first singularity, both vorticity blowup and implosion occur on a sphere $S^{d-2}$. Additionally, the solution exhibits a non-radial implosion, accompanied by a stable swirl velocity that is sufficiently strong to initially dominate the non-radial components and to generate the vorticity blowup.

math.AP

On the stability of blowup solutions to the complex Ginzburg-Landau equation in R^d

Building upon the idea in \cite{HNWarXiv24}, we establish stability of the type-I blowup with log correction for the complex Ginzburg-Landau equation. In the amplitude-phase representation, a generalized dynamic rescaling formulation is introduced, with modulation parameters capturing the spatial translation and rotation symmetries of the equation and novel additional modulation parameters perturbing the scaling symmetry. This new formulation provides enough degrees of freedom to impose normalization conditions on the rescaled solution, completely eliminating the unstable and neutrally stable modes of the linearized operator around the blowup profile. It enables us to establish the full stability of the blowup by enforcing vanishing conditions via the choice of normalization and using weighted energy estimates, without relying on a topological argument or a spectrum analysis. The log correction for the blowup rate is captured by the energy estimates and refined estimates of the modulation parameters.

math.AP