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Probabilistic Parallels in the Classical Limit of Quantum Mechanical Models
No full textAt large quantum numbers, the probability densities for particle-in-a-box or simple harmonic oscillator converge to the classical result upon coarse-graining the quantum mechanical probability densities by introducing a finite resolution in the measurement of the particle\u27s position. This resolution in the position can be related to the resolution of the secondary total angular momentum quantum number () when interpreting the probabilistic outcomes of the Stern--Gerlach-type thought experiments for large values of the angular momentum quantum numbers ().first draf
Exploring x-ray irradiation conditions for triggering ultrafast diamond graphitization
No full textIntense femtosecond x-ray pulses produced by an x-ray free-electron laser can trigger irreversible structural transitions in crystalline solids. For instance, irradiation of diamond can lead to graphitization and, at higher deposited doses, to amorphization. Our Monte Carlo simulations of irradiated diamond under realistic experimental conditions demonstrate that triggering graphitization or other phase transitions with hard x-ray photons can be challenging due to the ballistic escape of photoelectrons out of the beam focus. Decisive parameter here is the photoelectron range in proportion to the focal beam size. For future experiments on x-ray-induced transitions, such dedicated simulations of ballistic transport preceding the beamtime will be necessary. They can predict experimental conditions under which the desired distribution of the absorbed x-ray dose in the irradiated solid can be achieved.15 pages, 2 figures, 1 table. Submitted to Phys. Rev.
Training-free Regional Prompting for Diffusion Transformers
No full textDiffusion models have demonstrated excellent capabilities in text-to-image generation. Their semantic understanding (i.e., prompt following) ability has also been greatly improved with large language models (e.g., T5, Llama). However, existing models cannot perfectly handle long and complex text prompts, especially when the text prompts contain various objects with numerous attributes and interrelated spatial relationships. While many regional prompting methods have been proposed for UNet-based models (SD1.5, SDXL), but there are still no implementations based on the recent Diffusion Transformer (DiT) architecture, such as SD3 and FLUX.1.In this report, we propose and implement regional prompting for FLUX.1 based on attention manipulation, which enables DiT with fined-grained compositional text-to-image generation capability in a training-free manner. Code is available at https://github.com/antonioo-c/Regional-Prompting-FLUX.Code is available at https://github.com/antonioo-c/Regional-Prompting-FLU
Spatial Annealing for Efficient Few-shot Neural Rendering
No full textNeural Radiance Fields (NeRF) with hybrid representations have shown impressive capabilities for novel view synthesis, delivering high efficiency. Nonetheless, their performance significantly drops with sparse input views. Various regularization strategies have been devised to address these challenges. However, these strategies either require additional rendering costs or involve complex pipeline designs, leading to a loss of training efficiency. Although FreeNeRF has introduced an efficient frequency annealing strategy, its operation on frequency positional encoding is incompatible with the efficient hybrid representations. In this paper, we introduce an accurate and efficient few-shot neural rendering method named \textbf{S}patial \textbf{A}nnealing regularized \textbf{NeRF} (\textbf{SANeRF}), which adopts the pre-filtering design of a hybrid representation. We initially establish the analytical formulation of the frequency band limit for a hybrid architecture by deducing its filtering process. Based on this analysis, we propose a universal form of frequency annealing in the spatial domain, which can be implemented by modulating the sampling kernel to exponentially shrink from an initial one with a narrow grid tangent kernel spectrum. This methodology is crucial for stabilizing the early stages of the training phase and significantly contributes to enhancing the subsequent process of detail refinement. Our extensive experiments reveal that, by adding merely one line of code, SANeRF delivers superior rendering quality and much faster reconstruction speed compared to current few-shot neural rendering methods. Notably, SANeRF outperforms FreeNeRF on the Blender dataset, achieving 700 faster reconstruction speed.AAAI 2025, code available at https://github.com/pulangk97/SANeR
Magnetoresistance hysteresis in the superconduting state of Kagome CsVSb
Get PDFThe hysteresis of magnetoresistance observed in superconductors is of great interest due to its potential connection with unconventional superconductivity. In this study, we perform electrical transport measurements on Kagome superconductor CsVSb nanoflakes and uncover unusual hysteretic behaviour of magnetoresistance in the superconducting state. This hysteresis can be induced by applying either a large DC or AC current at temperatures () well below the superconducting transition temperature (). As approaches , similar weak hysteresis is also detected by applying a small current. Various scenarios are discussed, with particular focus on the effects of vortex pinning and the presence of time-reversal-symmtery-breaking superconducting domains. Our findings support the latter, hinting at chiral superconductivity in Kagome superconductors.9 pages, 3 figure
DFT: A Universal Quantum Chemistry Dataset of Drug-Like Molecules and a Benchmark for Neural Network Potentials
No full textMethods of computational quantum chemistry provide accurate approximations of molecular properties crucial for computer-aided drug discovery and other areas of chemical science. However, high computational complexity limits the scalability of their applications. Neural network potentials (NNPs) are a promising alternative to quantum chemistry methods, but they require large and diverse datasets for training. This work presents a new dataset and benchmark called DFT that is based on the nablaDFT. It contains twice as much molecular structures, three times more conformations, new data types and tasks, and state-of-the-art models. The dataset includes energies, forces, 17 molecular properties, Hamiltonian and overlap matrices, and a wavefunction object. All calculations were performed at the DFT level (B97X-D/def2-SVP) for each conformation. Moreover, DFT is the first dataset that contains relaxation trajectories for a substantial number of drug-like molecules. We also introduce a novel benchmark for evaluating NNPs in molecular property prediction, Hamiltonian prediction, and conformational optimization tasks. Finally, we propose an extendable framework for training NNPs and implement 10 models within it.Published as a conference paper at NeurIPS2024 Track on Datasets and Benchmarks (Poster
Minimal Attached Primes of Local Cohomology Modules of Binomial Edge Ideals of Block Graphs
Get PDFWe calculate the minimal attached primes of the local cohomology modules of the binomial edge ideals of block graphs. In particular, we obtain a combinatorial characterisation of which of these modules are non-vanishing.
We also show that the main result of this paper follows from a recent result of Lax, Rinaldo, and Romeo (arXiv:2405.08671, Theorem 3.2), which was published independently during the writing of this paper. This provides a short alternative proof of our result.17 pages, v3 replaces the erroneous propositions A.5 and A.6 and fixes typos; v2 replaces what was Section 5 in v1 to take into account recent work of Lax, Rinaldo, and Romeo (arXiv:2405.08671), in which they had in fact already proved a result we stated as a conjecture. Many thanks to Ernesto Lax for bringing this to our attentio
Amplitudes and Polarizations of Quadratic Quasi-Normal Modes for a Schwarzschild Black Hole
No full textGeneral Relativity predicts the existence of quadratic quasi-normal modes at second order in perturbation theory. Building on our recent work, we compute the amplitudes and polarizations of these modes for non-rotating black holes, showing that they are completely determined by the amplitudes and polarizations of linear modes. We obtain the ratio of quadratic to linear amplitudes, which still depends on the initial conditions of the merger through the polarization of linear modes. However, we demonstrate that this dependence is captured by four fundamental numbers, independent of initial conditions, representing four different combinations of linear modes parities. Additionally, we prove two selection rules regarding the vanishing of classes of quadratic modes. Our results are available online as a package which provides the ratio of amplitudes across a broad spectrum of angular momenta
Asymmetric fluctuations and self-folding of active interfaces
No full textWe study the structure and dynamics of the interface separating a passive fluid from a microtubule-based active fluid. Turbulent-like active flows power giant interfacial fluctuations, which exhibit pronounced asymmetry between regions of positive and negative curvature. Experiments, numerical simulations, and theoretical arguments reveal how the interface breaks up the spatial symmetry of the fundamental bend instability to generate local vortical flows that lead to asymmetric interface fluctuations. The magnitude of interface deformations increases with activity: In the high activity limit, the interface self-folds invaginating passive droplets and generating a foam-like phase, where active fluid is perforated with passive droplets. These results demonstrate how active stresses control the structure, dynamics, and break-up of soft, deformable, and reconfigurable liquid-liquid interfaces.26 pages, 22 figure
LPGD: A General Framework for Backpropagation through Embedded Optimization Layers
No full textEmbedding parameterized optimization problems as layers into machine learning architectures serves as a powerful inductive bias. Training such architectures with stochastic gradient descent requires care, as degenerate derivatives of the embedded optimization problem often render the gradients uninformative. We propose Lagrangian Proximal Gradient Descent (LPGD) a flexible framework for training architectures with embedded optimization layers that seamlessly integrates into automatic differentiation libraries. LPGD efficiently computes meaningful replacements of the degenerate optimization layer derivatives by re-running the forward solver oracle on a perturbed input. LPGD captures various previously proposed methods as special cases, while fostering deep links to traditional optimization methods. We theoretically analyze our method and demonstrate on historical and synthetic data that LPGD converges faster than gradient descent even in a differentiable setup.ICML 2024 conference pape