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What do the quantum eigenstates of 3D wells look like? In this video, we visualize the solutions of the 3D Schrödinger Equation computed for more than a total of 500 eigenstates of 2, 4, 8, and 12 wells, illustrating what the molecular orbitals for a molecule with that number of atoms look like. These simulations are made with qmsolve, an open-source python package that we are developing for solving and visualizing quantum physics. You can find the source code here: https://github.com/quantum-visualizations/qmsolve The way this simulator works is by discretizing the Hamiltonian of an arbitrary potential and diagonalizing it for getting the energies and the eigenstates of the system. The eigenstates of this video are computed with high accuracy (less than 1% of relative error) by diagonalizing a Hamiltonian matrix with a shape of 1,000,000 x 1,000,000. For a molecule that contains only a single electron, an orbital is exactly the same that its eigenstate. Therefore in these examples, the eigenstates are equivalent to the orbitals. In the video, it can be noticed that the first molecular orbitals can be visualized as a first-order approximation as a simple linear combination of the orbitals of a single well. However, as the energy of the eigenstates raises, their wave function starts to take much more complex shapes. Between each eigenstate is plotted a transition between two eigenstates. This is made by preparing a quantum superposition of the two eigenstates involved. #QuantumPhysics #MolecularOrbitals #QuantumChemistry

Humans live in a 24-hour environment, in which light and darkness follow a diurnal pattern. Our circadian pacemaker, the suprachiasmatic nuclei (SCN) in the hypothalamus, is entrained to the 24-hour solar day via a pathway from ...

This is the most step-by-step spelled-out explanation of backpropagation and training of neural networks.

Large-scale pretraining is fast becoming the norm in Vision-Language (VL) modeling. However, prevailing VL approaches are limited by the requirement for labeled data and the use of complex multi-step pretraining objectives. We present MAGMA - a simple method for augmenting generative language models with additional modalities using adapter-based finetuning. Building on Frozen, we train a series of VL models that autoregressively generate text from arbitrary combinations of visual and textual input. The pretraining is entirely end-to-end using a single language modeling objective, simplifying optimization compared to previous approaches. Importantly, the language model weights remain unchanged during training, allowing for transfer of encyclopedic knowledge and in-context learning abilities from language pretraining. MAGMA outperforms Frozen on open-ended generative tasks, achieving state of the art results on the OKVQA benchmark and competitive results on a range of other popular VL benchmarks, while pretraining on 0.2% of the number of samples used to train SimVLM.

Nietzsche "He who promises to love forever or hate forever or be forever faithful to someone is promising something that is not in his power."

DreamFusion: Text-to-3D using 2D Diffusion, 2022.

A bone marrow transplant is a medical procedure performed to replace bone marrow that has been damaged or destroyed by disease or chemotherapy.