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Hongyu Jia

Publications and source records attributed to Hongyu Jia.

8 recordsLinked to original sources

Functional identities of degree 2 at two-sided zero products on incidence algebras

Let $R$ be a commutative ring with unity such that $\frac{1}{2}\in R$. Let $X$ be a connected finite poset with $|X|>2$ and $I(X,R)$ be the incidence algebra of $X$ over $R$. In this paper, we characterize the forms of linear maps $F_1,F_2,F_3,F_4:I(X,R)\to I(X,R)$ satisfying \[ F_1(f)g+fF_2(g)+F_3(g)f+gF_4(f)=0, \] whenever $fg=gf=0$. We prove that the $F_i$'s are of the so-called standard form if and only if any two edges in the comparability graph of $X$ are contained in one cycle. The ingredients of the proof contain a characterization of $2$-connectedness in comparability graph and the two-sided zero product determined property of incidence algebras.

math.RA

Finite dimensional zero Jordan product determined algebras are generated by idempotents

Bre\v{s}ar showed that a finite dimensional unital associative algebra is zero product determined if and only if it is generated by idempotents. For the analogue of zero Jordan product determined algebras, only one direction was known: over a field of characteristic not 2, every algebra generated by idempotents is zero Jordan product determined. Whether the converse holds has remained an open problem. In this paper, we answer this question affirmatively in the finite dimensional case. Some related open problems are stated at the end.

math.RA

Commuting maps of inflated algebras

Commuting maps on a class of algebras called inflated algebras are investigated. In particular, we can prove that every commuting map $\theta$ on such an algebra is of the form $\theta(x)=c x+\mu(x)$, where $c$ belongs to the base field $K$ of characteristic not 2, and $\mu$ is a central-valued linear map.

math.RA

Speed by Simplicity: A Single-Stream Architecture for Fast Audio-Video Generative Foundation Model

We present daVinci-MagiHuman, an open-source audio-video generative foundation model for human-centric generation. daVinci-MagiHuman jointly generates synchronized video and audio using a single-stream Transformer that processes text, video, and audio within a unified token sequence via self-attention only. This single-stream design avoids the complexity of multi-stream or cross-attention architectures while remaining easy to optimize with standard training and inference infrastructure. The model is particularly strong in human-centric scenarios, producing expressive facial performance, natural speech-expression coordination, realistic body motion, and precise audio-video synchronization. It supports multilingual spoken generation across Chinese (Mandarin and Cantonese), English, Japanese, Korean, German, and French. For efficient inference, we combine the single-stream backbone with model distillation, latent-space super-resolution, and a Turbo VAE decoder, enabling generation of a 5-second 256p video in 2 seconds on a single H100 GPU. In automatic evaluation, daVinci-MagiHuman achieves the highest visual quality and text alignment among leading open models, along with the lowest word error rate (14.60%) for speech intelligibility. In pairwise human evaluation, it achieves win rates of 80.0% against Ovi 1.1 and 60.9% against LTX 2.3 over 2000 comparisons. We open-source the complete model stack, including the base model, the distilled model, the super-resolution model, and the inference codebase.

cs.CV

MAGI-1: Autoregressive Video Generation at Scale

We present MAGI-1, a world model that generates videos by autoregressively predicting a sequence of video chunks, defined as fixed-length segments of consecutive frames. Trained to denoise per-chunk noise that increases monotonically over time, MAGI-1 enables causal temporal modeling and naturally supports streaming generation. It achieves strong performance on image-to-video (I2V) tasks conditioned on text instructions, providing high temporal consistency and scalability, which are made possible by several algorithmic innovations and a dedicated infrastructure stack. MAGI-1 facilitates controllable generation via chunk-wise prompting and supports real-time, memory-efficient deployment by maintaining constant peak inference cost, regardless of video length. The largest variant of MAGI-1 comprises 24 billion parameters and supports context lengths of up to 4 million tokens, demonstrating the scalability and robustness of our approach. The code and models are available at https://github.com/SandAI-org/MAGI-1 and https://github.com/SandAI-org/MagiAttention. The product can be accessed at https://sand.ai.

cs.CV

Images of locally finite $\mathcal{E}$-derivations of bivariate polynomial algebras

This paper presents an $\mathcal{E}$-derivation analogue of a result on derivations due to van den Essen, Wright and Zhao. We prove that the image of a locally finite $K$-$\mathcal{E}$-derivation of polynomial algebras in two variables over a field $K$ of characteristic zero is a Mathieu-Zhao subspace. This result together with that of van den Essen, Wright and Zhao confirms the LFED conjecture in the case of polynomial algebras in two variables.

math.AC

Images of Linear Derivations and Linear E-derivations of K[x 1 ,x 2 ,x 3 ]

Let K be a field of characteristic zero. We prove that images of a linear K-derivation and a linear K-E-derivation of the ring K[x 1 ,x 2 ,x 3 ] of polynomial in three variables over K are Mathieu-Zhao subspaces, which affirms the LFED conjecture for linear K-derivations and linear K-E-derivations of K[x 1 ,x 2 ,x 3 ].

math.AC

Commuting maps on certain incidence algebras

Let $\mathcal{R}$ be a $2$-torsion free commutative ring with unity, $X$ a locally finite pre-ordered set and $I(X,\mathcal{R})$ the incidence algebra of $X$ over $\mathcal{R}$. If $X$ consists of a finite number of connected components, in this paper we give a sufficient and necessary condition for each commuting map on $I(X,\mathcal{R})$ being proper.

math.RA