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Each year, nearly 13,000 eviction orders are issued in Cook County, Illinois. While most of these orders have an enforcement deadline, a portion does not. The Cook County Sheriff's Office (CCSO) is responsible for enforcing these orders, which involves selecting the orders to prioritize and planning daily enforcement routes. This task presents a challenge: balancing "equity" (i.e., prioritizing orders that have been waiting longer) with "efficiency" (i.e., maximizing the number of orders served). Although the current CCSO policy is highly efficient, a significant fraction of eviction orders miss their deadline. Motivated by the CCSO's operations, we study a model of eviction enforcement planning and propose a policy that dynamically prioritizes orders based on their type (deadline or no deadline), location, and waiting time. Our approach employs a budgeted prize-collecting vehicle routing problem (VRP) for daily planning, where the "prizes" are determined by solving a stochastic control problem. This stochastic control problem, which relies on the VRP for determining feasible actions at each decision point, is high-dimensional due to its spatial nature, leading to the curse of dimensionality. We overcome this challenge by building on recent advances in high-dimensional stochastic control using deep neural networks. We compare the performance of our proposed policy with two practical benchmark policies, including one that mimics the current CCSO policy, using data from CCSO. Similar to the CCSO policy, our proposed policy leads to efficient resource utilization, but it also reduces the percentage of orders that miss their deadline by 72.38% without degrading the overall service effort for either type of orders. In a counterfactual study, we show that increasing the service capacity or extending the enforcement deadline further reduces the fraction of orders missing their deadline.

Multi-modal generative AI has received increasing attention in both academia and industry. Particularly, two dominant families of techniques are: i) The multi-modal large language model (MLLM) such as GPT-4V, which shows impressive ability for multi-modal understanding; ii) The diffusion model such as Sora, which exhibits remarkable multi-modal powers, especially with respect to visual generation. As such, one natural question arises: Is it possible to have a unified model for both understanding and generation? To answer this question, in this paper, we first provide a detailed review of both MLLM and diffusion models, including their probabilistic modeling procedure, multi-modal architecture design, and advanced applications to image/video large language models as well as text-to-image/video generation. Then, we discuss the two important questions on the unified model: i) whether the unified model should adopt the auto-regressive or diffusion probabilistic modeling, and ii) whether the model should utilize a dense architecture or the Mixture of Experts(MoE) architectures to better support generation and understanding, two objectives. We further provide several possible strategies for building a unified model and analyze their potential advantages and disadvantages. We also summarize existing large-scale multi-modal datasets for better model pretraining in the future. To conclude the paper, we present several challenging future directions, which we believe can contribute to the ongoing advancement of multi-modal generative AI.

The vanadium-based kagome metals $A$V$_3$Sb$_5$ ($A$ = K, Rb, and Cs) host a superconducting ground state that coexists with an unconventional charge density wave (CDW). The CDW state exhibits experimental signatures of chirality, electronic nematicity, and time-reversal-symmetry-breaking, raising the questions whether the superconductivity (SC) in $A$V$_3$Sb$_5$ may also be unconventional, how SC interplays with CDW, and how the two orders evolve upon tuning. This article reviews studies of the superconducting pairing symmetry, and the tuning of SC and CDW in the $A$V$_3$Sb$_5$ compounds. Various experimental techniques consistently find that CsV$_3$Sb$_5$ exhibits nodeless SC, which remains robust regardless whether the CDW is present. Under hydrostatic pressure, SC in $A$V$_3$Sb$_5$ becomes enhanced as the CDW is gradually suppressed, revealing a competition between the two orders. In CsV$_3$Sb$_5$, a new CDW state emerges under pressure that competes more strongly with SC relative to the CDW at ambient pressure, and results in two superconducting domes that coexist with CDW. After the CDW in $A$V$_3$Sb$_5$ is fully suppressed with hydrostatic pressure, a further increase in pressure leads to a nonmonotonic evolution of the superconducting transition temperature driven by lattice modulations. Thickness is shown to be a powerful tuning parameter in $A$V$_3$Sb$_5$ thin flakes, revealing the evolution of CDW and SC upon dimensional reduction, and can be combined with hydrostatic pressure to shed light on the interplay between SC and CDW. Based on results reviewed in this article, we discuss outstanding issues to be addressed in the $A$V$_3$Sb$_5$ systems.

Generating customized content in videos has received increasing attention recently. However, existing works primarily focus on customized text-to-video generation for single subject, suffering from subject-missing and attribute-binding problems when the video is expected to contain multiple subjects. Furthermore, existing models struggle to assign the desired actions to the corresponding subjects (action-binding problem), failing to achieve satisfactory multi-subject generation performance. To tackle the problems, in this paper, we propose DisenStudio, a novel framework that can generate text-guided videos for customized multiple subjects, given few images for each subject. Specifically, DisenStudio enhances a pretrained diffusion-based text-to-video model with our proposed spatial-disentangled cross-attention mechanism to associate each subject with the desired action. Then the model is customized for the multiple subjects with the proposed motion-preserved disentangled finetuning, which involves three tuning strategies: multi-subject co-occurrence tuning, masked single-subject tuning, and multi-subject motion-preserved tuning. The first two strategies guarantee the subject occurrence and preserve their visual attributes, and the third strategy helps the model maintain the temporal motion-generation ability when finetuning on static images. We conduct extensive experiments to demonstrate our proposed DisenStudio significantly outperforms existing methods in various metrics. Additionally, we show that DisenStudio can be used as a powerful tool for various controllable generation applications.

A graph G is said to be M-integral (resp. A-integral, D-integral, DL-integral or DQ-integral) if all eigenvalues of its matrix M (resp. adjacency matrix A(G), distance matrix D(G), distance Laplacian matrix DL(G) or distance signless Laplacian matrix DQ(G)) are integers. Lu et al. [Discrete Math, 346 (2023)] defined the generalized wheel graph GW(a, m, n) as the join of two regular graphs aKm and Cn, and obtained all D-integral generalized wheel graphs. Based on the above research, in this paper, we determine all DL-integral and DQ-integral generalized wheel graphs respectively. As byproducts, we give a sufficient and necessary condition for the join of two regular graphs G1 and G2 to be DL-integral, from which we can get infinitely many new classes of DL-integral graphs according to the large number of research results about the A-integral graphs.

Recently, researchers have attempted to investigate the capability of LLMs in handling videos and proposed several video LLM models. However, the ability of LLMs to handle video grounding (VG), which is an important time-related video task requiring the model to precisely locate the start and end timestamps of temporal moments in videos that match the given textual queries, still remains unclear and unexplored in literature. To fill the gap, in this paper, we propose the LLM4VG benchmark, which systematically evaluates the performance of different LLMs on video grounding tasks. Based on our proposed LLM4VG, we design extensive experiments to examine two groups of video LLM models on video grounding: (i) the video LLMs trained on the text-video pairs (denoted as VidLLM), and (ii) the LLMs combined with pretrained visual description models such as the video/image captioning model. We propose prompt methods to integrate the instruction of VG and description from different kinds of generators, including caption-based generators for direct visual description and VQA-based generators for information enhancement. We also provide comprehensive comparisons of various VidLLMs and explore the influence of different choices of visual models, LLMs, prompt designs, etc, as well. Our experimental evaluations lead to two conclusions: (i) the existing VidLLMs are still far away from achieving satisfactory video grounding performance, and more time-related video tasks should be included to further fine-tune these models, and (ii) the combination of LLMs and visual models shows preliminary abilities for video grounding with considerable potential for improvement by resorting to more reliable models and further guidance of prompt instructions.

Customized text-to-video generation aims to generate text-guided videos with customized user-given subjects, which has gained increasing attention recently. However, existing works are primarily limited to generating videos for a single subject, leaving the more challenging problem of customized multi-subject text-to-video generation largely unexplored. In this paper, we fill this gap and propose a novel VideoDreamer framework. VideoDreamer can generate temporally consistent text-guided videos that faithfully preserve the visual features of the given multiple subjects. Specifically, VideoDreamer leverages the pretrained Stable Diffusion with latent-code motion dynamics and temporal cross-frame attention as the base video generator. The video generator is further customized for the given multiple subjects by the proposed Disen-Mix Finetuning and Human-in-the-Loop Re-finetuning strategy, which can tackle the attribute binding problem of multi-subject generation. We also introduce MultiStudioBench, a benchmark for evaluating customized multi-subject text-to-video generation models. Extensive experiments demonstrate the remarkable ability of VideoDreamer to generate videos with new content such as new events and backgrounds, tailored to the customized multiple subjects. Our project page is available at https://videodreamer23.github.io/.

Subject-driven text-to-image generation aims to generate customized images of the given subject based on the text descriptions, which has drawn increasing attention. Existing methods mainly resort to finetuning a pretrained generative model, where the identity-relevant information (e.g., the boy) and the identity-irrelevant information (e.g., the background or the pose of the boy) are entangled in the latent embedding space. However, the highly entangled latent embedding may lead to the failure of subject-driven text-to-image generation as follows: (i) the identity-irrelevant information hidden in the entangled embedding may dominate the generation process, resulting in the generated images heavily dependent on the irrelevant information while ignoring the given text descriptions; (ii) the identity-relevant information carried in the entangled embedding can not be appropriately preserved, resulting in identity change of the subject in the generated images. To tackle the problems, we propose DisenBooth, an identity-preserving disentangled tuning framework for subject-driven text-to-image generation. Specifically, DisenBooth finetunes the pretrained diffusion model in the denoising process. Different from previous works that utilize an entangled embedding to denoise each image, DisenBooth instead utilizes disentangled embeddings to respectively preserve the subject identity and capture the identity-irrelevant information. We further design the novel weak denoising and contrastive embedding auxiliary tuning objectives to achieve the disentanglement. Extensive experiments show that our proposed DisenBooth framework outperforms baseline models for subject-driven text-to-image generation with the identity-preserved embedding. Additionally, by combining the identity-preserved embedding and identity-irrelevant embedding, DisenBooth demonstrates more generation flexibility and controllability

A system manager makes dynamic pricing and dispatch control decisions in a queueing network model motivated by ride-hailing applications. A novel feature of the model is that it incorporates travel times. Unfortunately, this renders the exact analysis of the problem intractable. Therefore, we study this problem in the heavy traffic regime. Under the assumptions of complete resource pooling and common travel distribution, we solve the problem in closed form by analyzing the corresponding Bellman equation. Using this solution, we propose a policy for the queueing system and illustrate its effectiveness in a simulation study.