This paper presents a neural network (NN)-based solver for an integro-differential equation that models shrinkage-induced fragmentation. The proposed method directly maps input parameters to the corresponding probability density function without numerically solving the governing equation, thereby significantly reducing computational costs. Specifically, it enables efficient evaluation of the density function in Monte Carlo simulations while maintaining accuracy comparable to or even exceeding that of conventional finite difference schemes. Validatation on synthetic data demonstrates both the method's computational efficiency and predictive reliability. This study establishes a foundation for the data-driven inverse analysis of fragmentation and suggests the potential for extending the framework beyond pre-specified model structures.

In cloud services, virtual machine (VM) scheduling is a typical Online Dynamic Multidimensional Bin Packing (ODMBP) problem, characterized by large-scale complexity and fluctuating demands. Traditional optimization methods struggle to adapt to real-time changes, domain-expert-designed heuristic approaches suffer from rigid strategies, and existing learning-based methods often lack generalizability and interpretability. To address these limitations, this paper proposes a hierarchical language agent framework named MiCo, which provides a large language model (LLM)-driven heuristic design paradigm for solving ODMBP. Specifically, ODMBP is formulated as a Semi-Markov Decision Process with Options (SMDP-Option), enabling dynamic scheduling through a two-stage architecture, i.e., Option Miner and Option Composer. Option Miner utilizes LLMs to discover diverse and useful non-context-aware strategies by interacting with constructed environments. Option Composer employs LLMs to discover a composing strategy that integrates the non-context-aware strategies with the contextual ones. Extensive experiments on real-world enterprise datasets demonstrate that MiCo achieves a 96.9\% competitive ratio in large-scale scenarios involving more than 10,000 virtual machines. It maintains high performance even under nonstationary request flows and diverse configurations, thus validating its effectiveness in complex and large-scale cloud environments.

Beautimeter is a new tool powered by generative pre-trained transformer (GPT) technology, designed to evaluate architectural and urban beauty. Rooted in Christopher Alexander's theory of centers, this work builds on the idea that all environments possess, to varying degrees, an innate sense of life. Alexander identified 15 fundamental properties, such as levels of scale and thick boundaries, that characterize living structure, which Beautimeter uses as a basis for its analysis. By integrating GPT's advanced natural language processing capabilities, Beautimeter assesses the extent to which a structure embodies these 15 properties, enabling a nuanced evaluation of architectural and urban aesthetics. Using ChatGPT, the tool helps users generate insights into the perceived beauty and coherence of spaces. We conducted a series of case studies, evaluating images of architectural and urban environments, as well as carpets, paintings, and other artifacts. The results demonstrate Beautimeter's effectiveness in analyzing aesthetic qualities across diverse contexts. Our findings suggest that by leveraging GPT technology, Beautimeter offers architects, urban planners, and designers a powerful tool to create spaces that resonate deeply with people. This paper also explores the implications of such technology for architecture and urban design, highlighting its potential to enhance both the design process and the assessment of built environments. Keywords: Living structure, structural beauty, Christopher Alexander, AI in Design, human centered design

Interpreting the representation and generalization powers has been a long-standing issue in the field of machine learning (ML) and artificial intelligence. This work contributes to uncovering the emergence of universal scaling laws in quantum-probabilistic ML. We take the generative tensor network (GTN) in the form of a matrix product state as an example and show that with an untrained GTN (such as a random TN state), the negative logarithmic likelihood (NLL) $L$ generally increases linearly with the number of features $M$, i.e., $L \simeq k M + const$. This is a consequence of the so-called ``catastrophe of orthogonality,'' which states that quantum many-body states tend to become exponentially orthogonal to each other as $M$ increases. We reveal that while gaining information through training, the linear scaling law is suppressed by a negative quadratic correction, leading to $L \simeq \beta M - \alpha M^2 + const$. The scaling coefficients exhibit logarithmic relationships with the number of training samples and the number of quantum channels $\chi$. The emergence of the quadratic correction term in NLL for the testing (training) set can be regarded as evidence of the generalization (representation) power of GTN. Over-parameterization can be identified by the deviation in the values of $\alpha$ between training and testing sets while increasing $\chi$. We further investigate how orthogonality in the quantum feature map relates to the satisfaction of quantum probabilistic interpretation, as well as to the representation and generalization powers of GTN. The unveiling of universal scaling laws in quantum-probabilistic ML would be a valuable step toward establishing a white-box ML scheme interpreted within the quantum probabilistic framework.

The choice of parameters in neural networks is crucial in the performance, and an oracle distribution derived from the ridgelet transform enables us to obtain suitable initial parameters. In other words, the distribution of parameters is connected to the integral representation of target functions. The oracle distribution allows us to avoid the conventional backpropagation learning process; only a linear regression is enough to construct the neural network in simple cases. This study provides a new look at the oracle distributions and ridgelet transforms, i.e., an aspect of importance sampling. In addition, we propose extensions of the parameter sampling methods. We demonstrate the aspect of importance sampling and the proposed sampling algorithms via one-dimensional and high-dimensional examples; the results imply that the magnitude of weight parameters could be more crucial than the intercept parameters.

We introduce a launch device, called the remotely-enabled modular release mechanism, to augment rapid testing and prototyping of cooperative autonomy maritime applications by facilitating autonomous deployment of an autonomous underwater vehicle (AUV) from an autonomous surface vessel (ASV). While we focus our development on a specific application of deploying an AUV from a catamaran style ASV, the release mechanism can be adapted to different deployable objects and towing vehicles, such as buoys and sensors for oceanographic surveys or mono-hull ASVs. In this paper we explore a number of hardware and software design considerations to facilitate ease of integration with existing maritime autonomy systems. We expound on bench tests and in-water tests used to explore the utility of the release system and diagnose system issues. Additionally, we make a first-principles argument, based on a hydrodynamics physics model, for assured deployment that is virtually independent of sea state, making the release system a suitable alternative for different maritime applications in varying environmental conditions.

Sigma-i Co., Ltd., Tokyo, 108-0075, Japan Model-based sequential approaches to discrete "black-box" optimization, including Bayesian optimization techniques, often access the same points multiple times for a given objective function in interest, resulting in many steps to find the global optimum. Here, we numerically study the effect of a postprocessing method on Bayesian optimization that strictly prohibits duplicated samples in the dataset. We find the postprocessing method significantly reduces the number of sequential steps to find the global optimum, especially when the acquisition function is of maximum a posteriori estimation. Our results provide a simple but general strategy to solve the slow convergence of Bayesian optimization for high-dimensional problems. This process is repeated until a termination criterion is fulfilled, e.g., exhausting the predeter-1/10 In recent years, several attempts have been made to apply Bayesian optimization to highdimensional combinatorial optimization problems.

The physics-informed neural network (PINN) is capable of recovering partial differential equation (PDE) coefficients that remain constant throughout the spatial domain directly from physical measurements. In this work, we propose a spatially dependent physics-informed neural network (SD-PINN), which enables the recovery of coefficients in spatially-dependent PDEs using a single neural network, eliminating the requirement for domain-specific physical expertise. We apply the SD-PINN to spatially-dependent wave equation coefficients recovery to reveal the spatial distribution of acoustical properties in the inhomogeneous medium. The proposed method exhibits robustness to noise owing to the incorporation of a loss function for the physical constraint that the assumed PDE must be satisfied. For the coefficients recovery of spatially two-dimensional PDEs, we store the PDE coefficients at all locations in the 2D region of interest into a matrix and incorporate the low-rank assumption for such a matrix to recover the coefficients at locations without available measurements.