Analytical solution of the linear fractional differential equation by Adomian decomposition method

AbstractIn this paper, we consider the n-term linear fractional-order differential equation with constant coefficients and obtain the solution of this kind of fractional differential equations by Adomian decomposition method. With the equivalent transmutation, we show that the solution by Adomian decomposition method is the same as the solution by the Green's function. Finally, we illustrate our result with some examples

Embodied Scene-aware Human Pose Estimation

We propose embodied scene-aware human pose estimation where we estimate 3D poses based on a simulated agent's proprioception and scene awareness, along with external third-person observations. Unlike prior methods that often resort to multistage optimization, non-causal inference, and complex contact modeling to estimate human pose and human scene interactions, our method is one stage, causal, and recovers global 3D human poses in a simulated environment. Since 2D third-person observations are coupled with the camera pose, we propose to disentangle the camera pose and use a multi-step projection gradient defined in the global coordinate frame as the movement cue for our embodied agent. Leveraging a physics simulation and prescanned scenes (e.g., 3D mesh), we simulate our agent in everyday environments (libraries, offices, bedrooms, etc.) and equip our agent with environmental sensors to intelligently navigate and interact with scene geometries. Our method also relies only on 2D keypoints and can be trained on synthetic datasets derived from popular human motion databases. To evaluate, we use the popular H36M and PROX datasets and, for the first time, achieve a success rate of 96.7% on the challenging PROX dataset without ever using PROX motion sequences for training.Comment: Project website: https://embodiedscene.github.io/embodiedpose/ Zhengyi Luo and Shun Iwase contributed equall

A Sophisticated Method of the Mechanical Design of Cable Accessories Focusing on Interface Contact Pressure

The most critical positions of a prefabricated cable accessory, from the electrical point of view, are the interfaces between the stress cone and its surroundings. Accordingly, the contact pressure on those interfaces needs to be carefully designed to assure both good dielectric strength and smooth installation of the stress cone. Nevertheless, since stress cones made from rubber are under large deformation after installation, their internal stress distribution is neither practical to measure directly by planting sensors, nor feasible to compute accurately with the conventional theory of linear structural mechanics. This paper presents one sophisticated method for computing the mechanical stress distribution in rubber stress cones of cable accessories by employing hyperelastic models in a computation model based on the finite element method. This method offers accurate results for rubber bodies of complex geometries and large deformations. Based on the method, a case study of a composite prefabricated termination for extruded cables is presented, and the sensitivity analysis is given as well

A new micro scale FE model of crystalline materials in micro forming process

Micro forming of metals has drawn global attention due to the increasing requirement of micro metal products. However, the size effects become significant in micro forming processes and affect the application of finite element (FE) simulation of micro forming processes. Dividing samples into small areas according to their microstructures and assigning individual properties to each small area are a possible access to micro forming simulation considering material size effects. In this study, a new model that includes both grains and their boundaries was developed based on the observed microstructures of samples. The divided subareas in the model have exact shapes and sizes with real crystals on the sample, and each grain and grain boundaries have their own properties. Moreover, two modelling methods using different information from the microstructural images were introduced in detail. The two modelling methods largely increase the availability of various microstructural images. The new model provides accurate results which present the size effects well

Special Libraries, January 1920

Volume 11, Issue 1https://scholarworks.sjsu.edu/sla_sl_1920/1000/thumbnail.jp

Evolutionary Stages and Disk Properties of Young Stellar Objects in the Perseus Cloud

We investigated the evolutionary stages and disk properties of 211 Young stellar objects (YSOs) across the Perseus cloud by modeling the broadband optical to mid-infrared (IR) spectral energy distribution (SED). By exploring the relationships among the turnoff wave bands lambda_turnoff (longward of which significant IR excesses above the stellar photosphere are observed), the excess spectral index alpha_excess at lambda <~ 24 microns, and the disk inner radius R_in (from SED modeling) for YSOs of different evolutionary stages, we found that the median and standard deviation of alpha_excess of YSOs with optically thick disks tend to increase with lambda_turnoff, especially at lambda_turnoff >= 5.8 microns, whereas the median fractional dust luminosities L_dust/L_star tend to decrease with lambda_turnoff. This points to an inside-out disk clearing of small dust grains. Moreover, a positive correlation between alpha_excess and R_in was found at alpha_excess > ~0 and R_in > ~10 $\times$ the dust sublimation radius R_sub, irrespective of lambda_turnoff, L_dust/L_star and disk flaring. This suggests that the outer disk flaring either does not evolve synchronously with the inside-out disk clearing or has little influence on alpha_excess shortward of 24 microns. About 23% of our YSO disks are classified as transitional disks, which have lambda_turnoff >= 5.8 microns and L_dust/L_star >10^(-3). The transitional disks and full disks occupy distinctly different regions on the L_dust/L_star vs. alpha_excess diagram. Taking L_dust/L_star as an approximate discriminator of disks with (>0.1) and without (<0.1) considerable accretion activity, we found that 65% and 35% of the transitional disks may be consistent with being dominantly cleared by photoevaporation and dynamical interaction respectively. [abridged]Comment: 31 pages, 13 figures, 2 tables. To appear in a special issue of RAA on LAMOST science

Large Language Model Can Interpret Latent Space of Sequential Recommender

Sequential recommendation is to predict the next item of interest for a user, based on her/his interaction history with previous items. In conventional sequential recommenders, a common approach is to model item sequences using discrete IDs, learning representations that encode sequential behaviors and reflect user preferences. Inspired by recent success in empowering large language models (LLMs) to understand and reason over diverse modality data (e.g., image, audio, 3D points), a compelling research question arises: ``Can LLMs understand and work with hidden representations from ID-based sequential recommenders?''.To answer this, we propose a simple framework, RecInterpreter, which examines the capacity of open-source LLMs to decipher the representation space of sequential recommenders. Specifically, with the multimodal pairs (\ie representations of interaction sequence and text narrations), RecInterpreter first uses a lightweight adapter to map the representations into the token embedding space of the LLM. Subsequently, it constructs a sequence-recovery prompt that encourages the LLM to generate textual descriptions for items within the interaction sequence. Taking a step further, we propose a sequence-residual prompt instead, which guides the LLM in identifying the residual item by contrasting the representations before and after integrating this residual into the existing sequence. Empirical results showcase that our RecInterpreter enhances the exemplar LLM, LLaMA, to understand hidden representations from ID-based sequential recommenders, especially when guided by our sequence-residual prompts. Furthermore, RecInterpreter enables LLaMA to instantiate the oracle items generated by generative recommenders like DreamRec, concreting the item a user would ideally like to interact with next. Codes are available at https://github.com/YangZhengyi98/RecInterpreter