Interactive design of complex time dependent lighting

Pedrosa et al.1 have recently used a [Formula: see text] symmetric linear invariant to study a unidimensional time-dependent [Formula: see text] symmetric harmonic oscillator with a complex time-dependent [Formula: see text] symmetric external force. We show in this comment that the normalization condition of the eigenfunctions of the invariant is not verified as claimed in Ref. 1. In order to obtain the normalization condition, we introduce a novel concept of the pseudoparity-time (pseudo-[Formula: see text]) symmetry.

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Engineer design process assisted by explainable deep learning network

Scientific Reports ◽

10.1038/s41598-021-01937-5 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Chia-Wei Hsu ◽

An-Cheng Yang ◽

Pei-Ching Kung ◽

Nien-Ti Tsou ◽

Nan-Yow Chen

Keyword(s):

Deep Learning ◽

Dental Implants ◽

Design Process ◽

Bone Healing ◽

Fluid Velocity ◽

Time Dependent ◽

Simulation Data ◽

Complex Time ◽

Learning Network ◽

Deep Learning Network

AbstractEngineering simulation accelerates the development of reliable and repeatable design processes in various domains. However, the computing resource consumption is dramatically raised in the whole development processes. Making the most of these simulation data becomes more and more important in modern industrial product design. In the present study, we proposed a workflow comprised of a series of machine learning algorithms (mainly deep neuron networks) to be an alternative to the numerical simulation. We have applied the workflow to the field of dental implant design process. The process is based on a complex, time-dependent, multi-physical biomechanical theory, known as mechano-regulatory method. It has been used to evaluate the performance of dental implants and to assess the tissue recovery after the oral surgery procedures. We provided a deep learning network (DLN) with calibrated simulation data that came from different simulation conditions with experimental verification. The DLN achieves nearly exact result of simulated bone healing history around implants. The correlation of the predicted essential physical properties of surrounding bones (e.g. strain and fluid velocity) and performance indexes of implants (e.g. bone area and bone-implant contact) were greater than 0.980 and 0.947, respectively. The testing AUC values for the classification of each tissue phenotype were ranging from 0.90 to 0.99. The DLN reduced hours of simulation time to seconds. Moreover, our DLN is explainable via Deep Taylor decomposition, suggesting that the transverse fluid velocity, upper and lower parts of dental implants are the keys that influence bone healing and the distribution of tissue phenotypes the most. Many examples of commercial dental implants with designs which follow these design strategies can be found. This work demonstrates that DLN with proper network design is capable to replace complex, time-dependent, multi-physical models/theories, as well as to reveal the underlying features without prior professional knowledge.

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ZND-ZeaD Models and Theoretics Including Proofs for Takagi Factorization of Complex Time-Dependent Symmetric Matrix

10.1109/ccdc52312.2021.9601621 ◽

2021 ◽

Author(s):

Zhuosong Fu ◽

Min Yang ◽

Jinjin Guo ◽

Jianrong Chen ◽

Yunong Zhang

Keyword(s):

Symmetric Matrix ◽

Time Dependent ◽

Complex Time ◽

Takagi Factorization

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Contract-Based Verification of Complex Time-Dependent Behaviors in Avionic Systems

Lecture Notes in Computer Science - NASA Formal Methods ◽

10.1007/978-3-319-40648-0_3 ◽

2016 ◽

pp. 34-40 ◽

Cited By ~ 1

Author(s):

Devesh Bhatt ◽

Arunabh Chattopadhyay ◽

Wenchao Li ◽

David Oglesby ◽

Sam Owre ◽

...

Keyword(s):

Time Dependent ◽

Complex Time

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