For any positive integer $k$, there exist neural networks with $\Theta(k^3)$ layers, $\Theta(1)$ nodes per layer, and $\Theta(1)$ distinct parameters which can not be approximated by networks with $\mathcal{O}(k)$ layers unless they are exponentially large --- they must possess $\Omega(2^k)$ nodes. This result is proved here for a class of nodes termed "semi-algebraic gates" which includes the common choices of ReLU, maximum, indicator, and piecewise polynomial functions, therefore establishing benefits of depth against not just standard networks with ReLU gates, but also convolutional networks with ReLU and maximization gates, sum-product networks, and boosted decision trees (in this last case with a stronger separation: $\Omega(2^{k^3})$ total tree nodes are required).

Benefits of depth in neural networks

Our experts at TÜV Rheinland have many years of experience and practice in NDT techniques and strive to provide clients with the most fitted and tailored nondestructive method for their pressure equipment while offering reliable, timeand cost-efficient solutions. Acoustic emission testing is one of the most comprehensive and adapted proceduresto detect defects and flaws in your pressure equipment because it can be conducted during operation and does not require any interruption of activity. It also allows for global monitoring of the complete pressure equipment asset and is the best solution for vessels with complex geometries.

Acoustic Emission 방법의 공학적 응용

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Fundamentals of drilling engineering

The market for industrial enzymes has witnessed constant growth, which is currently around 7% a year, projected to reach $10.5 billion in 2024. Lipases are hydrolase enzymes naturally responsible for triglyceride hydrolysis. They are the most expansively used industrial biocatalysts, with wide application in a broad range of industries. However, these biocatalytic processes are usually limited by the low stability of the enzyme, the half-life time, and the processes required to solve these problems are complex and lack application feasibility at the industrial scale. Emerging technologies create new materials for enzyme carriers and sophisticate the well-known immobilization principles to produce more robust, eco-friendlier, and cheaper biocatalysts. Therefore, this review discusses the trending studies and industrial applications of the materials and protocols for lipase immobilization, analyzing their advantages and disadvantages. Finally, it summarizes the current challenges and potential alternatives for lipases at the industrial level.

Current Status and Future Perspectives of Supports and Protocols for Enzyme Immobilization

High-throughput computational materials design is an emerging area of materials science. By combining advanced thermodynamic and electronic-structure methods with intelligent data mining and database construction, and exploiting the power of current supercomputer architectures, scientists generate, manage and analyse enormous data repositories for the discovery of novel materials. In this Review we provide a current snapshot of this rapidly evolving field, and highlight the challenges and opportunities that lie ahead.

Gang Liu

Papers

Vibration sensor approaches for sand detection in oil–water–sand multiphase flow

Acoustic sensor approaches for sand detection in sand–water two-phase flows

Quantitative risk analysis of offshore well blowout using bayesian network

Porous metal–organic frameworks for methane storage and capture: status and challenges

Vibration sensor approaches for the sand detection in gas–sand two phases flow