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Results for “dual norm”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2024

The Average Spectrum Norm and Near-Optimal Tensor Completion

We propose the average spectrum norm to study the minimum number of measurements required to approximate a multidimensional array (i.e., sample complexity) via low-rank tensor recovery. Our focus is on the tensor completion problem, where the aim is to estimate a multiway array using a subset of tensor entries corrupted by noise. Our average spectrum norm-based analysis provides near-optimal sample complexities, exhibiting dependence on the ambient dimensions and rank that do not suffer from exponential scaling as the order increases.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Dual Representations and H ∞ -Optimal Control of Partial Differential Equations

We consider H ∞ -optimal state-feedback control of the class of linear Partial Differential Equations (PDEs) which admit a Partial Integral Equation (PIE) representation. While linear matrix inequalities are commonly used for optimal control of Ordinary Differential Equations (ODEs), the absence of a universal state-space representation and suitable dual form prevents such methods from being applied to optimal control of PDEs. Specifically, for ODEs, the controller synthesis problem is defined in state-space, and duality is used to resolve the bilinearity of that synthesis problem. Recently, the PIE representation was proposed as a universal state-space representation for linear PDE systems. In this paper, we show that any PDE system represented by a PIE admits a dual PIE with identical stability and I/O properties. This result allows us to reformulate the stabilizing and optimal state-feedback control problems as convex optimization over the cone of positive Partial Integral (PI) operators. Operator inversion formulae then allow us to construct feedback gains for the original PDE system. The results are verified through application to several canonical problems in optimal control of PDEs and indicate the resulting bounds on H ∞ norm are not conservative.

42 ENGINEERING↗

DOE OSTI2024

Methods of Securing Chemical and Pharmaceutical Knowledge and Recommendations for International Institutions to Enhance Research Integrity

Here, this paper examines strategies for securing chemical and pharmaceutical expertise in a globalized research environment, focusing on safeguarding intellectual property and preventing the misuse of sensitive and potentially dual-use information. The product of collective efforts between Pacific Northwest National Laboratory, Carol Davila University of Medicine and Pharmacy, and New Bulgarian University, highlights the challenges and opportunities posed by cross-border research collaborations, particularly in the context of differing regulatory frameworks and research cultures. It explores current mechanisms to prevent data loss and unauthorized access to sensitive information while assessing the effectiveness of existing security measures, frameworks, and international export control regimes. The approach examines the differing methodologies for promoting transparency, trust-building, and mutual accountability in joint research projects to cultivate secure data-sharing practices and intellectual property. It provides recommendations for international institutions to implement security guidelines in framing research priorities, encourages continual training and education programs, and the integration of processes for monitoring research compliance. This partnership aims to advance scientific innovation while maintaining global stability, ensuring compliance with international norms, and safeguarding valuable intellectual property as measures in chemical and pharmaceutical research security practices continue to expand due to international collaboration and knowledge exchange.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗