Engineering topics

Tao, Terence

Publications and source records attributed to Tao, Terence.

15 records

DOE OSTI2024

PCAST: Letter to the President on Expanding STEM Talent in the Federal Workforce

The President’s Council of Advisors on Science and Technology (PCAST) is the sole body of advisors from outside the federal government charged with making science, technology, and innovation policy recommendations to the President and the White House. Established by Executive Order, it is an independent Federal Advisory Committee comprised of distinguished individuals from industry, academia, and non-profit organizations with a range of perspectives and expertise. On October 23, 2024, PCAST sent a letter to the President with recommendations to strengthen the science, technology, engineering, and mathematics (STEM) workforce in the federal government.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2024

PCAST: Report to the President on a Vision for Advancing Nutrition Science in the United States

The President’s Council of Advisors on Science and Technology (PCAST) is the sole body of advisors from outside the federal government charged with making science, technology, and innovation policy recommendations to the President and the White House. Established by Executive Order, it is an independent Federal Advisory Committee comprised of distinguished individuals from industry, academia, and non-profit organizations with a range of perspectives and expertise. On September 20, 2024, PCAST sent a report to the President with recommendations to advance nutrition science and to enable equitable access to the benefits of nutrition research.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

PCAST: Report to the President on Supercharging Research: Harnessing Artificial Intelligence to Meet Global Challenges

The President’s Council of Advisors on Science and Technology (PCAST) is the sole body of advisors from outside the federal government charged with making science, technology, and innovation policy recommendations to the President and the White House. Established by Executive Order, it is an independent Federal Advisory Committee comprised of distinguished individuals from industry, academia, and non-profit organizations with a range of perspectives and expertise. On April 29, 2024, PCAST sent a report to the President with recommendations to help the U.S. harness the full potential of AI to equitably and responsibly supercharge scientific discovery.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

PCAST: Report to the President on Strategy for Cyber-Physical Resilience: Fortifying Our Critical Infrastructure for a Digital World

The President’s Council of Advisors on Science and Technology (PCAST) is the sole body of advisors from outside the federal government charged with making science, technology, and innovation policy recommendations to the President and the White House. Established by Executive Order, it is an independent Federal Advisory Committee comprised of distinguished individuals from industry, academia, and non-profit organizations with a range of perspectives and expertise. On February 27, 2024, PCAST sent a report to the President with recommendations to bolster the resilience and adaptability of the nation’s cyber-physical infrastructure resources.

42 ENGINEERING↗

DOE OSTI2024

PCAST: Report to the President on Accelerating Effective Reduction of Greenhouse Gas Emissions

The President’s Council of Advisors on Science and Technology (PCAST) is the sole body of advisors from outside the federal government charged with making science, technology, and innovation policy recommendations to the President and the White House. Established by Executive Order, it is an independent Federal Advisory Committee comprised of distinguished individuals from industry, academia, and non-profit organizations with a range of perspectives and expertise. On February 20, 2024, PCAST sent a report to the President with recommendations to expedite the reduction of greenhouse gas emissions through whole-of-country coordinated efforts and expanded assessment and verification systems.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Report to the President: A Transformational Effort on Patient Safety

The President’s Council of Advisors on Science and Technology (PCAST) is the sole body of advisors from outside the federal government charged with making science, technology, and innovation policy recommendations to the President and the White House. Established by Executive Order, it is an independent Federal Advisory Committee comprised of distinguished individuals from industry, academia, and non-profit organizations with a range of perspectives and expertise. On September 7, 2023, PCAST sent a report to the President with recommendations to develop and deploy policies and technologies that will improve patient safety in the United States, dramatically reducing harms to patients and healthcare workers.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2023

PCAST: Letter to the President on Advancing Public Engagement with the Sciences

The President’s Council of Advisors on Science and Technology (PCAST) is the sole body of advisors from outside the federal government charged with making science, technology, and innovation policy recommendations to the President and the White House. Established by Executive Order, it is an independent Federal Advisory Committee comprised of distinguished individuals from industry, academia, and non-profit organizations with a range of perspectives and expertise. On August 29, 2023, PCAST sent a letter to the President with recommendations for catalyzing effective and systematic engagement between federal research and development agencies, science and technology experts, and the American people.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2023

PCAST: Report to the President and to Congress on the Seventh Assessment of the National Nanotechnology Initiative

The President’s Council of Advisors on Science and Technology (PCAST) is the sole body of advisors from outside the federal government charged with making science, technology, and innovation policy recommendations to the President and the White House. Established by Executive Order, it is an independent Federal Advisory Committee comprised of distinguished individuals from industry, academia, and non-profit organizations with a range of perspectives and expertise. On August 18, 2023, PCAST sent a report to the President and Congress with recommendations for updating federal government coordination and support for nanotechnology that reflect the success of the National Nanotechnology Initiative and the maturity and broad relevance of the field.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2023

PCAST: Report to the President on Supporting the U.S. Public Health Workforce

The President’s Council of Advisors on Science and Technology (PCAST) is the sole body of advisors from outside the federal government charged with making science, technology, and innovation policy recommendations to the President and the White House. Established by Executive Order, it is an independent Federal Advisory Committee comprised of distinguished individuals from industry, academia, and non-profit organizations with a range of perspectives and expertise. On May 1, 2023, PCAST sent a report to the President with recommendations for developing and sustaining the robust public health workforce that is essential for the United States to make long-needed, permanent improvements to our nation’s approach to public health.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2023

Report to the President: Extreme Weather Rik in a Changing Climate: Enhancing prediction and protecting communities

The President’s Council of Advisors on Science and Technology (PCAST) is the sole body of advisors from outside the federal government charged with making science, technology, and innovation policy recommendations to the President and the White House. Established by Executive Order, it is an independent Federal Advisory Committee comprised of distinguished individuals from industry, academia, and non-profit organizations with a range of perspectives and expertise. On April 24, 2023, PCAST sent a report to the President with recommendations on how science and technology can help inform and empower communities, businesses, and government agencies to prepare, respond, and adapt to extreme weather.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2023

PCAST: Report to the President on Modernizing Wildland Firefighting to Protect Our Firefighters

The President’s Council of Advisors on Science and Technology (PCAST) is the sole body of advisors from outside the federal government charged with making science, technology, and innovation policy recommendations to the President and the White House. Established by Executive Order, it is an independent Federal Advisory Committee comprised of distinguished individuals from industry, academia, and non-profit organizations with a range of perspectives and expertise. On February 22, 2023, PCAST sent a report to the President with recommendations for modernizing wildland firefighting to protect America’s firefighters.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Report to the President: Biomanufacturing to Advance the Bioeconomy

The President’s Council of Advisors on Science and Technology (PCAST) is the sole body of advisors from outside the federal government charged with making science, technology, and innovation policy recommendations to the President and the White House. Established by Executive Order, it is an independent Federal Advisory Committee comprised of distinguished individuals from industry, academia, and non-profit organizations with a range of perspectives and expertise. On December 8, 2022, PCAST sent a report to the President with recommendations to promote the growth of the U.S. bioeconomy.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

PCAST: Report to the President on Revitalizing the U.S. Semiconductor Ecosystem

The President’s Council of Advisors on Science and Technology (PCAST) is the sole body of advisors from outside the federal government charged with making science, technology, and innovation policy recommendations to the President and the White House. Established by Executive Order, it is an independent Federal Advisory Committee comprised of distinguished individuals from industry, academia, and non-profit organizations with a range of perspectives and expertise. On September 20, 2022, PCAST sent a report to the President with details on recommendations for implementing the CHIPS and Science Act funds appropriated for semiconductors research and development.

42 ENGINEERING↗

DOE OSTI2022

PCAST: Letter to the President on Recommendations for Semiconductors R&D

The President’s Council of Advisors on Science and Technology (PCAST) is the sole body of advisors from outside the federal government charged with making science, technology, and innovation policy recommendations to the President and the White House. Established by Executive Order, it is an independent Federal Advisory Committee comprised of distinguished individuals from industry, academia, and non-profit organizations with a range of perspectives and expertise. On August 9, 2022, PCAST sent a letter to the President with recommendations for implementing the CHIPS and Science Act funds appropriated for semiconductors research and development.

42 ENGINEERING↗

DOE OSTI2021

Eigenvectors from Eigenvalues: a survey of a basic identity in linear algebra

If $A$ is an $n \times n$ Hermitian matrix with eigenvalues $\lambda_1(A),\dots,\lambda_n(A)$ and $i,j = 1,\dots,n$, then the $j^{\mathrm{th}}$ component $v_{i,j}$ of a unit eigenvector $v_i$ associated to the eigenvalue $\lambda_i(A)$ is related to the eigenvalues $\lambda_1(M_j),\dots,\lambda_{n-1}(M_j)$ of the minor $M_j$ of $A$ formed by removing the $j^{\mathrm{th}}$ row and column by the formula $$ |v_{i,j}|^2\prod_{k=1;k\neq i}^{n}\left(\lambda_i(A)-\lambda_k(A)\right)=\prod_{k=1}^{n-1}\left(\lambda_i(A)-\lambda_k(M_j)\right)\,.$$ We refer to this identity as the \emph{eigenvector-eigenvalue identity}. Despite the simple nature of this identity and the extremely mature state of development of linear algebra, this identity was not widely known until very recently. In this survey we describe the many times that this identity, or variants thereof, have been discovered and rediscovered in the literature (with the earliest precursor we know of appearing in 1934). We also provide a number of proofs and generalizations of the identity.

97 MATHEMATICS AND COMPUTING↗