Lifeboat Foundation

The Electric Coin Company (ECC) says it discovered a new way to scale blockchains with “recursive proof composition,” a proof to verify the entirety of a blockchain in one function. For the ECC and zcash, the new project, Halo, may hold the key to privacy at scale.

A privacy coin based on zero-knowledge proofs, referred to as zk-SNARKs, zcash’s current underlying protocol relies on “trusted setups.” These mathematical parameters were used twice in zcash’s short history: upon its launch in 2016 and first large protocol change, Sapling, in 2018.

Zcash masks transations through zk-SNARKs but the creation of initial parameters remains an issue. By not destroying a transaction’s mathematical foundation – the trusted setup – the holder can produce forged zcash.

Breakthroughs in physics sometimes require an assist from the field of mathematics—and vice versa.

Using a global network of computers, mathematicians have finally solved a decades-old math conundrum — and possibly the meaning of life.

Women innovators across the United States have been selected as AAAS IF/THEN® Ambassadors by the American Association for the Advancement of Science and Lyda Hill Philanthropies to share their stories and serve as high-profile role models for middle-school girls.

Information about the 125 women selected as AAAS IF/THEN® Ambassadors can be found at www.ifthenshecan.org/ambassadors.

IF/THEN®, a national initiative of Lyda Hill Philanthropies, seeks to further women in science, technology, engineering and math by empowering current innovators and inspiring the next generation of pioneers.

An exotic physical phenomenon, involving optical waves, synthetic magnetic fields, and time reversal, has been directly observed for the first time, following decades of attempts. The new finding could lead to realizations of what are known as topological phases, and eventually to advances toward fault-tolerant quantum computers, the researchers say.

The new finding involves the non-Abelian Aharonov-Bohm Effect and is published in the journal Science by MIT graduate student Yi Yang, MIT visiting scholar Chao Peng (a professor at Peking University), MIT graduate student Di Zhu, Professor Hrvoje Buljan at University of Zagreb in Croatia, Francis Wright Davis Professor of Physics John Joannopoulos at MIT, Professor Bo Zhen at the University of Pennsylvania, and MIT professor of physics Marin Soljačić.

The finding relates to gauge fields, which describe transformations that particles undergo. Gauge fields fall into two classes, known as Abelian and non-Abelian. The Aharonov-Bohm Effect, named after the theorists who predicted it in 1959, confirmed that gauge fields — beyond being a pure mathematical aid — have physical consequences.

Quantum many-body systems (QMBs), which are physical systems made up of multiple interacting particles, are among the most challenging structures to reproduce in numerical simulations. In the past, researchers have attempted to simulate these systems using a variety of techniques, including Monte Carlo simulations and even exact diagonalizations.

Methods involving tensor networks (TNs), mathematical concepts that can be applied in a variety of scientific fields, have also shown some potential for the simulation of QMBs. However, so far, these techniques have only been successfully applied to small systems or those with a simple geometry.

In a recent study, researchers at the University of Central Florida were able to simulate QMBs on Amazon Web Services using a TN-based method. Their paper, pre-published on arXiv, highlights some of the potential advantages and implications of using cloud services for research purposes.

An exotic physical phenomenon, involving optical waves, synthetic magnetic fields, and time reversal, has been directly observed for the first time, following decades of attempts. The new finding could lead to realizations of what are known as topological phases, and eventually to advances toward fault-tolerant quantum computers, the researchers say.

The new finding involves the non-Abelian Aharonov-Bohm Effect and is reported today in the journal Science by MIT graduate student Yi Yang, MIT visiting scholar Chao Peng (a professor at Peking University), MIT graduate student Di Zhu, Professor Hrvoje Buljan at University of Zagreb in Croatia, Francis Wright Davis Professor of Physics John Joannopoulos at MIT, Professor Bo Zhen at the University of Pennsylvania, and MIT professor of physics Marin Soljacic.

The finding relates to gauge fields, which describe transformations that particles undergo. Gauge fields fall into two classes, known as Abelian and non-Abelian. The Aharonov-Bohm Effect, named after the theorists who predicted it in 1959, confirmed that gauge fields—beyond being a pure mathematical aid—have physical consequences.

From the fictional universe of Stargate Atlantis and Marvel Comic’s Realm of Kings to NASA’s Eagleworks Propulsion laboratory, zero-point energy, also known as vacuum energy, is touted as a potentially limitless and ubiquitous source of energy, if one can only find the means to harness it. [1] Zero-point energy can be formulated in a few different ways, but in its most basic form, it is the minimal yet non-zero energy of a quantum mechanical system. In quantum field theory, zero-point energy can be considered by computing the expected energy of the zero photon mode. [2] In a system with no physical boundaries, the expected energy of the zero photon mode diverges! Yet, if this energy uniformly permeates all of space-time, it is not directly observable.

Conceptual Framework

For pedagogical reasons, we will consider the popular formulation of zero-point energy. The most interesting and relevant framework for zero-point energy can be understood from the quantum field theory for photons and electrons: quantum electrodynamics. Glossing over an exceptional amount of mathematical and conceptual background, the energy of a state in quantum field theory is computed as an expectation of a Hamiltonian„ which describes the energy of the state in terms of operators acting on wavefunctions. The final computation usually requires an integral over the allowed momenta of particles in the state.

❤👍👍👍

Greetings with some good news for the women’s world. Just recently, one of the most prestigious mathematics prizes in the world – The Abel Prize was awarded to a woman for the first time ever. Yes! Karen Uhlenbeck is a mathematician and a professor at the University of Texas and is now the first woman to win this prize in mathematics. You go Karen!

The award, which is modeled by the Nobel Prize, is awarded by the king of Norway to honor mathematicians who have made an influence in their field including a cash prize of around $700,000. The award to Karen cites for “the fundamental impact of her work on analysis, geometry and mathematical physics.” This award exists since 2003 but has only been won by men since.

Continue reading “The ‘Nobel Prize of Math’ Has Been Won By A Woman For The First Time Ever” »