Blog

Archive for the ‘mathematics’ category

Sep 16, 2019

Was SHA-256 cracked? Don’t buy into retraction!

Posted by in categories: bitcoin, cryptocurrencies, encryption, government, hacking, internet, mathematics, military, privacy, security, software

SHA-256 is a one way hashing algorithm. Cracking it would have tectonic implications for consumers, business and all aspects of government including the military.

It’s not the purpose of this post to explain encryption, AES or SHA-256, but here is a brief description of SHA-256. Normally, I place reference links in-line or at the end of a post. But let’s get this out of the way up front:

One day after Treadwell Stanton DuPont claimed that a secret project cracked SHA-256 more than one year ago, they back-tracked. Rescinding the original claim, they announced that an equipment flaw caused them to incorrectly conclude that they had algorithmically cracked SHA-256.

All sectors can still sleep quietly tonight,” said CEO Mike Wallace. “Preliminary results in this cryptanalytic research led us to believe we were successful, but this flaw finally proved otherwise.

Continue reading “Was SHA-256 cracked? Don’t buy into retraction!” »

Sep 16, 2019

Mentors, Encouragement, Hands-on Learning Boost Girls’ Interest in STEM Substantially

Posted by in categories: computing, education, employment, engineering, mathematics

Generally girls lose interest in STEM careers as they get older. But, according to a new study, small changes at school and at home can have a profound impact on how girls perceive STEM careers, how confident they feel in class and how likely they are to pursue STEM academically and into their careers.

The study, “Closing the STEM Gap,” published today by Microsoft, surveyed more than 6,000 girls and young women on their interests and perceptions of science, technology, engineering and math. It found that girls tended to lose interest in STEM as they headed toward adulthood. And, by the time they’d finished high school, their interest had dropped substantially. For example, the report found that interest in computer science among females dropped 27 percentage points between middle school and college. According to the report: “In middle school … 31 percent of girls believe that jobs requiring coding and programming are ‘not for them.’ In high school, that percentage jumps up to 40. By the time they’re in college, 58 percent of girls count themselves out of these jobs.”

But, the study found, countermeasures both large and small can have a profound effect, including:

Sep 14, 2019

You Can Now Prove a Whole Blockchain With One Math Problem – Really

Posted by in categories: bitcoin, mathematics

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.

Sep 10, 2019

The coevolution of physics and math

Posted by in categories: mathematics, physics

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

Sep 9, 2019

Two Mathematicians Just Solved a Decades-Old Math Riddle — and Possibly the Meaning of Life

Posted by in categories: computing, mathematics

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

Sep 9, 2019

125 Women in STEM Selected as AAAS IF/THEN Ambassadors

Posted by in categories: education, engineering, mathematics

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.

Sep 8, 2019

Exotic Physics Phenomenon Involving Time Reversal Observed for First Time

Posted by in categories: computing, mathematics, particle physics, quantum physics

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.

Sep 7, 2019

Simulating quantum many-body systems on Amazon Web Services

Posted by in categories: mathematics, particle physics, quantum physics

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 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 for research purposes.

Sep 5, 2019

Exotic physics phenomenon is observed for first time

Posted by in categories: computing, mathematics, particle physics, quantum physics

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.

Sep 4, 2019

Harnessing Zero-Point Energy

Posted by in categories: computing, mathematics, particle physics, quantum physics

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.

Page 1 of 2712345678Last