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The computer scientist Marijn Heule is always on the lookout for a good mathematical challenge. An associate professor at Carnegie Mellon University, Heule has an impressive reputation for solving intractable math problems with computational tools. His 2016 result with the “Boolean Pythagorean triples problem” was an enormous headline-grabbing proof: “Two hundred terabyte maths proof is largest ever.” Now he’s deploying an automated approach to attack the beguilingly simple Collatz conjecture.

First proposed (according to some accounts) in the 1930s by the German mathematician Lothar Collatz, this number theory problem provides a recipe, or algorithm, for generating a numerical sequence: Start with any positive integer. If the number is even, divide by two. If the number is odd, multiply by three and add one. And then do the same, again and again. The conjecture asserts that the sequence will always end up at 1 (and then continually cycle through 4, 2, 1).

The number 5, for instance, generates only six terms:

 5, 16, 8, 4, 2, 1

The number 27 cycles through 111 terms, oscillating up and down—at its height reaching 9,232—before eventually landing at 1.

The number 40 generates another brief sequence:

40, 20, 10, 5, 16, 8, 4, 2, 1

To date, the conjecture has been checked by computer for all starting values up to nearly 300 billion billion and every number eventually reaches 1.

Most researchers believe the conjecture is true. It has enticed multitudes of mathematicians and non-mathematicians alike, but nobody has produced a proof. In the early 1980s, the Hungarian mathematician Paul Erdős declared: “Mathematics is not yet ready for such problems.”

“What we want to know is whether humans or computers are better at solving such problems.”

Marijn Heule

“And he’s probably right,” says Heule. For Heule, Collatz’s allure isn’t so much the prospect of a breakthrough as it is advancing automated reasoning techniques. After tinkering with it for five years, Heule and his collaborators, Scott Aaronson and Emre Yolcu, recently posted a paper on the arXiv preprint server. “Although we do not succeed in proving the Collatz conjecture,” they write, “we believe that the ideas here represent an interesting new approach.”

“It’s a noble failure,” says Aaronson, a computer scientist at the University of Texas at Austin. A failure because they didn’t prove the conjecture. Noble because they made progress in another sense: Heule views it as a starting point in determining whether humans or computers are better at proving such problems.

Translating math to computation

For many math problems, computers are hopeless, since they don’t have access to the vast oeuvre of mathematics amassed through history. But sometimes computers excel where humans are hopeless. Tell a computer what a solution looks like—give it a target and a well-defined search space—and then with brute force the computer might find it. Though it’s a matter of debate whether computational results amount to meaningful additions to the mathematical canon. The traditional view is that only human creativity and intuition, via concepts and ideas, extend the reach of mathematics, whereas advancements via computing are often dismissed as engineering.

In a sense, the computer and the Collatz conjecture are a perfect match. For one, as Jeremy Avigad, a logician and professor of philosophy at Carnegie Mellon notes, the notion of an iterative algorithm is at the foundation of computer science—and Collatz sequences are an example of an iterative algorithm, proceeding step-by-step according to a deterministic rule. Similarly, showing that a process terminates is a common problem in computer science. “Computer scientists generally want to know that their algorithms terminate, which is to say, that they always return an answer,” Avigad says. Heule and his collaborators are leveraging that technology in tackling the Collatz conjecture, which is really just a termination problem.

“The beauty of this automated method is that you can turn on the computer, and wait.”

Jeffrey Lagarias

Heule’s expertise is with a computational tool called a “SAT solver”—or a “satisfiability” solver, a computer program that determines whether there is a solution for a formula or problem given a set of constraints. Though crucially, in the case of a mathematical challenge, a SAT solver first needs the problem translated, or represented, in terms that the computer understands. And as Yolcu, a PhD student with Heule, puts it: “Representation matters, a lot.”

longshot, but worth a try

When Heule first mentioned tackling Collatz with a SAT solver, Aaronson thought, “There is no way in hell this is going to work.” But he was easily convinced it was worth a try, since Heule saw subtle ways to transform this old problem that might make

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By: Siobhan Roberts
Title: Are computers ready to solve this notoriously unwieldy math problem?
Sourced From: www.technologyreview.com/2021/07/02/1027475/computers-ready-solve-this-notorious-math-problem/
Published Date: Fri, 02 Jul 2021 10:00:00 +0000

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LATAM crypto exchange Bitso and FMF launch NFT of Mexico’s National Team jerseys

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Bitso, a leading cryptocurrency platform operating in Latin America, and the Mexican Football Federation (FMF), today announced the joint launch of the first collectible NFT of the Mexico National Team’s jerseys that was acquired in cryptocurrencies.

This morning through their social media platforms, the FMF and Bitso announced the opportunity to acquire the new official National Team fan jerseys ahead of the team’s participation in the 2022 World Cup. In just 20 minutes, the entire collection sold out.

bitsonftjeysey
The NFTs of the jerseys have an exclusive design for the metaverse – each is unique on the blockchain and can be resold by its owner in subsequent transactions.

The collection consisted of 100 official physical jerseys, each with a corresponding NFT version of the jersey that fans’ avatars can wear within the Decentraland metaverse. Each physical and NFT jersey set sold for the equivalent of $1,800 MXN in ethers.

“Our mission is to make cryptocurrency useful in the everyday life of Mexicans; we are committed to spreading the technology through innovative opportunities that help people throughout the country familiarize themselves with this new world. We are very excited to offer the incredible, historic opportunity for the fans of our National Team so that through their Bitso account, they can wear the colors of the National Team on and ‘off’ the field in the metaverse.”
– Bárbara González Briseño, General Director of Bitso México

Jersey NFTs

Created by Bitso, the virtual jersey sports the official colors of Mexico and the new National Team shield, characteristics that will make it stand out when users wear it in the virtual world of Decentraland.

The post LATAM crypto exchange Bitso and FMF launch NFT of Mexico’s National Team jerseys appeared first on CryptoNinjas.

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By: CryptoNinjas.net
Title: LATAM crypto exchange Bitso and FMF launch NFT of Mexico’s National Team jerseys
Sourced From: www.cryptoninjas.net/2022/07/29/latam-crypto-exchange-bitso-and-fmf-launch-nft-of-mexicos-national-team-jerseys/
Published Date: Fri, 29 Jul 2022 15:19:02 +0000

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Long-running crypto exchange EXMO unveils “lively” rebrand amidst growth

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EXMO, a crypto exchange platform operating since 2014, announced this week a rebranded visual identity with includes a new logo, brand colors, and design features. This new branding comes as EXMO continues to grow its crypto platform while also seeking to expand its presence in other jurisdictions.

Some new developments underway at EXMO:

Soon, users will be able to earn passive income from EXMO’s new staking platform.Plans to launch an EXMO crypto debit card.Expansion of its services in international markets with the opening of offices in Poland and Lithuania.

EXMO’s new logo

The rationale for the re-brand:

“At EXMO, we have a vision of a world where crypto is in every wallet. Hassle-free. We want to achieve this by making crypto as simple and accessible to everyone as possible. And we know that you already appreciate EXMO for offering user-friendly services and helpful support. Also for the opportunity to trade anywhere and anytime, closing deals in just a few taps. Such important changes required a rethinking of our corporate style, which has long needed a massive upgrade. So today we are introducing a new brand identity for EXMO with a completely new visual concept. We are launching a new logo, brand colors, and design elements. Our key design principles are simplicity, boldness, and a pinch of fun. But most importantly, we have changed our logo. Simple and easily recognizable, it represents the humanity of our brand. The logo stands out due to the wavy letter ‘m’ which symbolizes exchange rate charts and also resembles a spring that will launch you into the crypto world.”
– The EXMO Team regarding the re-branding

The post Long-running crypto exchange EXMO unveils “lively” rebrand amidst growth appeared first on CryptoNinjas.

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By: CryptoNinjas.net
Title: Long-running crypto exchange EXMO unveils “lively” rebrand amidst growth
Sourced From: www.cryptoninjas.net/2022/07/26/long-running-crypto-exchange-exmo-unveils-lively-rebrand-amidst-growth/
Published Date: Tue, 26 Jul 2022 08:10:38 +0000

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Stitching together the grid will save lives as extreme weather worsens

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The blistering heat waves that set temperature records across much of the US in recent days have strained electricity systems, threatening to knock out power in vulnerable regions of the country. 

The electricity has largely stayed online so far this summer, but there have been scattered problems and close calls already. 

Heavy use of energy-sucking air-conditioners is the biggest problem. But intense heat can also reduce the output of power plants, blow transformers, and force power lines to sag. Severe droughts across large parts of the country have also significantly reduced the availability of hydroelectric power, according to the North American Electric Reliability Corporation (NERC). 

It’s unlikely to get better soon. A number of grid operators may struggle to meet peak summer demand, creating the risk of rolling blackouts, the NERC report notes.

The nation’s isolated and antiquated grids are in desperate need of upgrades to keep the lights, heat, and air-conditioning on in the midst of extreme weather events that climate change is making more common, severe, and dangerous. One clear way to ease many of these issues is to more tightly integrate the country’s regional grids, stitching them together with more long-range transmission lines. 

If electricity generated in one area can be more easily shared across much wider regions, power can simply flow to where it’s needed at those moments when customers crank up air-conditioners en masse, or when power plants or fuel supply lines fail amid soaring temperatures, wildfires, hurricanes, or other events, says Liza Reed, a research manager focused on transmission at the Niskanen Center, a Washington, DC, think tank.  

The problem is it’s proved difficult to build more long-range transmission and grid interconnections for a variety of reasons, including the permitting challenges of erecting wires through private and public lands across cities, counties, and states and the reluctance of local authorities to forfeit control or submit to greater federal oversight.

The case of Texas

The unreliability of the US grid is not a new problem. Severe heat and winter storms have repeatedly exposed the frailty of electricity systems in recent years, leaving thousands to millions of people without power as temperatures spiked or plunged.

One of the fundamental challenges is that the grids today are highly fragmented. There are three main electricity networks within the US: the Eastern Grid, the Western Grid, and the Electric Reliability Council of Texas (ERCOT). But there are numerous regional transmission organizations within those first two systems, including the California Independent System Operator, Southwest Power Pool, PJM Interconnection, New York ISO, and more. 

These grids form a complex web of networks operating under different regulators, rules and market structures, and often with limited connections between them.

Map USA grid
A variety of regional transmission organizations oversee different parts of the nation’s aging and fragmented grids, which operate under different rules and with often limited connections between them.
legend

ERCOT is especially isolated, in part because of the desire among local politicians, citizens, and power companies to avoid added competition, the hassle of following other states’ rules, and oversight from the Federal Energy Regulatory Commission (FERC). But the state offers a case study in why that can be a serious problem amid increasingly harsh climate conditions, Reed says.

The Texas grid operator pleaded with customers several times earlier this month to cut electricity use as blistering summer temperatures created  demand surges that threatened to outstrip supply and require rolling blackouts.  Low wind conditions, cloud cover, and outages at fossil-fuel power plants added to the strains.

Shutting off the electricity needed to run air-conditioning in triple-digit temperatures

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By: James Temple
Title: Stitching together the grid will save lives as extreme weather worsens
Sourced From: www.technologyreview.com/2022/07/28/1056483/stitching-together-the-grid-will-save-lives-as-extreme-weather-worsens/
Published Date: Thu, 28 Jul 2022 08:00:00 +0000

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