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Category: mathematics

Created as an analogy for Quantum Electrodynamics (QED) — which describes the interactions due to the electromagnetic force carried by photons — Quantum Chromodynamics (QCD) is the theory of physics that explains the interactions mediated by the strong force — one of the four fundamental forces of nature.

A new collection of papers published in The European Physical Journal Special Topics and edited by Diogo Boito, Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, Brazil, and Irinel Caprini, Horia Hulubei National Institute for Physics and Nuclear Engineering, Bucharest, Romania, brings together recent developments in the investigation of QCD.

The editors explain in a special introduction to the collection that due to a much stronger coupling in the — carried by gluons between quarks, forming the fundamental building blocks of matter — described by QCD, than the , the divergence of perturbation expansions in the mathematical descriptions of a system can have important physical consequences. The editors point out that this has become increasingly relevant with recent high-precision calculations in QCD, due to advances in the so-called higher-order loop computations.

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He has done his math. The questions seem to be: How to put together viable payloads to make use of Stsrship launches? How to build new markets in space?

This again?! Game Over? Busted? We’re doing Starship again so soon because I’m an unoriginal hack. There’s also been new developments in Starship and I think it’s a perfect time to revisit the launch system. Get as mad as you wish.

Will Starship live up to expectations? Will it really revolutionize space travel? Is Mars and beyond finally within grasp? Why are Musk’s fans so strangely devoted to him? Will I stop asking dumb questions?

Corrections, Clarifications, and Notes.

1. Jesus Christ I forgot about Dear Moon again. It’s clear that Starship probably won’t be human-rated by NASA by 2023. The FAA, if I remember correctly, doesn’t regulate commercial crew vehicles (like airplanes) yet. You could always do a Crew Dragon to Starship for that or something along those lines. I’d anticipate Dear Moon being pushed or somehow incorporated into an HLS demonstration.

2. I’m not bringing up the early test program this time around. SpaceX has clearly gotten better at building tanks (though I suspect Starhopper was mostly a publicity stunt).

3. I didn’t include government launch contracts because those end up more expensive than commercial payloads due to more stringent requirements and specialized missions.

4. I didn’t talk about SpaceX finances since they’re private information. The Morgan Stanley valuation was made by people who I’d argue don’t know anything about the launch market. Their assessment is nonsensical. Also, I doubt SpaceX is making much money as a commercial launch provider—the launch side of the space industry is small; if it weren’t for Starship and Starlink, they might. It also appears that SpaceX is adept at burning cash, considering all the fundraising they do. It’s hard to say without industrial espionage.

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Lightelligence, the global optical computing innovator, revealed its Photonic Arithmetic Computing Engine (PACE), the company’s latest platform to fully integrate photonics and electronics in a small form factor.

As Lightelligence’s first demonstration of optical computing for use cases beyond AI and deep learning, PACE efficiently searches for solutions to several of the hardest computational math problems, including the Ising problem, and the graph Max-Cut and Min-Cut problems, illustrating the real-world potential of integrated photonics in advanced computation.

Visit https://www.lightelligence.ai/ to learn more.

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Biotechnology is a curious marriage of two seemingly disparate worlds. On one end, we have living organisms—wild, unpredictable celestial creations that can probably never be understood or appreciated enough, while on the other is technology—a cold, artificial entity that exists to bring convenience, structure and mathematical certainty in human lives. The contrast works well in combination, though, with biotechnology being an indispensable part of both healthcare and medicine. In addition to those two, there are several other applications in which biotechnology plays a central role—deep-sea exploration, protein synthesis, food quality regulation and preventing environmental degradation. The increasing involvement of AI in biotechnology is one of the main reasons for its growing scope of applications.

So, how exactly does AI impact biotechnology? For starters, AI fits in neatly with the dichotomous nature of biotechnology. After all, the technology contains a duality of its own—machine-like efficiency combined with the quaintly animalistic unpredictability in the way it works. In general terms, businesses and experts involved in biotechnology use AI to improve the quality of research and for improving compliance with regulatory standards.

More specifically, AI improves data capturing, analysis and pattern recognition in the following biotechnology-based applications:

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By Alex Hill, Senior Quantum Systems Engineer

Qubits are the basic building block of a quantum processor, and are so named because they represent a continuum of complex superpositions of two basic quantum states. The power of qubits comes in part from their ability to encode significantly more information than a classical bit — an infinite set of states between 0 and 1. In mathematical terms, quantum gates that manipulate the state of individual qubits are unitary operators drawn from SU.

Rigetti’s superconducting quantum processors are based on the transmon design [1]. Each physical qubit is an anharmonic oscillator, meaning that the energy gaps between subsequent qubit energy states decrease as the qubit climbs higher up the state ladder. We typically only address the first two states, 0 and 1 (in the literature, sometimes referred to as g(round) and e(xcited)); however, the design of our qubits supports even higher states. The simple structure of the transmon energy levels gives superconducting qubits the unique ability to address many of these states in a single circuit.

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The mathematician Ben Green of the University of Oxford has made a major stride toward understanding a nearly 100-year-old combinatorics problem, showing that a well-known recent conjecture is “not only wrong but spectacularly wrong,” as Andrew Granville of the University of Montreal put it. The new paper shows how to create much longer disordered strings of colored beads than mathematicians had thought possible, extending a line of work from the 1940s that has found applications in many areas of computer science.

The conjecture, formulated about 17 years ago by Ron Graham, one of the leading discrete mathematicians of the past half-century, concerns how many red and blue beads you can string together without creating any long sequences of evenly spaced beads of a single color. (You get to decide what “long” means for each color.)

This problem is one of the oldest in Ramsey theory, which asks how large various mathematical objects can grow before pockets of order must emerge. The bead-stringing question is easy to state but deceptively difficult: For long strings there are just too many bead arrangements to try one by one.

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Physicists from Trinity have unlocked the secret that explains how large groups of individual “oscillators”—from flashing fireflies to cheering crowds, and from ticking clocks to clicking metronomes—tend to synchronize when in each other’s company.

Their work, just published in the journal Physical Review Research, provides a mathematical basis for a phenomenon that has perplexed millions—their newly developed equations help explain how individual randomness seen in the and in electrical and computer systems can give rise to synchronization.

We have long known that when one clock runs slightly faster than another, physically connecting them can make them tick in time. But making a large assembly of clocks synchronize in this way was thought to be much more difficult—or even impossible, if there are too many of them.

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Strategy accelerates the best algorithmic solvers for large sets of cities.

Waiting for a holiday package to be delivered? There’s a tricky math problem that needs to be solved before the delivery truck pulls up to your door, and MIT researchers have a strategy that could speed up the solution.

The approach applies to vehicle routing problems such as last-mile delivery, where the goal is to deliver goods from a central depot to multiple cities while keeping travel costs down. While there are algorithms designed to solve this problem for a few hundred cities, these solutions become too slow when applied to a larger set of cities.

The solver algorithms work by breaking up the problem of delivery into smaller subproblems to solve — say, 200 subproblems for routing vehicles between 2,000 cities. Wu and her colleagues augment this process with a new machine-learning algorithm that identifies the most useful subproblems to solve, instead of solving all the subproblems, to increase the quality of the solution while using orders of magnitude less compute.

Their approach, which they call “learning-to-delegate,” can be used across a variety of solvers and a variety of similar problems, including scheduling and pathfinding for warehouse robots, the researchers say.

Full Story:

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