Cubitt, et.al., arXiv.org, Undecidability of the Spectral Gap, here. See Aaronson as well.
We show that the spectral gap problem is undecidable. Specifically, we construct families of translationally-invariant, nearest-neighbour Hamiltonians on a 2D square lattice of d-level quantum systems (d constant), for which determining whether the system is gapped or gapless is an undecidable problem. This is true even with the promise that each Hamiltonian is either gapped or gapless in the strongest sense: it is promised to either have continuous spectrum above the ground state in the thermodynamic limit, or its spectral gap is lower-bounded by a constant in the thermodynamic limit. Moreover, this constant can be taken equal to the local interaction strength of the Hamiltonian.
This implies that it is logically impossible to say in general whether a quantum many-body model is gapped or gapless. Our results imply that for any consistent, recursive axiomatisation of mathematics, there exist specific Hamiltonians for which the presence or absence of a spectral gap is independent of the axioms.
These results have a number of important implications for condensed matter and many-body quantum theory.
Oscar Williams-Grut, Business Insider,One epic slideshow tells you everything you need to know about the $180 billion world of online lending, here. NIMo
Fintech analyst Cormac Leech gave an epic presentation at LendIt Europe conference in London last week, answering pretty much every question you might have about the online direct lending market.
‘Banks really have to fear smarter banks’ — this CEO nails the dirty secret about fintech startups, here.
So why do journalists like me wastes so much oxygen on fintech? The main reason is the money going into the sector.
$50 billion has been pumped into fintech startups around the world over the last 5 years, with the amount growing every year. In the UK alone $5.4 billion has been invested between 2010 and 2015.
These VC backers are betting that fintech will be a game changer, either revolutionising systems within banks or heralding a huge shift in consumer behaviour. They may not be a Facebook or Google today, but one day they might be.
Nicole Hemsoth, The Next Platform, Inside the GPU Clusters that Power Baidu’s Neural Networks, here.
Baidu’s Silicon Valley AI Lab is at the heart of many of these efforts and according to one of the leads there, Bryan Catanzaro, the evolution of both these problems, and their potential solutions, at scale tends to be swifter than even his team of hardware, AI, and other experts expects.
Catanzaro was the first employee at the AI lab, right behind chief scientist Andrew Ng and research lead Adam Coates. Before moving to Baidu, Catanzaro worked at Nvidia, where he collaborated with Coates on large scale deep learning using commercial off the shelf HPC technologies. He continued this collaboration with Coates at Baidu, where they decided to apply HPC for deep learning to speech recognition. The team went from no infrastructure to their first functional speech recognition engine in just a few months and moved quickly from scaling from four to eight GPUs for model training—a notable feat given some of the communication and other hurdles of multi-GPU systems, particularly for data-rich training workloads.