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Category: mathematics

Glow is an iconic interesting research about deep neural networks that can generalize with small training sets.

Since the early days of machine learning, artificial intelligence scenarios have faced with two big challenges in order to experience mainstream adoption. First, we have the data efficiency problem that requires machine or deep learning models to be trained using large and accurate datasets which, as we know, are really expensive to build and maintain. Secondly, we have the generalization problem which AI agents face in order to build new knowledge that is different from the training data. Humans, by contrast, are incredibly efficient learning with minimum supervision and rapidly generalizing knowledge from a few data examples.

Generative models are one of the deep learning disciplines that focuses on addressing the two challenges mentioned above. Conceptually, generative models are focused on observing an initial dataset, like a set of pictures, and try to learn how the data was generated. Using more mathematical terms, generative models try to infer all dependencies within very high-dimensional input data, usually specified in the form of a full joint probability distribution. Entire deep learning areas such as speech synthesis or semi-supervised learning are based on generative models. Recently, generative models such as generative adversarial networks(GANs) have become extremely popular within the deep learning community. Recently, OpenAI experimented with a not-very well-known technique called Flow-Based Generative Models in order to improve over existing methods.

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A Penn State scientist studying crystal structures has developed a new mathematical formula that may solve a decades-old problem in understanding spacetime, the fabric of the universe proposed in Einstein’s theories of relativity.

“Relativity tells us space and time can mix to form a single entity called spacetime, which is four-dimensional: three space-axes and one time-axis,” said Venkatraman Gopalan, professor of materials science and engineering and physics at Penn State. “However, something about the time-axis sticks out like sore thumb.”

For calculations to work within relativity, scientists must insert a negative sign on time values that they do not have to place on space values. Physicists have learned to work with the negative values, but it means that spacetime cannot be dealt with using traditional Euclidean geometry and instead must be viewed with the more complex hyperbolic geometry.

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Quantum computing began in the early 1980s. It operates on principles of quantum physics rather than the limitations of circuits and electricity which is why it is capable of processing highly complex mathematical problems so efficiently. Quantum computing could one day achieve things that classical computing simply cannot. The evolution of quantum computers has been slow, but things are accelerating, thanks to the efforts of academic institutions such as Oxford, MIT, and the University of Waterloo, as well as companies like IBM, Microsoft, Google, and Honeywell.

IBM has held a leadership role in this innovation push and has named optimization as the most likely application for consumers and organizations alike.

Honeywell expects to release what it calls the “world’s most powerful quantum computer” for applications like fraud detection, optimization for trading strategies, security, machine learning, and chemistry and materials science.

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These groups of brain cells are called “assemblies,” which Papadimitriou describes as “a highly connected, stable set of neurons which represent something: a word, an idea, an object, etc.”

Award-winning neuroscientist György Buzsáki describes assemblies as “the alphabet of the brain.”

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The US Department of Energy on Thursday is officially dedicating Perlmutter, a next-generation supercomputer that will deliver nearly four exaflops of AI performance. The system, based at the National Energy Research Scientific Computing Center (NERSC) at Lawrence Berkeley National Laboratory, is the world’s fastest on the 16-bit and 32-bit mixed-precision math used for AI.

The HPE Cray system is being installed in two phases. Each of Phase 1’s GPU-accelerated nodes has four Nvidia A100 Tensor Core GPUs, for a total of 6159 Nvidia A100 Tensor Core GPUs. Each Phase 1 node also has a single AMD Milan CPU.

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## MATHEMATICS • MAY 24, 2021

# *Noise is commonly discarded, but identifying patterns in noise can be very useful.*

*Generalize the Hearst exponent by adding more coefficients in order to get a more complete description of the changing data. This makes it possible to find patterns in the data that are usually considered noise and were previously impossible to analyze.*

*The development of this mathematical apparatus can solve the issue of parameterisation and analysis of processes for which there is no exact mathematical description. This opens up enormous prospects in describing, analyzing and forecasting complex systems.*

*by moscow institute of physics and technology*

One of the metrics used in economics and natural sciences in time series analysis is the Hurst exponent. It suggests whether the trend present in the data will persist: for example, whether values will continue to increase, or whether growth will turn to decline. This assumption holds for many natural processes and is explained by the inertia of natural systems. For example, lake level change, which is consistent with predictions derived from analysis of the Hurst exponent value, is determined not only by the current amount of water, but also by evaporation rates, precipitation, snowmelt, etc. All of the above is a time-consuming process.

Thanks to folkstone design inc. & zoomers of the sunshine coast BC

**Relevant Stories**

https://www.youtube.com/channel/UCpEBFr960dwZqR-9HtCWIcQ

## ORIGINAL PAPER

Raoul Nigmatullin et al, **Generalized Hurst Hypothesis: Description of Time-Series in Communication Systems**, Mathematics (2021). DOI: 10.3390/math9040381

https://www.mdpi.com/2227-7390/9/4/381

#ComplexSystems #forecasting #Noise #GeneralizedHurstHypothesis.

A team of scientists from MIPT and Kazan National Research Technical University is developing a mathematical apparatus that could lead to a breakthrough in network security. The results of the work have been published in the journal Mathematics.

Complex systems, such as or living organisms, do not have deterministic physical laws to accurately describe them and predict future behavior. In this case, an important role is played by , which describes the behavior of the system in terms of sets of statistical parameters.

Such complex systems are described by trendless sequences, often defined as long-term time series or “noise”. They are fluctuations produced by a combination of different sources and are among the most difficult data to analyze and extract reliable, stable information.

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From a purely scientific frame of reference, many quantum phenomena like non-local correlations between distant entities and wave-particle duality, the wave function collapse and consistent histories, quantum entanglement and teleportation, the uncertainty principle and overall observer-dependence of reality pin down our conscious mind being intrinsic to reality. And this is the one thing the current physicalist paradigm fails to account for. Critical-mass anomalies will ultimately lead to the full paradigm shift in physics. It’s just a matter of time.

With consciousness as primary, everything remains the same and everything changes. Mathematics, physics, chemistry, biology are unchanged. What changes is our interpretation as to what they are describing. They are not describing the unfolding of an objective physical world, but transdimensional evolution of one’s conscious mind. There’s nothing “physical” about our physical reality except that we perceive it that way. By playing the “Game of Life” we evolved to survive not to see quantum mechanical reality. At our classical level of experiential reality we perceive ourselves as physical, at the quantum level we are a probabilistic wave function, which is pure information.

No matter how you slice it, reality is contextual, the notion that immediately dismisses ‘observer-independent’ interpretations of quantum mechanics and endorses the Mental Universe hypothesis. But we have to be careful here not to throw the baby out with the bathwater, so to speak. I’d like to make a very important point at this juncture of our discussion: Mental and physical are two sides of the same coin made of information. Both should be viewed as the same substance.

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Engineering A Safer World For Humans With Self Driving Cars, Drones, and Robots — Dr. Missy Cummings PhD, Professor, Duke University, Director, Humans and Autonomy Laboratory, Duke Engineering.

Dr. Mary “Missy” Cummings, is a Professor in the Department of Electrical and Computer Engineering, at the Pratt School of Engineering, at Duke University, the Duke Institute of Brain Sciences, and is the Director of the Humans and Autonomy Laboratory and Duke Robotics.

Dr. Cummings received her B.S. in Mathematics from the US Naval Academy in 1988, her M.S. in Space Systems Engineering from the Naval Postgraduate School in 1994, and her Ph.D. in Systems Engineering from the University of Virginia in 2004.

Dr… Cummings was one of the Navy’s first female fighter pilots earning the rank of lieutenant and serving as naval officer and military pilot from 1988–1999.

Dr. Cummings research interests include human-unmanned vehicle interaction, human-autonomous system collaboration, human-systems engineering, public policy implications of unmanned vehicles, and the ethical and social impact of technology.

Dr. Cummings is an American Institute of Aeronautics and Astronautics (AIAA) Fellow, a member of their Board of Trustees, the Defense Innovation Advisory Board, and Veoneer, Inc. Board of Directors.

Dr. Cummings previously served as an instructor for the U.S. Navy at Pennsylvania State University, an assistant professor at Virginia Tech in their Engineering Fundamentals Division, and an associate professor of Aeronautics and Astronautics at the Massachusetts Institute of Technology.

Dr. Cummings is also an accomplished author with her book Hornet’s Nest: The Experiences of One of the Navy’s First Female Fighter Pilots.

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Protocol to reverse engineer Hamiltonian models advances automation of quantum devices.

Scientists from the University of Bristol ’s Quantum Engineering Technology Labs (QETLabs) have developed an algorithm that provides valuable insights into the physics underlying quantum systems — paving the way for significant advances in quantum computation and sensing, and potentially turning a new page in scientific investigation.

In physics, systems of particles and their evolution are described by mathematical models, requiring the successful interplay of theoretical arguments and experimental verification. Even more complex is the description of systems of particles interacting with each other at the quantum mechanical level, which is often done using a Hamiltonian model. The process of formulating Hamiltonian models from observations is made even harder by the nature of quantum states, which collapse when attempts are made to inspect them.

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