We analyze deep Neural Network emulation rates of smooth functions with point singularities in bounded, polytopal domains $\mathrm{D} \subset \mathbb{R}^d$, $d=2,3$. We prove exponential emulation rates in Sobolev spaces in terms of the number of neurons and in terms of the number of nonzero coefficients for Gevrey-regular solution classes defined in terms of weighted Sobolev scales in $\mathrm{D}$, comprising the countably-normed spaces of I.M. Babu\v{s}ka and B.Q. Guo. As intermediate result, we prove that continuous, piecewise polynomial high order (``$p$-version'') finite elements with elementwise polynomial degree $p\in\mathbb{N}$ on arbitrary, regular, simplicial partitions of polyhedral domains $\mathrm{D} \subset \mathbb{R}^d$, $d\geq 2$ can be exactly emulated by neural networks combining ReLU and ReLU$^2$ activations. On shape-regular, simplicial partitions of polytopal domains $\mathrm{D}$, both the number of neurons and the number of nonzero parameters are proportional to the number of degrees of freedom of the finite element space, in particular for the $hp$-Finite Element Method of I.M. Babu\v{s}ka and B.Q. Guo.

Approximation rates are analyzed for deep surrogates of maps between infinite-dimensional function spaces, arising e.g. as data-to-solution maps of linear and nonlinear partial differential equations. Specifically, we study approximation rates for Deep Neural Operator and Generalized Polynomial Chaos (gpc) Operator surrogates for nonlinear, holomorphic maps between infinite-dimensional, separable Hilbert spaces. Operator in- and outputs from function spaces are assumed to be parametrized by stable, affine representation systems. Admissible representation systems comprise orthonormal bases, Riesz bases or suitable tight frames of the spaces under consideration. Algebraic expression rate bounds are established for both, deep neural and spectral operator surrogates acting in scales of separable Hilbert spaces containing domain and range of the map to be expressed, with finite Sobolev or Besov regularity. We illustrate the abstract concepts by expression rate bounds for the coefficient-to-solution map for a linear elliptic PDE on the torus.

Abstract: The Fourth Industrial Revolution, particularly Artificial Intelligence (AI), has had a profound impact on society, raising concerns about its implications and ethical considerations. This study aims to examine the perceptions of individuals in different information flow categorizations toward AI. The results reveal key themes in participant-supplied definitions of AI and the fourth industrial revolution, emphasizing the replication of human intelligence, machine learning, automation, and the integration of digital technologies. Participants expressed concerns about job replacement, privacy invasion, and inaccurate information provided by AI. However, they also recognized the benefits of AI, such as solving complex problems and increasing convenience. Views on government involvement in shaping the fourth industrial revolution varied, with some advocating for strict regulations and others favoring support and development. The anticipated changes brought by the fourth industrial revolution include automation, potential job impacts, increased social disconnect, and reliance on technology. Understanding these perceptions is crucial for effectively managing the challenges and opportunities associated with AI in the evolving digital landscape. Abstract: The Fourth Industrial Revolution, particularly Artificial Intelligence (AI), has had a profound impact on society, raising concerns about its implications and ethical considerations. This study aims to examine the perceptions of individuals in different information flow categorizations toward AI.

We establish universality and expression rate bounds for a class of neural Deep Operator Networks (DON) emulating Lipschitz (or H\"older) continuous maps $\mathcal G:\mathcal X\to\mathcal Y$ between (subsets of) separable Hilbert spaces $\mathcal X$, $\mathcal Y$. The DON architecture considered uses linear encoders $\mathcal E$ and decoders $\mathcal D$ via (biorthogonal) Riesz bases of $\mathcal X$, $\mathcal Y$, and an approximator network of an infinite-dimensional, parametric coordinate map that is Lipschitz continuous on the sequence space $\ell^2(\mathbb N)$. Unlike previous works ([Herrmann, Schwab and Zech: Neural and Spectral operator surrogates: construction and expression rate bounds, SAM Report, 2022], [Marcati and Schwab: Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations, SAM Report, 2022]), which required for example $\mathcal G$ to be holomorphic, the present expression rate results require mere Lipschitz (or H\"older) continuity of $\mathcal G$. Key in the proof of the present expression rate bounds is the use of either super-expressive activations (e.g. [Yarotski: Elementary superexpressive activations, Int. Conf. on ML, 2021], [Shen, Yang and Zhang: Neural network approximation: Three hidden layers are enough, Neural Networks, 2021], and the references there) which are inspired by the Kolmogorov superposition theorem, or of nonstandard NN architectures with standard (ReLU) activations as recently proposed in [Zhang, Shen and Yang: Neural Network Architecture Beyond Width and Depth, Adv. in Neural Inf. Proc. Sys., 2022]. We illustrate the abstract results by approximation rate bounds for emulation of a) solution operators for parametric elliptic variational inequalities, and b) Lipschitz maps of Hilbert-Schmidt operators.

There are many companies angling to make money in the metaverse at the moment, but far fewer trying to use its technology for public good. The World Economic Forum hopes to change that with the Global Collaboration Village, which will be introduced at Davos this year ahead of a full rollout. The virtual village has been designed to function--and look--like the real Swiss town, except that here the people convening in co-working spaces, attending conferences in government buildings, and browsing museums will be doing so as avatars. WEF executive chairman Klaus Schwab, who has spent decades cultivating in-person interactions between world leaders, hopes the village will serve as a consistent meeting ground for Davos' stakeholders, transforming the conference from a cloistered one-week gathering to a year-round project. "This could revolutionize global collaboration," Schwab told TIME in the weeks before the January gathering.

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Center for American Security's Fred Fleitz unpacks the national security risks posed by China's access to TikTok data and Chinese-made drones flying over Washington D.C. World Economic Forum founder and Chair Klaus Schwab recently sat down for an interview with a Chinese state media outlet and proclaimed that China was a "role model" for other nations. Schwab, 84, made these comments during an interview with CGTN's Tian Wei on the sidelines of last week's APEC CEO Summit in Bangkok, Thailand. Schwab said he respected China's "tremendous" achievements at modernizing its economy over the last 40 years. FILE: World Economic Forum (WEF) founder and Executive Chairman Klaus Schwab sits, as German Chancellor Olaf Scholz (not pictured) addresses the delegates, during the last day of the WEF in Davos, Switzerland May 26, 2022. "I think it's a role model for many countries," Schwab said, before qualifying that he thinks each country should make its own decisions about what system it wants to adapt.

Hand-coded finite-state machines and behavior trees are the go-to techniques for artificial intelligence (AI) developers that want full control over their character's bearing. However, manually crafting behaviors for computer-controlled agents is a tedious and parameter-dependent task. From a high-level view, the process of designing agent AI by hand usually starts with the determination of a suitable set of action sequences. Once the AI developer has identified these sequences he merges them into a complete behavior by specifying appropriate transitions between them. Automated techniques, such as learning, tree search and planning, are on the other end of the AI toolset's spectrum.

There's no denying the pandemic accelerated the fourth industrial revolution, a concept coined by professor Klaus Schwab at the World Economic Forum five years ago to describe the vast digital transition that is fundamentally changing our lives. But the breadth of the tech transition Schwab predicted in 2016 seemed far-off to most at the time. Now, with a post-Covid era in our sights, we've learned how viable remote school and work is, we've seen the most archaic institutions embrace the change, and we've at long last witnessed the adoption of digital healthcare. Accept it, and then enjoy it. We've officially entered an era in which new technologies fuse the physical, digital, and biological worlds. Advancements in artificial intelligence are an integral part of that shift.

November 10, 2020 (LifeSiteNews) -- The COVID-19 pandemic was manufactured by the world's elites as part of a plan to globally advance "transhumanism" -- literally, the fusion of human beings with technology in an attempt to alter human nature itself and create a superhuman being and an "earthly paradise," according to a Peruvian academic and expert in technology. This dystopian nightmare scenario is no longer the stuff of science fiction, but an integral part of the proposed post-pandemic "Great Reset," Dr. Miklos Lukacs de Pereny said at a recent summit on COVID-19. Indeed, to the extent that implementing the transhumanist agenda is possible, it requires the concentration of political and economic power in the hands of a global elite and the dependence of people on the state, said Lukacs. That's precisely the aim of the Great Reset, promoted by German economist Klaus Schwab, CEO and founder of World Economic Forum, along with billionaire "philanthropists" George Soros and Bill Gates and other owners, managers, and shareholders of Big Tech, Big Pharma, and Big Finance who meet at the WEF retreats at Davos, Switzerland, contended Lukacs. Transhumanism is far from a benign doctrine.