On the appearance of Eisenstein series through degeneration

Let $\Gamma$ be a Fuchsian group of the first kind acting on the hyperbolic upper half plane $\mathbb H$, and let $M = \Gamma \backslash \mathbb H$ be the associated finite volume hyperbolic Riemann surface. If $\gamma$ is parabolic, there is an associated (parabolic) Eisenstein series, which, by now, is a classical part of mathematical literature. If $\gamma$ is hyperbolic, then, following ideas due to Kudla-Millson, there is a corresponding hyperbolic Eisenstein series. In this article, we study the limiting behavior of parabolic and hyperbolic Eisenstein series on a degenerating family of finite volume hyperbolic Riemann surfaces. In particular, we prove the following result. If $\gamma \in \Gamma$ corresponds to a degenerating hyperbolic element, then a multiple of the associated hyperbolic Eisenstein series converges to parabolic Eisenstein series on the limit surface.Comment: 15 pages, 2 figures. This paper has been accepted for publication in Commentarii Mathematici Helvetic

RTN in GexSe1-x OTS Selector Devices

Random telegraph noise (RTN) signals in GexSe1-x ovonic threshold switching (OTS) selector have been analyzed in this work, both before and after the first-fire (FF) operation and at on- and off-states. It is observed that RTN appears after the FF, and its absolute amplitude at the off-state is small and negligible in comparison with the RTN signals in RRAM devices. At the on-state, large RTN signals are observed, which can either partially or fully block the conduction path, supporting that a conductive filament is formed or activated by FF and then modulated during switching. Statistical analysis reveals that the relative RTN amplitude at on-state in GexSe1-x OTS selector is smaller than or equivalent to those in RRAM devices

Stochastic computing based on volatile GeSe ovonic threshold switching selectors

Stochastic computing (SC) is a special type of digital compute strategy where values are represented by the probability of 1 and 0 in stochastic bit streams, which leads to superior hardware simplicity and error-tolerance. In this paper, we propose and demonstrate SC with GeSe based Ovonic Threshold Switching (OTS) selector devices by exploiting their probabilistic switching behavior. The stochastic bit streams generated by OTS are demonstrated with good computation accuracy in both multiplication operation and image processing circuit. Moreover, the bit distribution has been statistically studied and linked to the collective defect de/localization behavior in the chalcogenide material. Weibull distribution of the delay time supports the origin of such probabilistic switching, facilitates further optimization of the operation condition, and lays the foundation for device modelling and circuit design. Considering its other advantages such as simple structure, fast speed, and volatile nature, OTS is a promising material for implementing SC in a wide range of novel applications, such as image processors, neural networks, control systems and reliability analysis

GeSe-based Ovonic Threshold Switching Volatile True Random Number Generator

In this paper, we propose and demonstrate a novel technique for true random number generator (TRNG) application using GeSe-based Ovonic threshold switching (OTS) selector devices. The inherent variability in OTS threshold voltage results in a bimodal distribution of on/off states which can be easily converted into digital bits. The experimental evaluation shows that the proposed TRNG enables the generation of high-quality random bits that passed 12 tests in the National Institute of Standards and Technology statistical test suite without complex external circuits for post-processing. The randomness is further evidenced by the prediction rate of ∼50% using machine learning algorithm. Compared with the TRNGs based on non-volatile memories, the volatile nature of OTS avoids the reset operation, thus further simplifying the operation and improving the generation frequency

Rudolf Otto’s ‘The Absolute Other’ and a radical postsecular urban contextualization

This article proposes an idea of radical urban contextualisation that follows Rudolf Otto’s discussion on an encounter with the Absolute Other. The article critically reviews current applications of postsecularism to urban theory formulated in a general framework of Jurgen Habermas’ intervention in the early 21st century. The article argues that contemporary postsecular urban theory cannot fully answer fundamental challenges that contemporary cities are facing – both political and environmental – mostly because it focuses on linguistic and cultural aspects of a city. The article proposes the ‘radicalization’ of postsecularism, engaging directly with the ‘religious experience’ defined by Rudolf Otto as an encounter with The Absolute Other – the unknown and unpredictable. The Absolute Other notion allows to ultimately contextualize every urban situation in order to formulate conditions for future-oriented (post-capitalist) urbanism