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## How Singular Is the Twenty-First-Century Singularity?

Ch. 26. P. 571-595.

This chapter discusses in some detail the possibility of the Singularity being a product of biased human perception described by the Weber–Fechner law. It is shown that though the Weber–Fechner effect can produce series with a hyperbolic shape, the hyperbolic acceleration pattern with the twenty-first century Singularity detected in Panov and Modis–Kurzweil series is explained first of all by the actual hyperbolic acceleration of the global megaevolution.

### In book

Switzerland: Springer, 2020

Posypkin M., Маминов А. Д., , in: IEEE NW Russia Young Researchers in Electrical and Electronic Engineering Conference (EIConRusNW) 2020. .: IEEE, 2020.. P. 1992-1995.

In this article, we consider an approach for the
optimal multi-objective constrained design of the parallel robots.
Optimization is carried out according to two key criteria: the
workspace area and the global dexterity index (GDI) concerning
constrain. The workspace is the area that the robot can serve.
The value of the GDI correlates with the quality of this service.
Both objectives ...

Added: November 1, 2020

Avetisov V. A., Nechaev S., Gorsky A. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2018 Vol. 98 No. 3 P. 032308-1-032308-11

We propose two models of social segregation inspired by the Schelling model. Agents in our models are nodes of evolving social networks. The total number of social connections of each node remains constant in time, though may vary from one node to the other. The first model describes a “polychromatic” society, in which colors designate ...

Added: September 29, 2018

Korotayev A., Journal of Big History 2018 Vol. 2 No. 3 P. 73-119

The idea that in the near future we should expect “the Singularity” has become quite popular recently, primarily thanks to the activities of Google technical director in the field of machine training Raymond Kurzweil and his book The Singularity Is Near (2005). It is shown that the mathematical analysis of the series of events (described ...

Added: June 30, 2018

Switzerland: Springer, 2020

This book introduces a 'Big History' perspective to understand the acceleration of social, technological and economic trends towards a near-term singularity, marking a radical turning point in the evolution of our planet. It traces the emergence of accelerating innovation rates through global history and highlights major historical transformations throughout the evolution of life, humans, and civilization. ...

Added: January 27, 2020

Smirnov A. D., Экономический журнал Высшей школы экономики 2010 Т. 14 № 3 С. 275-310

Proposed a model of financial bubbles and crises based upon the methodology of complex systems analysis. The irrationality of financial investors, as it was well known, had been empirically explained by «the greater fool theory». This process, in modern terms, was represented as the autocatalytic process leading to a system's singularity. It was shown how ...

Added: October 13, 2012

Kurakin D., В кн.: XIV Апрельская международная научная конференция по проблемам развития экономики и общества: в 4-х книгах. Книга 3. .: М.: Издательский дом НИУ ВШЭ, 2014.. С. 485-491.

Сборник составлен по итогам XIV Апрельской международной научной конференции по проблемам развития экономики и общества, организованной Национальным исследовательским университетом «Высшая школа экономики» при участии Всемирного банка и Международного валютного фонда и проходившей 2–5 апреля 2013 г. в Москве.
Рассматриваются следующие темы: региональное развитие, города и агломерации; менеджмент; наука и инновации; социально-культурные процессы; общество и социальная политика; ...

Added: April 1, 2014

Dmitriev A., Dmitriev V., Complexity 2021 Vol. 2021 Article 6612785

There is a number of studies, in which it is established that the observed flows of microposts generated by microblogging social networks (e.g., Twitter) are characterized by avalanche-like behavior. Time series of microposts depicting such streams are the time series with a power-law distribution, with 1/f noise and long memory. Despite this, there are no studies ...

Added: May 31, 2021

Molchanov S., Panov V., Stochastics-An International Journal of Probability and Stochastic Processes 2019 Vol. 91 No. 5 P. 754-772

In this paper, we consider limit laws for the model, which is a generalisation of the random energy model (REM) to the case when the energy levels have the mixture distribution. More precisely, the distribution of the energy levels is assumed to be a mixture of two normal distributions, one of which is standard normal, ...

Added: November 19, 2018

Chetverikov V., Aminova A., Journal of Physics: Conference Series 2019 Vol. 1163 No. 012078 P. 1-6

The results of numerical calculations for the mathematical model proposed for describing the magnetization in a thin film of a ferromagnetic semiconductor at temperatures below the Curie temperature in the presence of an external electric field are presented. The theoretical prediction of the existence of a piecewise continuous solution, which describes the presence of the ...

Added: April 2, 2019

Korotayev A., LePoire D. J., , in: The 21st Century Singularity and Global Futures. A Big History Perspective. .: Switzerland: Springer, 2020.. P. 599-620.

This concluding chapter summarizes major findings of the present collective monograph. It traces the emergence of accelerating innovation rates through history and the major historical transformations through the evolution of life, humans, and civilization. It draws on the concepts from physics and evolutionary biology to offer potential models of the underlying mechanisms driving this acceleration ...

Added: November 13, 2020

Kazaryan M., Uribe-Vargas R., Moscow Mathematical Journal 2020 Vol. 20 No. 3 P. 511-530

We define local indices for projective umbilics and godrons (also called cusps of Gauss) on generic smooth surfaces in projective 3-space. By means of these indices, we provide formulas that relate the algebraic numbers of those characteristic points on a surface (and on domains of the surface) with the Euler characteristic of that surface (resp. ...

Added: August 24, 2020

Panov A., LePoire D. J., Korotayev A., , in: The 21st Century Singularity and Global Futures. A Big History Perspective. .: Switzerland: Springer, 2020.. Ch. 1. P. 1-18.

This introductory chapter discusses the overall place of the twenty-first-century Singularity within the overall Big History. It is shown that to place the accelerating trend of complexity in the context of Big History, we need to distinguish the two forms (arms) of megaevolution so far in the universe. The first arm of evolution is the ...

Added: February 3, 2020

Korotayev A., , in: The 21st Century Singularity and Global Futures. A Big History Perspective. .: Switzerland: Springer, 2020.. Ch. 2. P. 19-75.

The idea that in the near future we should expect “the Singularity” has become quite popular recently, primarily thanks to the activities of Google technical director in the field of machine training Raymond Kurzweil and his book The Singularity Is Near (2005). It is shown that the mathematical analysis of the series of events (described by Kurzweil ...

Added: January 27, 2020

Arzhantsev I., Braun L., Hausen J. et al., European Journal of Mathematics 2018 Vol. 4 No. 1 P. 242-312

Looking at the well understood case of log terminal surface singularities, one observes that each of them is the quotient of a factorial one by a finite solvable group. The derived series of this group reflects an iteration of Cox rings of surface singularities. We extend this picture to log terminal singularities in any dimension ...

Added: March 4, 2018

Valba O. V., Gorsky A., Physical Review D - Particles, Fields, Gravitation and Cosmology 2021 Vol. 103 No. 10 Article 106013

We discuss numerically the nonperturbative effects in exponential random graphs which are analogue of eigenvalue instantons in matrix models. The phase structure of exponential random graphs with chemical potential for C4 μ4 and degree preserving constraint is clarified. The first order phase transition at critical value of chemical potential for C4 μRRG 4 into bipartite ...

Added: August 17, 2021

Popov V., , in: Oberwolfach Reports. Vol. 11. Issue 1.: European Mathematical Society Publishing house, 2014.. P. 156-159.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 R. Steinberg proved that if G is
simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes.
We prove that in arbitrary G such a cross-section exists if and only if ...

Added: February 26, 2014

Malkov S. Y., , in: The 21st Century Singularity and Global Futures. A Big History Perspective. .: Switzerland: Springer, 2020.. Ch. 23. P. 517-534.

Using mathematical modeling, we consider the phenomenon of singularity in the biological and social history. It is shown that hyperbolic trends in biological and social evolution can be explained by transitional processes that accompany the expansion of ecological niches due to periodically occurring revolutionary innovations. During these periods, strong positive feedbacks are actualized, leading to ...

Added: February 3, 2020

Grinin L. E., Grinin A., Korotayev A., , in: The 21st Century Singularity and Global Futures. A Big History Perspective. .: Switzerland: Springer, 2020.. Ch. 15. P. 287-344.

In this chapter, we consider the process of technological progress presenting one of the options for measuring its speed throughout the entire historical process. We find that the general dynamics of accelerating technological growth over the past 40 thousand years can be described with amazing accuracy (R2 = 0.99) using the following simplest hyperbolic equation: yt = C/t0 − t, where yt is the ...

Added: February 3, 2020

Berezutskii A., Beketov M., Yudin D. et al., Journal of Physics: Complexity 2020 Vol. 1 No. 3 Article 03LT01

The numerical emulation of quantum systems often requires an exponential number of degrees of freedom which translates to a computational bottleneck. Methods of machine learning have been used in adjacent fields for effective feature extraction and dimensionality reduction of high-dimensional datasets. Recent studies have revealed that neural networks are further suitable for the determination of ...

Added: October 5, 2021

Koralov L., Molchanov S., Vainberg B., Applicable Analysis 2020

We consider a mean-field model of a polymer with a spherically symmetric finitely supported potential. We describe how the typical size of the polymer depends on the two parameters: the temperature, which approaches the critical value, and the length of the polymer chain, which goes to infinity. ...

Added: October 28, 2020

Smirnov A. D., Экономический журнал Высшей школы экономики 2010 Т. 141 № 4 С. 401-439

Proposed a model of financial bubbles and crises based upon the methodology of complex systems analysis. It was shown how the procedures (slice and dice) of a CDO synthesis generated the excess growth of the securitized assets value. The latter being coupled with the high leverage might produce the total collapse of a financial system. ...

Added: October 13, 2012

Negodin V., Polyachenko Y., Fleita D. et al., Journal of Molecular Liquids 2021 Vol. 322 No. 1-3 Article 114954

The equilibrium and metastable states of the Lennard-Jones vapor, liquid, and crystal, are studied in the vicinity of the phase transition points. Vapor-liquid, liquid-vapor, liquid-crystal, and crystal-liquid transitions are modeled within the molecular dynamics method. As a research tool, a four-point correlation function is used for the qualitative detection of collective motions of atoms in ...

Added: May 14, 2021

Korotayev A., Meshcherina K., Shishkina A., Democracy and Security 2018 Vol. 14 No. 4 P. 331-357

After the beginning of the Arab Spring in 2011, explosive global growth was observed for the majority of indicators of sociopolitical destabilization in all parts of the World System. In order to identify the structure of this destabilization wave, we apply a series of statistical techniques such as trend analysis and t-tests to study the ...

Added: August 27, 2018

Grinin L. E., Grinin A., Korotayev A., Technological Forecasting and Social Change 2020 Vol. 155 P. 1-15

The authors quantitatively analyse the long-term dynamics of technological progress from 40,000 BCE and offer projections through the 22nd century. We provide one method to measure technological progress over that time period, using a simple hyperbolic equation, yt = C/(t0 – t), as our model. We define yt as the technological growth rate, measured as number of technological phase transitions ...

Added: March 6, 2020