LIVIVO - Search results -

Search results

Result 1 - 10 of total 12

Search options

Article ; Online: General H-theorem and Entropies that Violate the Second Law

Alexander N. Gorban

Entropy, Vol 16, Iss 5, Pp 2408-

2014 Volume 2432

Abstract: H-theorem states that the entropy production is nonnegative and, therefore, the entropy of a closed system should monotonically change in time. In information processing, the entropy production is positive for random transformation of signals (the ... ...

Abstract	H-theorem states that the entropy production is nonnegative and, therefore, the entropy of a closed system should monotonically change in time. In information processing, the entropy production is positive for random transformation of signals (the information processing lemma). Originally, the H-theorem and the information processing lemma were proved for the classical Boltzmann-Gibbs-Shannon entropy and for the correspondent divergence (the relative entropy). Many new entropies and divergences have been proposed during last decades and for all of them the H-theorem is needed. This note proposes a simple and general criterion to check whether the H-theorem is valid for a convex divergence H and demonstrates that some of the popular divergences obey no H-theorem. We consider systems with n states Ai that obey first order kinetics (master equation). A convex function H is a Lyapunov function for all master equations with given equilibrium if and only if its conditional minima properly describe the equilibria of pair transitions Ai ⇌ Aj . This theorem does not depend on the principle of detailed balance and is valid for general Markov kinetics. Elementary analysis of pair equilibria demonstrate that the popular Bregman divergences like Euclidian distance or Itakura-Saito distance in the space of distribution cannot be the universal Lyapunov functions for the first-order kinetics and can increase in Markov processes. Therefore, they violate the second law and the information processing lemma. In particular, for these measures of information (divergences) random manipulation with data may add information to data. The main results are extended to nonlinear generalized mass action law kinetic equations.
Keywords	Markov process ; Lyapunov function ; non-classical entropy ; information processing ; quasiconvexity ; directional convexity ; Schur convexity ; Science ; Q ; Astrophysics ; QB460-466 ; Physics ; QC1-999
Subject code	510
Language	English
Publishing date	2014-04-01T00:00:00Z
Publisher	MDPI AG
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

Full text online

Full text

Inter-library loan at ZB MED

Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

Article ; Online: High-Dimensional Brain in a High-Dimensional World

Alexander N. Gorban / Valery A. Makarov / Ivan Y. Tyukin

Entropy, Vol 22, Iss 1, p

Blessing of Dimensionality

2020 Volume 82

Abstract: High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the “curse of dimensionality” states: many problems ... ...

Abstract	High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the “curse of dimensionality” states: many problems become exponentially difficult in high dimensions. Recently, the other side of the coin, the “blessing of dimensionality”, has attracted much attention. It turns out that generic high-dimensional datasets exhibit fairly simple geometric properties. Thus, there is a fundamental tradeoff between complexity and simplicity in high dimensional spaces. Here we present a brief explanatory review of recent ideas, results and hypotheses about the blessing of dimensionality and related simplifying effects relevant to machine learning and neuroscience.
Keywords	artificial intelligence ; mistake correction ; concentration of measure ; discriminant ; data mining ; geometry ; Science ; Q ; Astrophysics ; QB460-466 ; Physics ; QC1-999
Language	English
Publishing date	2020-01-01T00:00:00Z
Publisher	MDPI AG
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

Full text online

Full text

Inter-library loan at ZB MED

Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

Article ; Online: High-Dimensional Separability for One- and Few-Shot Learning

Alexander N. Gorban / Bogdan Grechuk / Evgeny M. Mirkes / Sergey V. Stasenko / Ivan Y. Tyukin

Entropy, Vol 23, Iss 1090, p

2021 Volume 1090

Abstract: This work is driven by a practical question: corrections of Artificial Intelligence (AI) errors. These corrections should be quick and non-iterative. To solve this problem without modification of a legacy AI system, we propose special ‘external’ devices, ...

Abstract	This work is driven by a practical question: corrections of Artificial Intelligence (AI) errors. These corrections should be quick and non-iterative. To solve this problem without modification of a legacy AI system, we propose special ‘external’ devices, correctors. Elementary correctors consist of two parts, a classifier that separates the situations with high risk of error from the situations in which the legacy AI system works well and a new decision that should be recommended for situations with potential errors. Input signals for the correctors can be the inputs of the legacy AI system, its internal signals, and outputs. If the intrinsic dimensionality of data is high enough then the classifiers for correction of small number of errors can be very simple. According to the blessing of dimensionality effects, even simple and robust Fisher’s discriminants can be used for one-shot learning of AI correctors. Stochastic separation theorems provide the mathematical basis for this one-short learning. However, as the number of correctors needed grows, the cluster structure of data becomes important and a new family of stochastic separation theorems is required. We refuse the classical hypothesis of the regularity of the data distribution and assume that the data can have a rich fine-grained structure with many clusters and corresponding peaks in the probability density. New stochastic separation theorems for data with fine-grained structure are formulated and proved. On the basis of these theorems, the multi-correctors for granular data are proposed. The advantages of the multi-corrector technology were demonstrated by examples of correcting errors and learning new classes of objects by a deep convolutional neural network on the CIFAR-10 dataset. The key problems of the non-classical high-dimensional data analysis are reviewed together with the basic preprocessing steps including the correlation transformation, supervised Principal Component Analysis (PCA), semi-supervised PCA, transfer component analysis, and new ...
Keywords	Artificial Intelligence ; blessing of dimensionality ; clusters ; errors ; separability ; discriminant ; Science ; Q ; Astrophysics ; QB460-466 ; Physics ; QC1-999
Subject code	006
Language	English
Publishing date	2021-08-01T00:00:00Z
Publisher	MDPI AG
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

Full text online

Full text

Inter-library loan at ZB MED

Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

Article ; Online: Scikit-Dimension

Jonathan Bac / Evgeny M. Mirkes / Alexander N. Gorban / Ivan Tyukin / Andrei Zinovyev

Entropy, Vol 23, Iss 1368, p

A Python Package for Intrinsic Dimension Estimation

2021 Volume 1368

Abstract: Dealing with uncertainty in applications of machine learning to real-life data critically depends on the knowledge of intrinsic dimensionality (ID). A number of methods have been suggested for the purpose of estimating ID, but no standard package to ... ...

Abstract	Dealing with uncertainty in applications of machine learning to real-life data critically depends on the knowledge of intrinsic dimensionality (ID). A number of methods have been suggested for the purpose of estimating ID, but no standard package to easily apply them one by one or all at once has been implemented in Python. This technical note introduces scikit-dimension, an open-source Python package for intrinsic dimension estimation. The scikit-dimension package provides a uniform implementation of most of the known ID estimators based on the scikit-learn application programming interface to evaluate the global and local intrinsic dimension, as well as generators of synthetic toy and benchmark datasets widespread in the literature. The package is developed with tools assessing the code quality, coverage, unit testing and continuous integration. We briefly describe the package and demonstrate its use in a large-scale (more than 500 datasets) benchmarking of methods for ID estimation for real-life and synthetic data.
Keywords	intrinsic dimension ; effective dimension ; Python package ; method benchmarking ; Science ; Q ; Astrophysics ; QB460-466 ; Physics ; QC1-999
Language	English
Publishing date	2021-10-01T00:00:00Z
Publisher	MDPI AG
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

Full text online

Full text

Inter-library loan at ZB MED

Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

Article ; Online: Modeling Progression of Single Cell Populations Through the Cell Cycle as a Sequence of Switches

Andrei Zinovyev / Michail Sadovsky / Laurence Calzone / Aziz Fouché / Clarice S. Groeneveld / Alexander Chervov / Emmanuel Barillot / Alexander N. Gorban

Frontiers in Molecular Biosciences, Vol

2022 Volume 8

Abstract: Cell cycle is a biological process underlying the existence and propagation of life in time and space. It has been an object for mathematical modeling for long, with several alternative mechanistic modeling principles suggested, describing in more or ... ...

Abstract	Cell cycle is a biological process underlying the existence and propagation of life in time and space. It has been an object for mathematical modeling for long, with several alternative mechanistic modeling principles suggested, describing in more or less details the known molecular mechanisms. Recently, cell cycle has been investigated at single cell level in snapshots of unsynchronized cell populations, exploiting the new methods for transcriptomic and proteomic molecular profiling. This raises a need for simplified semi-phenomenological cell cycle models, in order to formalize the processes underlying the cell cycle, at a higher abstracted level. Here we suggest a modeling framework, recapitulating the most important properties of the cell cycle as a limit trajectory of a dynamical process characterized by several internal states with switches between them. In the simplest form, this leads to a limit cycle trajectory, composed by linear segments in logarithmic coordinates describing some extensive (depending on system size) cell properties. We prove a theorem connecting the effective embedding dimensionality of the cell cycle trajectory with the number of its linear segments. We also develop a simplified kinetic model with piecewise-constant kinetic rates describing the dynamics of lumps of genes involved in S-phase and G2/M phases. We show how the developed cell cycle models can be applied to analyze the available single cell datasets and simulate certain properties of the observed cell cycle trajectories. Based on our model, we can predict with good accuracy the cell line doubling time from the length of cell cycle trajectory.
Keywords	cell cycle ; mathematical modeling ; molecular switches ; transcription epoch ; single cell data ; Biology (General) ; QH301-705.5
Subject code	612
Language	English
Publishing date	2022-02-01T00:00:00Z
Publisher	Frontiers Media S.A.
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

Full text online

Full text

Inter-library loan at ZB MED

Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

Article ; Online: Social stress drives the multi-wave dynamics of COVID-19 outbreaks

Innokentiy A. Kastalskiy / Evgeniya V. Pankratova / Evgeny M. Mirkes / Victor B. Kazantsev / Alexander N. Gorban

Scientific Reports, Vol 11, Iss 1, Pp 1-

2021 Volume 12

Abstract: Abstract The dynamics of epidemics depend on how people's behavior changes during an outbreak. At the beginning of the epidemic, people do not know about the virus, then, after the outbreak of epidemics and alarm, they begin to comply with the ... ...

Abstract	Abstract The dynamics of epidemics depend on how people's behavior changes during an outbreak. At the beginning of the epidemic, people do not know about the virus, then, after the outbreak of epidemics and alarm, they begin to comply with the restrictions and the spreading of epidemics may decline. Over time, some people get tired/frustrated by the restrictions and stop following them (exhaustion), especially if the number of new cases drops down. After resting for a while, they can follow the restrictions again. But during this pause the second wave can come and become even stronger then the first one. Studies based on SIR models do not predict the observed quick exit from the first wave of epidemics. Social dynamics should be considered. The appearance of the second wave also depends on social factors. Many generalizations of the SIR model have been developed that take into account the weakening of immunity over time, the evolution of the virus, vaccination and other medical and biological details. However, these more sophisticated models do not explain the apparent differences in outbreak profiles between countries with different intrinsic socio-cultural features. In our work, a system of models of the COVID-19 pandemic is proposed, combining the dynamics of social stress with classical epidemic models. Social stress is described by the tools of sociophysics. The combination of a dynamic SIR-type model with the classical triad of stages of the general adaptation syndrome, alarm-resistance-exhaustion, makes it possible to describe with high accuracy the available statistical data for 13 countries. The sets of kinetic constants corresponding to optimal fit of model to data were found. These constants characterize the ability of society to mobilize efforts against epidemics and maintain this concentration over time and can further help in the development of management strategies specific to a particular society.
Keywords	Medicine ; R ; Science ; Q
Subject code	300
Language	English
Publishing date	2021-11-01T00:00:00Z
Publisher	Nature Portfolio
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

Full text online

Full text

Inter-library loan at ZB MED

Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

Article ; Online: The Michaelis-Menten-Stueckelberg Theorem

Alexander N. Gorban / Muhammad Shahzad

Entropy, Vol 13, Iss 5, Pp 966-

2011 Volume 1019

Abstract: We study chemical reactions with complex mechanisms under two assumptions: (i) intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS) and (ii) they are in equilibrium relations with substrates (this is the ... ...

Abstract	We study chemical reactions with complex mechanisms under two assumptions: (i) intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS) and (ii) they are in equilibrium relations with substrates (this is the quasiequilibrium hypothesis or QE). Under these assumptions, we prove the generalized mass action law together with the basic relations between kinetic factors, which are sufficient for the positivity of the entropy production but hold even without microreversibility, when the detailed balance is not applicable. Even though QE and QSS produce useful approximations by themselves, only the combination of these assumptions can render the possibility beyond the “rarefied gas” limit or the “molecular chaos” hypotheses. We do not use any a priori form of the kinetic law for the chemical reactions and describe their equilibria by thermodynamic relations. The transformations of the intermediate compounds can be described by the Markov kinetics because of their low density (low density of elementary events). This combination of assumptions was introduced by Michaelis and Menten in 1913. In 1952, Stueckelberg used the same assumptions for the gas kinetics and produced the remarkable semi-detailed balance relations between collision rates in the Boltzmann equation that are weaker than the detailed balance conditions but are still sufficient for the Boltzmann H-theorem to be valid. Our results are obtained within the Michaelis-Menten-Stueckelbeg conceptual framework.
Keywords	chemical kinetics ; Lyapunov function ; entropy ; quasiequilibrium ; detailed balance ; complex balance ; Science ; Q ; Astrophysics ; QB460-466 ; Physics ; QC1-999
Subject code	660
Language	English
Publishing date	2011-05-01T00:00:00Z
Publisher	MDPI AG
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

Full text online

Full text

Inter-library loan at ZB MED

Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

Article ; Online: Simple model of complex dynamics of activity patterns in developing networks of neuronal cultures.

Ivan Y Tyukin / Dmitriy Iudin / Feodor Iudin / Tatiana Tyukina / Victor Kazantsev / Irina Mukhina / Alexander N Gorban

PLoS ONE, Vol 14, Iss 6, p e

2019 Volume 0218304

Abstract: Living neuronal networks in dissociated neuronal cultures are widely known for their ability to generate highly robust spatiotemporal activity patterns in various experimental conditions. Such patterns are often treated as neuronal avalanches that ... ...

Abstract	Living neuronal networks in dissociated neuronal cultures are widely known for their ability to generate highly robust spatiotemporal activity patterns in various experimental conditions. Such patterns are often treated as neuronal avalanches that satisfy the power scaling law and thereby exemplify self-organized criticality in living systems. A crucial question is how these patterns can be explained and modeled in a way that is biologically meaningful, mathematically tractable and yet broad enough to account for neuronal heterogeneity and complexity. Here we derive and analyse a simple network model that may constitute a response to this question. Our derivations are based on few basic phenomenological observations concerning the input-output behavior of an isolated neuron. A distinctive feature of the model is that at the simplest level of description it comprises of only two variables, the network activity variable and an exogenous variable corresponding to energy needed to sustain the activity, and few parameters such as network connectivity and efficacy of signal transmission. The efficacy of signal transmission is modulated by the phenomenological energy variable. Strikingly, this simple model is already capable of explaining emergence of network spikes and bursts in developing neuronal cultures. The model behavior and predictions are consistent with published experimental evidence on cultured neurons. At the larger, cellular automata scale, introduction of the energy-dependent regulatory mechanism results in the overall model behavior that can be characterized as balancing on the edge of the network percolation transition. Network activity in this state shows population bursts satisfying the scaling avalanche conditions. This network state is self-sustainable and represents energetic balance between global network-wide processes and spontaneous activity of individual elements.
Keywords	Medicine ; R ; Science ; Q
Subject code	612
Language	English
Publishing date	2019-01-01T00:00:00Z
Publisher	Public Library of Science (PLoS)
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

Full text online

Full text

Inter-library loan at ZB MED

Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

Article ; Online: Singularities of transition processes in dynamical systems

Alexander N. Gorban

Electronic Journal of Differential Equations, Vol Monograph, Iss 05, Pp 1-

Qualitative theory of critical delays

2004 Volume 55

Abstract: This monograph presents a systematic analysis of the singularities in the transition processes for dynamical systems. We study general dynamical systems, with dependence on a parameter, and construct relaxation times that depend on three variables: ... ...

Abstract	This monograph presents a systematic analysis of the singularities in the transition processes for dynamical systems. We study general dynamical systems, with dependence on a parameter, and construct relaxation times that depend on three variables: Initial conditions, parameters $k$ of the system, and accuracy $varepsilon$ of the relaxation. We study the singularities of relaxation times as functions of $(x_0,k)$ under fixed $varepsilon$, and then classify the bifurcations (explosions) of limit sets. We study the relationship between singularities of relaxation times and bifurcations of limit sets. An analogue of the Smale order for general dynamical systems under perturbations is constructed. It is shown that the perturbations simplify the situation: the interrelations between the singularities of relaxation times and other peculiarities of dynamics for general dynamical system under small perturbations are the same as for the Morse-Smale systems.
Keywords	Dynamical system ; transition process ; relaxation time ; bifurcation ; limit set ; Smale order. ; Mathematics ; QA1-939 ; Science ; Q ; DOAJ:Mathematics ; DOAJ:Mathematics and Statistics
Subject code	515
Language	English
Publishing date	2004-08-01T00:00:00Z
Publisher	Texas State University
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

Full text online

Full text

Inter-library loan at ZB MED

Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

Article ; Online: Entropy

Alexander N. Gorban / Pavel A. Gorban / George Judge

Entropy, Vol 12, Iss 5, Pp 1145-

The Markov Ordering Approach

2010 Volume 1193

Abstract: The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant “additivity” properties: (i) existence of a monotonic ... ...

Abstract	The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant “additivity” properties: (i) existence of a monotonic transformation which makes the functional additive with respect to the joining of independent systems and (ii) existence of a monotonic transformation which makes the functional additive with respect to the partitioning of the space of states. All Lyapunov functionals for Markov chains which have properties (i) and (ii) are derived. We describe the most general ordering of the distribution space, with respect to which all continuous-time Markov processes are monotonic (the Markov order). The solution differs significantly from the ordering given by the inequality of entropy growth. For inference, this approach results in a convex compact set of conditionally “most random” distributions.
Keywords	Markov process ; Lyapunov function ; entropy functionals ; attainable region ; MaxEnt ; inference ; Science ; Q ; Astrophysics ; QB460-466 ; Physics ; QC1-999
Subject code	510
Language	English
Publishing date	2010-05-01T00:00:00Z
Publisher	MDPI AG
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

Full text online

Full text

Inter-library loan at ZB MED

Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

To top

Full text online

More links

Kategorien

Inter-library loan at ZB MED

Full text online

More links

Kategorien

Inter-library loan at ZB MED

Full text online

More links

Kategorien

Inter-library loan at ZB MED

Full text online

More links

Kategorien

Inter-library loan at ZB MED

Full text online

More links

Kategorien

Inter-library loan at ZB MED

Full text online

More links

Kategorien

Inter-library loan at ZB MED

Full text online

More links

Kategorien

Inter-library loan at ZB MED

Full text online

More links

Kategorien

Inter-library loan at ZB MED

Full text online

More links

Kategorien

Inter-library loan at ZB MED

Full text online

More links

Kategorien

Inter-library loan at ZB MED