arXiv subjects

A. N. Gorban

Publications and source records attributed to A. N. Gorban.

At least 19 recordsLinked to original sources

arXiv2022

It is useful to analyze correlation graphs

In 1987, we analyzed the changes in correlation graphs between various features of the organism during stress and adaptation. After 33 years of research of many authors, discoveries and rediscoveries, we can say with complete confidence: It is useful to analyze correlation graphs. In addition, we should add that the concept of adaptability ('adaptation energy') introduced by Selye is useful, especially if it is supplemented by 'adaptation entropy' and free energy, as well as an analysis of limiting factors. Our review of these topics, Dynamic and Thermodynamic Adaptation Models" (Phys Life Rev, 2021, arXiv:2103.01959 [q-bio.OT]), attracted many comments from leading experts, with new ideas and new problems, from the dynamics of aging and the training of athletes to single-cell omics. Methodological backgrounds, like free energy analysis, were also discussed in depth. In this article, we provide an analytical overview of twelve commenting papers and some related publications.

q-bio.TO↗

arXiv2021

Social stress drives the multi-wave dynamics of COVID-19 outbreaks

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. They characterize the ability of society to mobilize efforts against epidemics and maintain this concentration over time, and can further help in the development of strategies specific to a particular society.

physics.soc-ph↗

arXiv2021

Coloring Panchromatic Nighttime Satellite Images: Comparing the Performance of Several Machine Learning Methods

Artificial light-at-night (ALAN), emitted from the ground and visible from space, marks human presence on Earth. Since the launch of the Suomi National Polar Partnership satellite with the Visible Infrared Imaging Radiometer Suite Day/Night Band (VIIRS/DNB) onboard, global nighttime images have significantly improved; however, they remained panchromatic. Although multispectral images are also available, they are either commercial or free of charge, but sporadic. In this paper, we use several machine learning techniques, such as linear, kernel, random forest regressions, and elastic map approach, to transform panchromatic VIIRS/DBN into Red Green Blue (RGB) images. To validate the proposed approach, we analyze RGB images for eight urban areas worldwide. We link RGB values, obtained from ISS photographs, to panchromatic ALAN intensities, their pixel-wise differences, and several land-use type proxies. Each dataset is used for model training, while other datasets are used for the model validation. The analysis shows that model-estimated RGB images demonstrate a high degree of correspondence with the original RGB images from the ISS database. Yet, estimates, based on linear, kernel and random forest regressions, provide better correlations, contrast similarity and lower WMSEs levels, while RGB images, generated using elastic map approach, provide higher consistency of predictions.

stat.AP↗

arXiv2021

Dynamic and Thermodynamic Models of Adaptation

The concept of biological adaptation was closely connected to some mathematical, engineering and physical ideas from the very beginning. Cannon in his "The wisdom of the body" (1932) used the engineering vision of regulation. In 1938, Selye enriched this approach by the notion of adaptation energy. This term causes much debate when one takes it literally, i.e. as a sort of energy. Selye did not use the language of mathematics, but the formalization of his phenomenological theory in the spirit of thermodynamics was simple and led to verifiable predictions. In 1980s, the dynamics of correlation and variance in systems under adaptation to a load of environmental factors were studied and the universal effect in ensembles of systems under a load of similar factors was discovered: in a crisis, as a rule, even before the onset of obvious symptoms of stress, the correlation increases together with variance (and volatility). During 30 years, this effect has been supported by many observations of groups of humans, mice, trees, grassy plants, and on financial time series. In the last ten years, these results were supplemented by many new experiments, from gene networks in cardiology and oncology to dynamics of depression and clinical psychotherapy. Several systems of models were developed: the thermodynamic-like theory of adaptation of ensembles and several families of models of individual adaptation. Historically, the first group of models was based on Selye's concept of adaptation energy and used fitness estimates. Two other groups of models are based on the idea of hidden attractor bifurcation and on the advection--diffusion model for distribution of population in the space of physiological attributes. We explore this world of models and experiments, starting with classic works, with particular attention to the results of the last ten years and open questions.

q-bio.OT↗

arXiv2020

Handling missing data in large healthcare dataset: a case study of unknown trauma outcomes

Handling of missed data is one of the main tasks in data preprocessing especially in large public service datasets. We have analysed data from the Trauma Audit and Research Network (TARN) database, the largest trauma database in Europe. For the analysis we used 165,559 trauma cases. Among them, there are 19,289 cases (13.19\%) with unknown outcome. We have demonstrated that these outcomes are not missed `completely at random' and, hence, it is impossible just to exclude these cases from analysis despite the large amount of available data. We have developed a system of non-stationary Markov models for the handling of missed outcomes and validated these models on the data of 15,437 patients which arrived into TARN hospitals later than 24 hours but within 30 days from injury. We used these Markov models for the analysis of mortality. In particular, we corrected the observed fraction of death. Two naïve approaches give 7.20\% (available case study) or 6.36\% (if we assume that all unknown outcomes are `alive'). The corrected value is 6.78\%. Following the seminal paper of Trunkey (1983) the multimodality of mortality curves has become a much discussed idea. For the whole analysed TARN dataset the coefficient of mortality monotonically decreases in time but the stratified analysis of the mortality gives a different result: for lower severities the coefficient of mortality is a non-monotonic function of the time after injury and may have maxima at the second and third weeks. The approach developed here can be applied to various healthcare datasets which experience the problem of lost patients and missed outcomes.

stat.AP↗

arXiv2019

How deep should be the depth of convolutional neural networks: a backyard dog case study

The work concerns the problem of reducing a pre-trained deep neuronal network to a smaller network, with just few layers, whilst retaining the network's functionality on a given task The proposed approach is motivated by the observation that the aim to deliver the highest accuracy possible in the broadest range of operational conditions, which many deep neural networks models strive to achieve, may not necessarily be always needed, desired, or even achievable due to the lack of data or technical constraints. In relation to the face recognition problem, we formulated an example of such a usecase, the `backyard dog' problem. The `backyard dog', implemented by a lean network, should correctly identify members from a limited group of individuals, a `family', and should distinguish between them. At the same time, the network must produce an alarm to an image of an individual who is not in a member of the family. To produce such a network, we propose a shallowing algorithm. The algorithm takes an existing deep learning model on its input and outputs a shallowed version of it. The algorithm is non-iterative and is based on the Advanced Supervised Principal Component Analysis. Performance of the algorithm is assessed in exhaustive numerical experiments. In the above usecase, the `backyard dog' problem, the method is capable of drastically reducing the depth of deep learning neural networks, albeit at the cost of mild performance deterioration. We developed a simple non-iterative method for shallowing down pre-trained deep networks. The method is generic in the sense that it applies to a broad class of feed-forward networks, and is based on the Advanced Supervise Principal Component Analysis. The method enables generation of families of smaller-size shallower specialized networks tuned for specific operational conditions and tasks from a single larger and more universal legacy network.

cs.NE↗

arXiv2019

Law of the Minimum Paradoxes

The "Law of the Minimum" states that growth is controlled by the scarcest resource (limiting factor). This concept was originally applied to plant or crop growth (Justus von Liebig, 1840) and quantitatively supported by many experiments. Some generalizations based on more complicated "dose-response" curves were proposed. Violations of this law in natural and experimental ecosystems were also reported. We study models of adaptation in ensembles of similar organisms under load of environmental factors and prove that violation of Liebig's law follows from adaptation effects. If the fitness of an organism in a fixed environment satisfies the Law of the Minimum then adaptation equalizes the pressure of essential factors and therefore acts against the Liebig's law. This is the the Law of the Minimum paradox: if for a randomly chosen pair "organism-environment" the Law of the Minimum typically holds, then, in a well-adapted system, we have to expect violations of this law. For the opposite interaction of factors (a synergistic system of factors which amplify each other) adaptation leads from factor equivalence to limitations by a smaller number of factors. For analysis of adaptation we develop a system of models based on Selye's idea of the universal adaptation resource (adaptation energy). These models predict that under the load of an environmental factor a population separates into two groups (phases): a less correlated, well adapted group and a highly correlated group with a larger variance of attributes, which experiences problems with adaptation. Some empirical data are presented and evidences of interdisciplinary applications to econometrics are discussed.

q-bio.PE↗

arXiv2019

New universal Lyapunov functions for non-linear reaction networks

In 1961, Rényi discovered a rich family of non-classical Lyapunov functions for kinetics of the Markov chains, or, what is the same, for the linear kinetic equations. This family was parameterised by convex functions on the positive semi-axis. After works of Csiszár and Morimoto, these functions became widely known as $f$-divergences or the Csiszár--Morimoto divergences. These Lyapunov functions are universal in the following sense: they depend only on the state of equilibrium, not on the kinetic parameters themselves. Despite many years of research, no such wide family of universal Lyapunov functions has been found for nonlinear reaction networks. For general non-linear networks with detailed or complex balance, the classical thermodynamics potentials remain the only universal Lyapunov functions. We constructed a rich family of new universal Lyapunov functions for {\em any non-linear reaction network} with detailed or complex balance. These functions are parameterised by compact subsets of the projective space. They are universal in the same sense: they depend only on the state of equilibrium and on the network structure, but not on the kinetic parameters themselves. The main elements and operations in the construction of the new Lyapunov functions are partial equilibria of reactions and convex envelopes of families of functions.

physics.chem-ph↗

arXiv2019

Three waves of chemical dynamics

Three epochs in development of chemical dynamics are presented. We try to understand the modern research programs in the light of classical works. Three eras (or waves) of chemical dynamics can be revealed in the flux of research and publications. These waves may be associated with leaders: the first is the van't Hoof wave, the second may be called the Semenov--Hinshelwood wave and the third is definitely the Aris wave. Of course, the whole building was impossible without efforts of hundreds of other researchers. Some of of them are mentioned in our brief review.

physics.chem-ph↗

arXiv2018

Simple model of complex dynamics of activity patterns in developing networks of neuronal cultures

Living neuronal networks in dissociated neuronal cultures are widely known for their ability to generate highly robust spatiotemporal activity patterns in various experimental conditions. These include neuronal avalanches satisfying the power scaling law and thereby exemplifying 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 propose a simple model which may offer an answer to this question. Our derivations are based on just few phenomenological observations concerning 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, a network activity variable and an exogenous variable corresponding to energy needed to sustain the activity and modulate the efficacy of signal transmission. 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 supported by empirical observations and published experimental evidence on cultured neurons behavior exposed to oxygen and energy deprivation. At the larger, network scale, introduction of the energy-dependent regulatory mechanism enables the network to balance 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 a balance between global network-wide processes and spontaneous activity of individual elements.

nlin.AO↗

arXiv2018

Correction of AI systems by linear discriminants: Probabilistic foundations

Artificial Intelligence (AI) systems sometimes make errors and will make errors in the future, from time to time. These errors are usually unexpected, and can lead to dramatic consequences. Intensive development of AI and its practical applications makes the problem of errors more important. Total re-engineering of the systems can create new errors and is not always possible due to the resources involved. The important challenge is to develop fast methods to correct errors without damaging existing skills. We formulated the technical requirements to the 'ideal' correctors. Such correctors include binary classifiers, which separate the situations with high risk of errors from the situations where the AI systems work properly. Surprisingly, for essentially high-dimensional data such methods are possible: simple linear Fisher discriminant can separate the situations with errors from correctly solved tasks even for exponentially large samples. The paper presents the probabilistic basis for fast non-destructive correction of AI systems. A series of new stochastic separation theorems is proven. These theorems provide new instruments for fast non-iterative correction of errors of legacy AI systems. The new approaches become efficient in high-dimensions, for correction of high-dimensional systems in high-dimensional world (i.e. for processing of essentially high-dimensional data by large systems).

cs.LG↗

arXiv2018

The unreasonable effectiveness of small neural ensembles in high-dimensional brain

Despite the widely-spread consensus on the brain complexity, sprouts of the single neuron revolution emerged in neuroscience in the 1970s. They brought many unexpected discoveries, including grandmother or concept cells and sparse coding of information in the brain. In machine learning for a long time, the famous curse of dimensionality seemed to be an unsolvable problem. Nevertheless, the idea of the blessing of dimensionality becomes gradually more and more popular. Ensembles of non-interacting or weakly interacting simple units prove to be an effective tool for solving essentially multidimensional problems. This approach is especially useful for one-shot (non-iterative) correction of errors in large legacy artificial intelligence systems. These simplicity revolutions in the era of complexity have deep fundamental reasons grounded in geometry of multidimensional data spaces. To explore and understand these reasons we revisit the background ideas of statistical physics. In the course of the 20th century they were developed into the concentration of measure theory. New stochastic separation theorems reveal the fine structure of the data clouds. We review and analyse biological, physical, and mathematical problems at the core of the fundamental question: how can high-dimensional brain organise reliable and fast learning in high-dimensional world of data by simple tools? Two critical applications are reviewed to exemplify the approach: one-shot correction of errors in intellectual systems and emergence of static and associative memories in ensembles of single neurons.

cs.AI↗

arXiv2018

Model reduction in chemical dynamics: slow invariant manifolds, singular perturbations, thermodynamic estimates, and analysis of reaction graph

The paper has two goals: It presents basic ideas, notions, and methods for reduction of reaction kinetics models: quasi-steady-state, quasi-equilibrium, slow invariant manifolds, and limiting steps. It describes briefly the current state of the art and some latest achievements in the broad area of model reduction in chemical and biochemical kinetics, including new results in methods of invariant manifolds, computation singular perturbation, bottleneck methods, asymptotology, tropical equilibration, and reaction mechanism skeletonisation.

physics.chem-ph↗

arXiv2018

Basic Model of Purposeful Kinesis

The notions of taxis and kinesis are introduced and used to describe two types of behavior of an organism in non-uniform conditions: (i) Taxis means the guided movement to more favorable conditions; (ii) Kinesis is the non-directional change in space motion in response to the change of conditions. Migration and dispersal of animals has evolved under control of natural selection. In a simple formalisation, the strategy of dispersal should increase Darwinian fitness. We introduce new models of purposeful kinesis with diffusion coefficient dependent on fitness. The local and instant evaluation of Darwinian fitness is used, the reproduction coefficient. New models include one additional parameter, intensity of kinesis, and may be considered as the {\em minimal models of purposeful kinesis}. The properties of models are explored by a series of numerical experiments. It is demonstrated how kinesis could be beneficial for assimilation of patches of food or of periodic fluctuations. Kinesis based on local and instant estimations of fitness is not always beneficial: for species with the Allee effect it can delay invasion and spreading. It is proven that kinesis cannot modify stability of positive homogeneous steady states.

q-bio.PE↗

arXiv2018

Blessing of dimensionality: mathematical foundations of the statistical physics of data

The concentration of measure phenomena were discovered as the mathematical background of statistical mechanics at the end of the XIX - beginning of the XX century and were then explored in mathematics of the XX-XXI centuries. At the beginning of the XXI century, it became clear that the proper utilisation of these phenomena in machine learning might transform the curse of dimensionality into the blessing of dimensionality. This paper summarises recently discovered phenomena of measure concentration which drastically simplify some machine learning problems in high dimension, and allow us to correct legacy artificial intelligence systems. The classical concentration of measure theorems state that i.i.d. random points are concentrated in a thin layer near a surface (a sphere or equators of a sphere, an average or median level set of energy or another Lipschitz function, etc.). The new stochastic separation theorems describe the thin structure of these thin layers: the random points are not only concentrated in a thin layer but are all linearly separable from the rest of the set, even for exponentially large random sets. The linear functionals for separation of points can be selected in the form of the linear Fisher's discriminant. All artificial intelligence systems make errors. Non-destructive correction requires separation of the situations (samples) with errors from the samples corresponding to correct behaviour by a simple and robust classifier. The stochastic separation theorems provide us by such classifiers and a non-iterative (one-shot) procedure for learning.

cs.LG↗

arXiv2017

Beyond Navier--Stokes equations: Capillarity of ideal gas

The system of Navier--Stokes--Fourier equations is one of the most celebrated systems of equations in modern science. It describes dynamics of fluids in the limit when gradients of density, velocity and temperature are sufficiently small, and loses its applicability when the flux becomes so non-equilibrium that the changes of velocity, density or temperature on the length compatible with the mean free path are non-negligible. The question is: how to model such fluxes? This problem is still open. (Despite the fact that the first `final equations of motion' modified for analysis of thermal creep in rarefied gas were proposed by Maxwell in 1879.) There are, at least, three possible answers: (i) use molecular dynamics with individual particles, (ii) use kinetic equations, like Boltzmann's equation, or (iii) find a new system of equations for description of fluid dynamics with better accounting of non-equilibrium effects. These three approaches work at different scales. We explore the third possibility using the recent findings of capillarity of internal layers in ideal gases and of saturation effect in dissipation (there is a limiting attenuation rate for very short waves in ideal gas and it cannot increase infinitely). One candidate equation is discussed in more detail, the Korteweg system proposed in 1901. The main ideas and approaches are illustrated by a kinetic system for which the problem of reduction of kinetics to fluid dynamics is analytically solvable.

cond-mat.stat-mech↗

arXiv2017

Stochastic Separation Theorems

The problem of non-iterative one-shot and non-destructive correction of unavoidable mistakes arises in all Artificial Intelligence applications in the real world. Its solution requires robust separation of samples with errors from samples where the system works properly. We demonstrate that in (moderately) high dimension this separation could be achieved with probability close to one by linear discriminants. Surprisingly, separation of a new image from a very large set of known images is almost always possible even in moderately high dimensions by linear functionals, and coefficients of these functionals can be found explicitly. Based on fundamental properties of measure concentration, we show that for $M 1-\vartheta$, where $1>\vartheta>0$ is a given small constant. Exact values of $a,b>0$ depend on the probability distribution that determines how the random $M$-element sets are drawn, and on the constant $\vartheta$. These {\em stochastic separation theorems} provide a new instrument for the development, analysis, and assessment of machine learning methods and algorithms in high dimension. Theoretical statements are illustrated with numerical examples.

cs.LG↗

arXiv2017

The Five Factor Model of personality and evaluation of drug consumption risk

The problem of evaluating an individual's risk of drug consumption and misuse is highly important. An online survey methodology was employed to collect data including Big Five personality traits (NEO-FFI-R), impulsivity (BIS-11), sensation seeking (ImpSS), and demographic information. The data set contained information on the consumption of 18 central nervous system psychoactive drugs. Correlation analysis demonstrated the existence of groups of drugs with strongly correlated consumption patterns. Three correlation pleiades were identified, named by the central drug in the pleiade: ecstasy, heroin, and benzodiazepines pleiades. An exhaustive search was performed to select the most effective subset of input features and data mining methods to classify users and non-users for each drug and pleiad. A number of classification methods were employed (decision tree, random forest, $k$-nearest neighbors, linear discriminant analysis, Gaussian mixture, probability density function estimation, logistic regression and na{ï}ve Bayes) and the most effective classifier was selected for each drug. The quality of classification was surprisingly high with sensitivity and specificity (evaluated by leave-one-out cross-validation) being greater than 70\% for almost all classification tasks. The best results with sensitivity and specificity being greater than 75\% were achieved for cannabis, crack, ecstasy, legal highs, LSD, and volatile substance abuse (VSA).

stat.AP↗