Flows of Substances in Networks and Network Channels: Selected Results and Applications

Dimitrova, Zlatinka I.

doi:10.3390/e24101485

Cited by 7 publications

(6 citation statements)

References 304 publications

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“…In (5), σ is the incubation rate, τ is the transmission rate, and ρ is the recovery rate. We assume constant values of these rates.…”

Section: Sesm and Exact Analytical Solutions For A Sequence Of Equati...mentioning

confidence: 99%

“…In (11), we substitute dS dt and dE dt by the corresponding relationships from the first two equations of (5). The result is a relationship which relates R and E. From this relationship, we obtain…”

Section: Sesm and Exact Analytical Solutions For A Sequence Of Equati...mentioning

confidence: 99%

“…The spread of an epidemic is an example of a nonlinear process in a complex system. Such processes are frequently observed in nature and in society [1][2][3][4][5][6][7][8]. They are usually studied by the methodology of nonlinear time series analysis or by numerical simulations of models containing nonlinear differential or difference equations [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

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Computation of the Exact Forms of Waves for a Set of Differential Equations Associated with the SEIR Model of Epidemics

Vitanov

Dimitrova

2023

Computation

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We studied obtaining exact solutions to a set of equations related to the SEIR (Susceptible-Exposed-Infectious-Recovered) model of epidemic spread. These solutions may be used to model epidemic waves. We transformed the SEIR model into a differential equation that contained an exponential nonlinearity. This equation was then approximated by a set of differential equations which contained polynomial nonlinearities. We solved several equations from the set using the Simple Equations Method (SEsM). In doing so, we obtained many new exact solutions to the corresponding equations. Several of these solutions can describe the evolution of epidemic waves that affect a small percentage of individuals in the population. Such waves have frequently been observed in the COVID-19 pandemic in recent years. The discussion shows that SEsM is an effective methodology for computing exact solutions to nonlinear differential equations. The exact solutions obtained can help us to understand the evolution of various processes in the modeled systems. In the specific case of the SEIR model, some of the exact solutions can help us to better understand the evolution of the quantities connected to the epidemic waves.

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“…In (5), σ is the incubation rate, τ is the transmission rate, and ρ is the recovery rate. We assume constant values of these rates.…”

Section: Sesm and Exact Analytical Solutions For A Sequence Of Equati...mentioning

confidence: 99%

Section: Sesm and Exact Analytical Solutions For A Sequence Of Equati...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Computation of the Exact Forms of Waves for a Set of Differential Equations Associated with the SEIR Model of Epidemics

Vitanov

Dimitrova

2023

Computation

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“…We show that this is the case when learning probabilistic models from data sets which feature a linearly conserved quantity in a discrete label space (see Figure 1). Such data sets can arise naturally from experiments involving conserved quantities, zero-sum game scenarios [33,34], logistics with conserved resources, substance diffusion [35,36,37] in biological systems, and human mobility [38] and migration [39]. We show that the ability of a model to encode the conserved quantity as an inductive bias directly links to a central concept in generalised contextuality, called operational equivalence.…”

Section: Introductionmentioning

confidence: 98%

Contextuality and inductive bias in quantum machine learning

Bowles¹,

Wright²,

Farkas³

et al. 2023

Preprint

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Generalisation in machine learning often relies on the ability to encode structures present in data into an inductive bias of the model class. To understand the power of quantum machine learning, it is therefore crucial to identify the types of data structures that lend themselves naturally to quantum models. In this work we look to quantum contextuality-a form of nonclassicality with links to computational advantage-for answers to this question. We introduce a framework for studying contextuality in machine learning, which leads us to a definition of what it means for a learning model to be contextual. From this, we connect a central concept of contextuality, called operational equivalence, to the ability of a model to encode a linearly conserved quantity in its label space. A consequence of this connection is that contextuality is tied to expressivity: contextual model classes that encode the inductive bias are generally more expressive than their noncontextual counterparts. To demonstrate this, we construct an explicit toy learning problem-based on learning the payoff behaviour of a zero-sum game-for which this is the case. By leveraging tools from geometric quantum machine learning, we then describe how to construct quantum learning models with the associated inductive bias, and show through our toy problem that they outperform their corresponding classical surrogate models. This suggests that understanding learning problems of this form may lead to useful insights about the power of quantum machine learning.

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“…Examples range from atomic chains and lattices to systems of animals, humans and groups of humans, for example, research groups and social networks, economic systems, etc. [ 1 , 2 , 3 , 4 , 5 , 6 , 7 ]. These complex systems are usually nonlinear [ 8 , 9 , 10 ], and this complicates the study.…”

Section: Introductionmentioning

confidence: 99%

Epidemic Waves and Exact Solutions of a Sequence of Nonlinear Differential Equations Connected to the SIR Model of Epidemics

Vitanov

2023

Entropy

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The SIR model of epidemic spreading can be reduced to a nonlinear differential equation with an exponential nonlinearity. This differential equation can be approximated by a sequence of nonlinear differential equations with polynomial nonlinearities. The equations from the obtained sequence are treated by the Simple Equations Method (SEsM). This allows us to obtain exact solutions to some of these equations. We discuss several of these solutions. Some (but not all) of the obtained exact solutions can be used for the description of the evolution of epidemic waves. We discuss this connection. In addition, we use two of the obtained solutions to study the evolution of two of the COVID-19 epidemic waves in Bulgaria by a comparison of the solutions with the available data for the infected individuals.

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Flows of Substances in Networks and Network Channels: Selected Results and Applications

Cited by 7 publications

References 304 publications

Computation of the Exact Forms of Waves for a Set of Differential Equations Associated with the SEIR Model of Epidemics

Computation of the Exact Forms of Waves for a Set of Differential Equations Associated with the SEIR Model of Epidemics

Contextuality and inductive bias in quantum machine learning

Epidemic Waves and Exact Solutions of a Sequence of Nonlinear Differential Equations Connected to the SIR Model of Epidemics

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