On stabilization of an automaton model of migration processes

2020 ◽  
Vol 30 (2) ◽  
pp. 117-128
Author(s):  
Denis I. Vasiliev ◽  
Élyar É. Gasanov ◽  
Valerii B. Kudryavtsev
Keyword(s):  
Dynamic System ◽  
Initial Distribution ◽  
Transition Function ◽  
Final State ◽  
System Of Cities ◽  
The City ◽  
Wage Function

AbstractA dynamic system of cities with migrants is considered. The wage function is each city depends on the number of migrants in the city. The system is modeled by an automaton whose state is the vector consisting of the numbers of migrants in the cities. The transition function of the automaton reflects the conditions for transfers of migrants between cities. The system stabilizes if the moves are stopped at some point. We find conditions for stabilization of such system depending on the restrictions on the wage function and the automaton transition function. It is shown that if the functions of wages are strictly decreasing, if their ranges are disjoint, and if the transition function is defined so that a migrant moves to another city if and only if its salary increases, then the system necessarily stabilizes and its final state depends only on the total number of migrants and does not depend on their initial distribution over the cities. However, if the transition function is changed so that a migrant moves also if its salary is preserved, but the total wages in all cities are increased, then a monotonous decrease in the wage functions is sufficient for stabilization of the system.

URBAN SPACE/THE CITY AS AN OBJECT OF RESEARCH: HISTORIOGRAPHY OF THE ISSUE

2021 ◽  
pp. 94-105
Author(s):  
Natalia SINYAVINA
Keyword(s):  
Dynamic System ◽  
Urban Space ◽  
Scientific Interest ◽  
Xix Century ◽  
The City

The article reveals the reasons for the scientific interest in the phenomenon of urban space / city. The author traces the historiography of this issue from the middle of the XIX century to the present day, highlighting the main areas of research. In conclusion, it is concluded that modern works rely on interdisciplinarity in the study of urban space, considering it as a dynamic system.

scholarly journals Market Access and the Concentration of Economic Activity in a System of Declining Cities

REGION ◽  
2018 ◽  
Vol 5 (3) ◽  
pp. 97-109
Author(s):  
Luis Eduardo Quintero ◽  
Paula Restrepo
Keyword(s):  
Population Growth ◽  
Market Access ◽  
Population Decline ◽  
Market Potential ◽  
Population Loss ◽  
City Population ◽  
Alternative Measures ◽  
System Of Cities ◽  
The Impact ◽  
The City

Market access has been widely used as a measure of agglomeration spillovers in models that seek to explain productivity, economic or population growth at the city level. Most results have shown that having higher market access is beneficial to these outcomes. These results, both theoretical and empirical, have been obtained in a context of population growth. This article examines the impact that market access has on a system of cities that has suffered a negative population shock. An extended version of the Brezis and Krugman (1997) model of life cycle of cities predicts that a system of cities experiencing population loss will see a relative reorganization of its population from small to larger cities, and that higher market potential will make this movement stronger. We test these predictions with a comprehensive sample of cities in Eastern Europe and Central Asia. We find that having higher market access - when operating in an environment of population decline - is detrimental to city population growth. This result is robust to different measures of market access that use population. Alternative measures that use economic size rather population are tested, and the result weaker. A possible explanation is that using NLs restricts the sample to only using larger cities. 

Ergodicity of age structure in populations with Markovian vital rates. II. General states

1977 ◽  
Vol 9 (01) ◽  
pp. 18-37 ◽  
Author(s):  
Joel E. Cohen
Keyword(s):  
Markov Chain ◽  
Age Structure ◽  
Joint Distribution ◽  
Sample Path ◽  
Initial Distribution ◽  
Transition Function ◽  
Leslie Matrix ◽  
Vital Rates ◽  
Closed Population ◽  
Leslie Matrices

The age structure of a large, unisexual, closed population is described here by a vector of the proportions in each age class. Non-negative matrices of age-specific birth and death rates, called Leslie matrices, map the age structure at one point in discrete time into the age structure at the next. If the sequence of Leslie matrices applied to a population is a sample path of an ergodic Markov chain, then: (i) the joint process consisting of the age structure vector and the Leslie matrix which produced that age structure is a Markov chain with explicit transition function; (ii) the joint distribution of age structure and Leslie matrix becomes independent of initial age structure and of the initial distribution of the Leslie matrix after a long time; (iii) when the Markov chain governing the Leslie matrix is homogeneous, the joint distribution in (ii) approaches a limit which may be easily calculated as the solution of a renewal equation. A numerical example will be given in Cohen (1977).

scholarly journals On the Equivalence between Small-Step and Big-Step Abstract Machines: A Simple Application of Lightweight Fusion

2007 ◽  
Vol 14 (16) ◽  
Author(s):  
Olivier Danvy ◽  
Kevin Millikin
Keyword(s):  
Fixed Point ◽  
Simple Proof ◽  
Recursive Function ◽  
State Transition ◽  
Transition Function ◽  
Simple Application ◽  
Small Step ◽  
Final State ◽  
Abstract Machines ◽  
State Transition Function

We show how Ohori and Sasano's recent lightweight fusion by fixed-point promotion provides a simple way to prove the equivalence of the two standard styles of specification of abstract machines: (1) in small-step form, as a state-transition function together with a `driver loop,' i.e., a function implementing the iteration of this transition function; and (2) in big-step form, as a tail-recursive function that directly maps a given configuration to a final state, if any. The equivalence hinges on our observation that for abstract machines, fusing a small-step specification yields a big-step specification. We illustrate this observation here with a recognizer for Dyck words, the CEK machine, and Krivine's machine with call/cc.<br /> <br />The need for such a simple proof is motivated by our current work on small-step abstract machines as obtained by refocusing a function implementing a reduction semantics (a syntactic correspondence), and big-step abstract machines as obtained by CPS-transforming and then defunctionalizing a function implementing a big-step semantics (a functional correspondence).

The Final State of an Epidemic in a Large Heterogeneous Population with a Large Initial Number of Infectives

1994 ◽  
Vol 26 (03) ◽  
pp. 656-670
Author(s):  
Steven M. Butler
Keyword(s):  
Size Distribution ◽  
Random Number ◽  
Asymptotic Properties ◽  
Initial Distribution ◽  
Heterogeneous Population ◽  
Initial Number ◽  
Final Size ◽  
Final State ◽  
The Mean ◽  
The Relationship

We describe some asymptotic properties of a general S–I–R epidemic process in a large heterogeneous population. We assume that the infectives behave independently, that each infective has a generally distributed random number of contacts with the others in the population, and that among the initial susceptibles there is an arbitrary initial distribution of susceptibility. For the case of a large number of initial infectives, we demonstrate the asymptotic normality of the final size distribution as well as convergence of the final distribution of susceptibility as the population size approaches infinity. The relationship between the mean of the limiting final size distribution and the initial heterogeneity of susceptibility is explored, for a parametric example.

Ergodicity of age structure in populations with Markovian vital rates. II. General states

1977 ◽  
Vol 9 (1) ◽  
pp. 18-37 ◽  
Author(s):  
Joel E. Cohen
Keyword(s):  
Markov Chain ◽  
Age Structure ◽  
Joint Distribution ◽  
Sample Path ◽  
Initial Distribution ◽  
Transition Function ◽  
Leslie Matrix ◽  
Vital Rates ◽  
Closed Population ◽  
Leslie Matrices

The age structure of a large, unisexual, closed population is described here by a vector of the proportions in each age class. Non-negative matrices of age-specific birth and death rates, called Leslie matrices, map the age structure at one point in discrete time into the age structure at the next. If the sequence of Leslie matrices applied to a population is a sample path of an ergodic Markov chain, then: (i) the joint process consisting of the age structure vector and the Leslie matrix which produced that age structure is a Markov chain with explicit transition function; (ii) the joint distribution of age structure and Leslie matrix becomes independent of initial age structure and of the initial distribution of the Leslie matrix after a long time; (iii) when the Markov chain governing the Leslie matrix is homogeneous, the joint distribution in (ii) approaches a limit which may be easily calculated as the solution of a renewal equation. A numerical example will be given in Cohen (1977).

Floating-point Semantics of Analyzed Programs

2019 ◽  
pp. 167-190
Author(s):  
Pierre-Loïc Garoche
Keyword(s):  
Dynamic System ◽  
Transition Function ◽  
Floating Point ◽  
Rounding Error ◽  
Single Loop ◽  
System Transition ◽  
Loop Body ◽  
Internal Loops

This chapter focuses on floating-point semantics. It first outlines these semantics. The chapter then revisits previous results and adapts them to account for floating-point computations, assuming a bound on the rounding error is provided. A last part focuses on the approaches to bound these imprecisions, over-approximating the floating-point errors. Here, provided bounds on each variable, computing the floating-point error can be performed with classical interval-based analysis. Kleene-based iterations with interval abstract domain provide the appropriate framework to compute such bounds. This is even simpler in this setting because of the focus on bounding the floating-point error on a single call of the dynamic system transition function, that is, a single loop body execution without internal loops.

The Final State of an Epidemic in a Large Heterogeneous Population with a Large Initial Number of Infectives

1994 ◽  
Vol 26 (3) ◽  
pp. 656-670
Author(s):  
Steven M. Butler
Keyword(s):  
Size Distribution ◽  
Random Number ◽  
Asymptotic Properties ◽  
Initial Distribution ◽  
Heterogeneous Population ◽  
Initial Number ◽  
Final Size ◽  
Final State ◽  
The Mean ◽  
The Relationship

We describe some asymptotic properties of a general S–I–R epidemic process in a large heterogeneous population. We assume that the infectives behave independently, that each infective has a generally distributed random number of contacts with the others in the population, and that among the initial susceptibles there is an arbitrary initial distribution of susceptibility. For the case of a large number of initial infectives, we demonstrate the asymptotic normality of the final size distribution as well as convergence of the final distribution of susceptibility as the population size approaches infinity. The relationship between the mean of the limiting final size distribution and the initial heterogeneity of susceptibility is explored, for a parametric example.

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