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Prof. Maria Letizia Bertotti
Free University of Bozen-Bolzano

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0 Complex Systems
0 Dynamical Systems
0 Ordinary Differential Equations
0 Complex Networks
0 socio-economic systems

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Ordinary Differential Equations
Complex Systems
Complex Networks
Dynamical Systems

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Journal article
Published: 09 March 2021 in Sustainability
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In this paper, we present a successful experimental validation of the velocity optimization for a cable car passing over a support. We apply the theoretical strategy developed in a previous work, refined by taking into account in a simple manner the hauling cable dynamics. The experiments at the ropeway Postal–Verano (South Tirol, Italy) have shown a significant reduction of the pendulum angle amplitude for both the descent and the ascending rides, as predicted from simulations. Furthermore, we measured a smoother progress of the torque at the driving engine during the vehicle support crossings.

ACS Style

Markus Wenin; Siegfried Ladurner; Daniel Reiterer; Maria Bertotti; Giovanni Modanese. Validation of the Velocity Optimization for a Ropeway Passing over a Support. Sustainability 2021, 13, 2986 .

AMA Style

Markus Wenin, Siegfried Ladurner, Daniel Reiterer, Maria Bertotti, Giovanni Modanese. Validation of the Velocity Optimization for a Ropeway Passing over a Support. Sustainability. 2021; 13 (5):2986.

Chicago/Turabian Style

Markus Wenin; Siegfried Ladurner; Daniel Reiterer; Maria Bertotti; Giovanni Modanese. 2021. "Validation of the Velocity Optimization for a Ropeway Passing over a Support." Sustainability 13, no. 5: 2986.

Journal article
Published: 18 February 2021 in International Journal of Nonlinear Sciences and Numerical Simulation
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In this article, we discuss a dynamical stochastic model that represents the time evolution of income distribution of a population, where the dynamics develops from an interplay of multiple economic exchanges in the presence of multiplicative noise. The model remit stretches beyond the conventional framework of a Langevin-type kinetic equation in that our model dynamics is self-consistently constrained by dynamical conservation laws emerging from population and wealth conservation. This model is numerically solved and analysed to evaluate the inequality of income in correlation to other relevant dynamical parameters like the mobility M and the total income μ. Inequality is quantified by the Gini index G. In particular, correlations between any two of the mobility index M and/or the total income μ with the Gini index G are investigated and compared with the analogous quantities resulting from an additive noise model.

ACS Style

Maria Letizia Bertotti; Amit K Chattopadhyay; Giovanni Modanese. Stochastic models with multiplicative noise for economic inequality and mobility. International Journal of Nonlinear Sciences and Numerical Simulation 2021, 22, 287 -301.

AMA Style

Maria Letizia Bertotti, Amit K Chattopadhyay, Giovanni Modanese. Stochastic models with multiplicative noise for economic inequality and mobility. International Journal of Nonlinear Sciences and Numerical Simulation. 2021; 22 (3-4):287-301.

Chicago/Turabian Style

Maria Letizia Bertotti; Amit K Chattopadhyay; Giovanni Modanese. 2021. "Stochastic models with multiplicative noise for economic inequality and mobility." International Journal of Nonlinear Sciences and Numerical Simulation 22, no. 3-4: 287-301.

Journal article
Published: 16 January 2021 in Symmetry
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It is well known that dynamical processes on complex networks are influenced by the degree correlations. A common way to take these into account in a mean-field approach is to consider the function knn(k) (average nearest neighbors degree). We re-examine the standard choices of knn for scale-free networks and a new family of functions which is independent from the simple ansatz knn∝kα but still displays a remarkable scale invariance. A rewiring procedure is then used to explicitely construct synthetic networks using the full correlation P(h|k) from which knn is derived. We consistently find that the knn functions of concrete synthetic networks deviate from ideal assortativity or disassortativity at large k. The consequences of this deviation on a diffusion process (the network Bass diffusion and its peak time) are numerically computed and discussed for some low-dimensional samples. Finally, we check that although the knn functions of the new family have an asymptotic behavior for large networks different from previous estimates, they satisfy the general criterium for the absence of an epidemic threshold.

ACS Style

Maria Letizia Bertotti; Giovanni Modanese. Comparison of Simulations with a Mean-Field Approach vs. Synthetic Correlated Networks. Symmetry 2021, 13, 141 .

AMA Style

Maria Letizia Bertotti, Giovanni Modanese. Comparison of Simulations with a Mean-Field Approach vs. Synthetic Correlated Networks. Symmetry. 2021; 13 (1):141.

Chicago/Turabian Style

Maria Letizia Bertotti; Giovanni Modanese. 2021. "Comparison of Simulations with a Mean-Field Approach vs. Synthetic Correlated Networks." Symmetry 13, no. 1: 141.

Journal article
Published: 13 June 2020 in Entropy
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We generate correlated scale-free networks in the configuration model through a new rewiring algorithm that allows one to tune the Newman assortativity coefficient r and the average degree of the nearest neighbors K (in the range − 1 ≤ r ≤ 1 , K ≥ ⟨ k ⟩ ). At each attempted rewiring step, local variations Δ r and Δ K are computed and then the step is accepted according to a standard Metropolis probability exp ( ± Δ r / T ) , where T is a variable temperature. We prove a general relation between Δ r and Δ K , thus finding a connection between two variables that have very different definitions and topological meaning. We describe rewiring trajectories in the r-K plane and explore the limits of maximally assortative and disassortative networks, including the case of small minimum degree ( k m i n ≥ 1 ), which has previously not been considered. The size of the giant component and the entropy of the network are monitored in the rewiring. The average number of second neighbors in the branching approximation z ¯ 2 , B is proven to be constant in the rewiring, and independent from the correlations for Markovian networks. As a function of the degree, however, the number of second neighbors gives useful information on the network connectivity and is also monitored.

ACS Style

Maria Letizia Bertotti; Giovanni Modanese. Network Rewiring in the r-K Plane. Entropy 2020, 22, 653 .

AMA Style

Maria Letizia Bertotti, Giovanni Modanese. Network Rewiring in the r-K Plane. Entropy. 2020; 22 (6):653.

Chicago/Turabian Style

Maria Letizia Bertotti; Giovanni Modanese. 2020. "Network Rewiring in the r-K Plane." Entropy 22, no. 6: 653.

Articles
Published: 03 September 2019 in Mathematical and Computer Modelling of Dynamical Systems
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This paper deals with a generalization of the Bass model for the description of the diffusion of innovations. The generalization keeps into account heterogeneity of the interactions of the consumers and is expressed by a system of several nonlinear differential equations on complex networks. The following contributions can be singled out: first, explicit algorithms are provided for the construction of various families of assortative scale-free networks; second, a method is provided for the identification of the takeoff time and of the peak time, which represent important turning points in the life cycle of an innovation/product; third, the emergence of specific patterns in connection with networks of the same family is observed, whose tentative interpretation is then given. Also, a comparison with an alternative approach is given, within which adoption times of different communities are evaluated of a network describing firm cooperations in South Tyrol.

ACS Style

Maria Letizia Bertotti; Giovanni Modanese. On the evaluation of the takeoff time and of the peak time for innovation diffusion on assortative networks. Mathematical and Computer Modelling of Dynamical Systems 2019, 25, 482 -498.

AMA Style

Maria Letizia Bertotti, Giovanni Modanese. On the evaluation of the takeoff time and of the peak time for innovation diffusion on assortative networks. Mathematical and Computer Modelling of Dynamical Systems. 2019; 25 (5):482-498.

Chicago/Turabian Style

Maria Letizia Bertotti; Giovanni Modanese. 2019. "On the evaluation of the takeoff time and of the peak time for innovation diffusion on assortative networks." Mathematical and Computer Modelling of Dynamical Systems 25, no. 5: 482-498.

Research article
Published: 01 April 2019 in Complexity
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Using a heterogeneous mean-field network formulation of the Bass innovation diffusion model and recent exact results on the degree correlations of Barabasi-Albert networks, we compute the times of the diffusion peak and compare them with those on scale-free networks which have the same scale-free exponent but different assortativity properties. We compare our results with those obtained for the SIS epidemic model with the spectral method applied to adjacency matrices. It turns out that diffusion times on finite Barabasi-Albert networks are at a minimum. This may be due to a little-known property of these networks: whereas the value of the assortativity coefficient is close to zero, they look disassortative if one considers only a bounded range of degrees, including the smallest ones, and slightly assortative on the range of the higher degrees. We also find that if the trickle-down character of the diffusion process is enhanced by a larger initial stimulus on the hubs (via a inhomogeneous linear term in the Bass model), the relative difference between the diffusion times for BA networks and uncorrelated networks is even larger, reaching, for instance, the 34% in a typical case on a network with 104 nodes.

ACS Style

M. L. Bertotti; G. Modanese. The Bass Diffusion Model on Finite Barabasi-Albert Networks. Complexity 2019, 2019, 1 -12.

AMA Style

M. L. Bertotti, G. Modanese. The Bass Diffusion Model on Finite Barabasi-Albert Networks. Complexity. 2019; 2019 ():1-12.

Chicago/Turabian Style

M. L. Bertotti; G. Modanese. 2019. "The Bass Diffusion Model on Finite Barabasi-Albert Networks." Complexity 2019, no. : 1-12.

Journal article
Published: 03 October 2018 in European Journal of Mechanics - A/Solids
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In this paper, we present a theoretical model that solves the problem of minimization of aerial ropeway vehicle oscillations that are induced as the vehicle passes over a support. The task is formulated as an inverse problem, where the vehicle oscillations are minimized by an appropriate choice of the velocity profile of the hauling cable. We study two general cases numerically, a single vehicle system (FUNIFOR), as well as a classical aerial ropeway with two vehicles. In both cases we find optimal velocity profiles that show a considerable improvement of the oscillatory behavior of the vehicles as compared to constant velocity profiles and optimal profiles that have been obtained analytically by loosening some of the constraints for the system. In addition to a minimization of the vehicle oscillations, we also optimize the time that elapses as the vehicle is hauled through the system. We believe that this exploratory study lays a sound basis for various possible future studies and practical applications (Computer Aided Engineering).

ACS Style

M. Wenin; A. Windisch; S. Ladurner; M.L. Bertotti; G. Modanese. Optimal velocity profile for a cable car passing over a support. European Journal of Mechanics - A/Solids 2018, 73, 366 -372.

AMA Style

M. Wenin, A. Windisch, S. Ladurner, M.L. Bertotti, G. Modanese. Optimal velocity profile for a cable car passing over a support. European Journal of Mechanics - A/Solids. 2018; 73 ():366-372.

Chicago/Turabian Style

M. Wenin; A. Windisch; S. Ladurner; M.L. Bertotti; G. Modanese. 2018. "Optimal velocity profile for a cable car passing over a support." European Journal of Mechanics - A/Solids 73, no. : 366-372.

Chapter
Published: 20 May 2018 in Advanced Structured Materials
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In the dynamic behaviour of a cable railway oscillations of cables and cars play an important role. We present a simple model to describe and investigate oscillations of a cable, spanned over a support and charged with an arbitrary number of point loads with arbitrary masses. We construct a time-dependent propagator, which contains the full intrinsic information of the mechanical system and represents a linear map between the initial state, t = 0 (initial condition of a set of linear differential equations) and the state at a time t. We consider undamped and damped oscillations, where damping is introduced by a phenomenological way (Onsager’s lineare ansätze). A numerical example is given.

ACS Style

Markus Wenin; Michael Irschara; Stephan Obexer; Maria Letizia Bertotti; Giovanni Modanese. Cable Railway Simulation: A Two-Span Oscillator Model. Advanced Structured Materials 2018, 65 -79.

AMA Style

Markus Wenin, Michael Irschara, Stephan Obexer, Maria Letizia Bertotti, Giovanni Modanese. Cable Railway Simulation: A Two-Span Oscillator Model. Advanced Structured Materials. 2018; ():65-79.

Chicago/Turabian Style

Markus Wenin; Michael Irschara; Stephan Obexer; Maria Letizia Bertotti; Giovanni Modanese. 2018. "Cable Railway Simulation: A Two-Span Oscillator Model." Advanced Structured Materials , no. : 65-79.

Journal article
Published: 05 March 2018 in Entropy
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In our recently proposed stochastic version of discretized kinetic theory, the exchange of wealth in a society is modelled through a large system of Langevin equations. The deterministic part of the equations is based on non-linear transition probabilities between income classes. The noise terms can be additive, multiplicative or mixed, both with white or Ornstein–Uhlenbeck spectrum. The most important measured correlations are those between Gini inequality index G and social mobility M, between total income and G, and between M and total income. We describe numerical results concerning these correlations and a quantity which gives average stochastic deviations from the equilibrium solutions in dependence on the noise amplitude.

ACS Style

Maria Letizia Bertotti; Amit K. Chattopadhyay; Giovanni Modanese. Statistics of Correlations and Fluctuations in a Stochastic Model of Wealth Exchange. Entropy 2018, 20, 166 .

AMA Style

Maria Letizia Bertotti, Amit K. Chattopadhyay, Giovanni Modanese. Statistics of Correlations and Fluctuations in a Stochastic Model of Wealth Exchange. Entropy. 2018; 20 (3):166.

Chicago/Turabian Style

Maria Letizia Bertotti; Amit K. Chattopadhyay; Giovanni Modanese. 2018. "Statistics of Correlations and Fluctuations in a Stochastic Model of Wealth Exchange." Entropy 20, no. 3: 166.

Journal article
Published: 02 September 2017 in Entropy
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Why does the Maxwell-Boltzmann energy distribution for an ideal classical gas have an exponentially thin tail at high energies, while the Kaniadakis distribution for a relativistic gas has a power-law fat tail? We argue that a crucial role is played by the kinematics of the binary collisions. In the classical case the probability of an energy exchange far from the average (i.e., close to 0% or 100%) is quite large, while in the extreme relativistic case it is small. We compare these properties with the concept of “saving propensity”, employed in econophysics to define the fraction of their money that individuals put at stake in economic interactions.

ACS Style

Maria Letizia Bertotti; Giovanni Modanese. Statistics of Binary Exchange of Energy or Money. Entropy 2017, 19, 465 .

AMA Style

Maria Letizia Bertotti, Giovanni Modanese. Statistics of Binary Exchange of Energy or Money. Entropy. 2017; 19 (9):465.

Chicago/Turabian Style

Maria Letizia Bertotti; Giovanni Modanese. 2017. "Statistics of Binary Exchange of Energy or Money." Entropy 19, no. 9: 465.

Preprint
Published: 23 February 2017
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In this article, we discuss a dynamical stochastic model that represents the time evolution of income distribution of a population, where the dynamics develop from an interplay of multiple economic exchanges in the presence of multiplicative noise. The model remit stretches beyond the conventional framework of a Langevin-type kinetic equation in that our model dynamics is self-consistently constrained by dynamical conservation laws emerging from population and wealth conservation. This model is numerically solved and analyzed to interpret the inequality of income as a function of relevant dynamical parameters like the {\it mobility} $M$ and the {\it total income} $\mu$. In our model, inequality is quantified by the {\it Gini index} $G$. In particular, correlations between any two of the mobility index $M$ and/or the total income $\mu$ with the Gini index $G$ are investigated and compared with the analogous correlations resulting from an equivalent additive noise model. Our findings highlight the importance of a multiplicative noise based economic modeling structure in the analysis of inequality. The model also depicts the nature of correlation between mobility and total income of a population from the perspective of inequality measure.

ACS Style

Maria Letizia Bertotti; Amit K Chattopadhyay; Giovanni Modanese. Economic inequality and mobility for stochastic models with multiplicative noise. 2017, 1 .

AMA Style

Maria Letizia Bertotti, Amit K Chattopadhyay, Giovanni Modanese. Economic inequality and mobility for stochastic models with multiplicative noise. . 2017; ():1.

Chicago/Turabian Style

Maria Letizia Bertotti; Amit K Chattopadhyay; Giovanni Modanese. 2017. "Economic inequality and mobility for stochastic models with multiplicative noise." , no. : 1.

Journal article
Published: 01 January 2017 in Results in Physics
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ACS Style

Maria Letizia Bertotti; Amit K. Chattopadhyay; Giovanni Modanese. Correlation between Gini index and mobility in a stochastic kinetic model of economic exchange. Results in Physics 2017, 7, 2081 -2084.

AMA Style

Maria Letizia Bertotti, Amit K. Chattopadhyay, Giovanni Modanese. Correlation between Gini index and mobility in a stochastic kinetic model of economic exchange. Results in Physics. 2017; 7 ():2081-2084.

Chicago/Turabian Style

Maria Letizia Bertotti; Amit K. Chattopadhyay; Giovanni Modanese. 2017. "Correlation between Gini index and mobility in a stochastic kinetic model of economic exchange." Results in Physics 7, no. : 2081-2084.

Regular article
Published: 26 December 2016 in Journal of Economic Interaction and Coordination
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Microscopic models describing a whole of economic interactions in a closed society are considered. The presence of a tax system combined with a redistribution process is taken into account, as well as the occurrence of tax evasion. In particular, the existence is postulated, in relation to the level of evasion, of different individual taxpayer behaviors. The effects of the mentioned different behaviors on shape and features of the emerging income distribution profile are investigated qualitatively and quantitatively. Numerical solutions show that the Gini inequality index of the total population increases when the evasion level is higher, but does not depend significantly on the evasion spread. For fixed spread, the relative difference between the average incomes of the worst evaders and honest taxpayers increases approximately as a quadratic function of the evasion level.

ACS Style

M. L. Bertotti; G. Modanese. Mathematical models describing the effects of different tax evasion behaviors. Journal of Economic Interaction and Coordination 2016, 13, 351 -363.

AMA Style

M. L. Bertotti, G. Modanese. Mathematical models describing the effects of different tax evasion behaviors. Journal of Economic Interaction and Coordination. 2016; 13 (2):351-363.

Chicago/Turabian Style

M. L. Bertotti; G. Modanese. 2016. "Mathematical models describing the effects of different tax evasion behaviors." Journal of Economic Interaction and Coordination 13, no. 2: 351-363.

Journal article
Published: 26 December 2016 in Physica A: Statistical Mechanics and its Applications
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Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock trade; the latter is based on systems of ordinary differential equations and is better suited for the description of binary interactions, taxation and welfare redistribution. We propose a new framework which establishes a connection between the two approaches by introducing random fluctuations into the kinetic model based on Langevin and Fokker–Planck formalisms. Numerical simulations of the resulting model indicate positive correlations between the Gini index and the total wealth, that suggest a growing inequality with increasing income. Further analysis shows, in the presence of a conserved total wealth, a simultaneous decrease in inequality as social mobility increases, in conformity with economic data.

ACS Style

M.L. Bertotti; A.K. Chattopadhyay; G. Modanese. Stochastic effects in a discretized kinetic model of economic exchange. Physica A: Statistical Mechanics and its Applications 2016, 471, 724 -732.

AMA Style

M.L. Bertotti, A.K. Chattopadhyay, G. Modanese. Stochastic effects in a discretized kinetic model of economic exchange. Physica A: Statistical Mechanics and its Applications. 2016; 471 ():724-732.

Chicago/Turabian Style

M.L. Bertotti; A.K. Chattopadhyay; G. Modanese. 2016. "Stochastic effects in a discretized kinetic model of economic exchange." Physica A: Statistical Mechanics and its Applications 471, no. : 724-732.

Journal article
Published: 26 October 2016 in The European Physical Journal Special Topics
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ACS Style

Maria Letizia Bertotti; Giovanni Modanese. Discretized kinetic theory on scale-free networks. The European Physical Journal Special Topics 2016, 225, 1879 -1891.

AMA Style

Maria Letizia Bertotti, Giovanni Modanese. Discretized kinetic theory on scale-free networks. The European Physical Journal Special Topics. 2016; 225 (10):1879-1891.

Chicago/Turabian Style

Maria Letizia Bertotti; Giovanni Modanese. 2016. "Discretized kinetic theory on scale-free networks." The European Physical Journal Special Topics 225, no. 10: 1879-1891.

Journal article
Published: 26 October 2016 in The European Physical Journal Special Topics
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ACS Style

Maria Letizia Bertotti; Giovanni Modanese. Economic inequality and mobility in kinetic models for social sciences. The European Physical Journal Special Topics 2016, 225, 1945 -1958.

AMA Style

Maria Letizia Bertotti, Giovanni Modanese. Economic inequality and mobility in kinetic models for social sciences. The European Physical Journal Special Topics. 2016; 225 (10):1945-1958.

Chicago/Turabian Style

Maria Letizia Bertotti; Giovanni Modanese. 2016. "Economic inequality and mobility in kinetic models for social sciences." The European Physical Journal Special Topics 225, no. 10: 1945-1958.

Journal article
Published: 01 September 2016 in Chaos, Solitons & Fractals
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The Bass model, which is an effective forecasting tool for innovation diffusion based on large collections of empirical data, assumes an homogeneous diffusion process. We introduce a network structure into this model and we investigate numerically the dynamics in the case of networks with link density P(k)=c/kγ,P(k)=c/kγ, where k=1,…,Nk=1,…,N. The resulting curve of the total adoptions in time is qualitatively similar to the homogeneous Bass curve corresponding to a case with the same average number of connections. The peak of the adoptions, however, tends to occur earlier, particularly when γ and N are large (i.e., when there are few hubs with a large maximum number of connections). Most interestingly, the adoption curve of the hubs anticipates the total adoption curve in a predictable way, with peak times which can be, for instance when N=100,N=100, between 10% and 60% of the total adoptions peak. This may allow to monitor the hubs for forecasting purposes. We also consider the case of networks with assortative and disassortative correlations and a case of inhomogeneous advertising where the publicity terms are “targeted” on the hubs while maintaining their total cost constant.

ACS Style

M.L. Bertotti; J. Brunner; Giovanni Modanese. The Bass diffusion model on networks with correlations and inhomogeneous advertising. Chaos, Solitons & Fractals 2016, 90, 55 -63.

AMA Style

M.L. Bertotti, J. Brunner, Giovanni Modanese. The Bass diffusion model on networks with correlations and inhomogeneous advertising. Chaos, Solitons & Fractals. 2016; 90 ():55-63.

Chicago/Turabian Style

M.L. Bertotti; J. Brunner; Giovanni Modanese. 2016. "The Bass diffusion model on networks with correlations and inhomogeneous advertising." Chaos, Solitons & Fractals 90, no. : 55-63.

Journal article
Published: 01 August 2016 in International Journal of Modern Physics C
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A microscopic dynamic model is here constructed and analyzed, describing the evolution of the income distribution in the presence of taxation and redistribution in a society in which also tax evasion and auditing processes occur. The focus is on effects of enforcement regimes, characterized by different choices of the audited taxpayer fraction and of the penalties imposed to noncompliant individuals. A complex systems perspective is adopted: society is considered as a system composed by a large number of heterogeneous individuals. These are divided into income classes and may as well have different tax evasion behaviors. The variation in time of the number of individuals in each class is described by a system of nonlinear differential equations of the kinetic discretized Boltzmann type involving transition probabilities. A priori, one could think that audits and fines should have a positive effect on the reduction of economic inequality and correspondingly of the Gini index G. According to our model, however, such effect is rather small. In contrast, the effect on the increase of the tax revenue may be significant.

ACS Style

Maria Letizia Bertotti; Giovanni Modanese. Microscopic models for the study of taxpayer audit effects. International Journal of Modern Physics C 2016, 27, 1650100 .

AMA Style

Maria Letizia Bertotti, Giovanni Modanese. Microscopic models for the study of taxpayer audit effects. International Journal of Modern Physics C. 2016; 27 (9):1650100.

Chicago/Turabian Style

Maria Letizia Bertotti; Giovanni Modanese. 2016. "Microscopic models for the study of taxpayer audit effects." International Journal of Modern Physics C 27, no. 9: 1650100.

Journal article
Published: 01 July 2016 in Physics Letters A
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We introduce a heterogeneous network structure into the Bass diffusion model, in order to study the diffusion times of innovation or information in networks with a scale-free structure, typical of regions where diffusion is sensitive to geographic and logistic influences (like for instance Alpine regions). We consider both the diffusion peak times of the total population and of the link classes. In the familiar trickle-down processes the adoption curve of the hubs is found to anticipate the total adoption in a predictable way. In a major departure from the standard model, we model a trickle-up process by introducing heterogeneous publicity coefficients (which can also be negative for the hubs, thus turning them into stiflers) and a stochastic term which represents the erratic generation of innovation at the periphery of the network. The results confirm the robustness of the Bass model and expand considerably its range of applicability.

ACS Style

M.L. Bertotti; J. Brunner; G. Modanese. Innovation diffusion equations on correlated scale-free networks. Physics Letters A 2016, 380, 2475 -2479.

AMA Style

M.L. Bertotti, J. Brunner, G. Modanese. Innovation diffusion equations on correlated scale-free networks. Physics Letters A. 2016; 380 (33):2475-2479.

Chicago/Turabian Style

M.L. Bertotti; J. Brunner; G. Modanese. 2016. "Innovation diffusion equations on correlated scale-free networks." Physics Letters A 380, no. 33: 2475-2479.

Journal article
Published: 11 March 2015 in Complexity
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We formulate a flexible micro-to-macro kinetic model which is able to explain the emergence of income profiles out of a whole of individual economic interactions. The model is expressed by a system of several nonlinear differential equations which involve parameters defined by probabilities. Society is described as an ensemble of individuals divided into income classes; the individuals exchange money through binary and ternary interactions, leaving the total wealth unchanged. The ternary interactions represent taxation and redistribution effects. Dynamics is investigated through computational simulations, the focus being on the effects that different fiscal policies and differently weighted welfare policies have on the long-run income distributions. The model provides a tool which may contribute to the identification of the most effective actions towards a reduction of economic inequality. We find for instance that, under certain hypotheses, the Gini index is more affected by a policy of reduction of the welfare and subsidies for the rich classes than by an increase of the upper tax rate. Such a policy also has the effect of slightly increasing the total tax revenue.Comment: 15 pages, 3 figures. arXiv admin note: text overlap with arXiv:1403.001

ACS Style

Maria Letizia Bertotti; Giovanni Modanese. Microscopic models for welfare measures addressing a reduction of economic inequality. Complexity 2015, 21, 89 -98.

AMA Style

Maria Letizia Bertotti, Giovanni Modanese. Microscopic models for welfare measures addressing a reduction of economic inequality. Complexity. 2015; 21 (6):89-98.

Chicago/Turabian Style

Maria Letizia Bertotti; Giovanni Modanese. 2015. "Microscopic models for welfare measures addressing a reduction of economic inequality." Complexity 21, no. 6: 89-98.