A trace formula for activated escape in noisy maps

Demaeyer, Jonathan; Gaspard, Pierre

doi:10.1088/1742-5468/2013/10/p10026

Cited by 6 publications

(9 citation statements)

References 39 publications

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“…It is straightforward to generalize the approach of ref. 37 and see that the jump rate has the same exponential dependence on σ 2 when the correlation time Tη is nonzero, as confirmed by Fig. 3.…”

Section: Phase Diagramsupporting

confidence: 74%

Confidence collapse in a multihousehold, self-reflexive DSGE model

Morelli

Benzaquen

Tarzia

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

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We investigate a multihousehold dynamic stochastic general equilibrium (DSGE) model in which past aggregate consumption impacts the confidence, and therefore consumption propensity, of individual households. We find that such a minimal setup is extremely rich and leads to a variety of realistic output dynamics: high output with no crises; high output with increased volatility and deep, short-lived recessions; and alternation of high- and low-output states where a relatively mild drop in economic conditions can lead to a temporary confidence collapse and steep decline in economic activity. The crisis probability depends exponentially on the parameters of the model, which means that markets cannot efficiently price the associated risk premium. We conclude by stressing that within our framework, narratives become an important monetary policy tool that can help steer the economy back on track.

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Section: Phase Diagramsupporting

confidence: 74%

Confidence collapse in a multihousehold, self-reflexive DSGE model

Morelli

Benzaquen

Tarzia

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

show abstract

“…It is straightforward to generalise the approach of (34) and see that the jump rate has the same exponential dependence on σ 2 when the correlation time Tη is non-zero, as confirmed by Fig 3 . However, finding the value of W is more complicated. Approximation methods can been devised in the continuous time limit, that we describe now.…”

Section: Discrete Mapssupporting

confidence: 60%

“…η = 0 in Eq. ( 7)), this is precisely the general problem studied in (34) in the case where H(x) = x has two stable solutions and an unstable one in-between. The authors show that the average time before jumping from one stable solution to another is given, for small σ, by Eq.…”

Section: Discrete Mapsmentioning

confidence: 94%

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Confidence Collapse in a Multi-Household, Self-Reflexive DSGE Model

Morelli,

Benzaquen,

Tarzia

et al. 2019

Preprint

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We investigate a multi-household DSGE model in which past aggregate consumption impacts the confidence, and therefore consumption propensity, of individual households. We find that such a minimal setup is extremely rich, and leads to a variety of realistic output dynamics: high output with no crises; high output with increased volatility and deep, short lived recessions; alternation of high and low output states where relatively mild drop in economic conditions can lead to a temporary confidence collapse and steep decline in economic activity. The crisis probability depends exponentially on the parameters of the model, which means that markets cannot efficiently price the associated risk premium. We conclude by stressing that within our framework, narratives become an important monetary policy tool, that can help steering the economy back on track. Significance statement: Despite their inability to cope with the Global Financial Crisis and various subsequent calls to "Rebuild Macroeconomics", Dynamics Stochastic General equilibrium (DSGE) models are still at the forefront of monetary policy around the world. Like many standard economic models, DSGE models rely on the figment of representative agents, abolishing the possibility of genuine collective effects (such as crises like the 2008 GFC) induced by heterogeneities and interactions. By allowing feedback of past aggregate consumption on the sentiment of individual households, we pave the way for a class of more realistic DSGE models that allow for large output swings induced by relatively minor variations in economic conditions and amplified by interactions. Several important conceptual messages follow from our work,for example the de facto impossibility to price extreme risks and the importance of narratives, which may be an efficient depression-prevention policy tool whenever confidence collapse is looming. * Quoting O. Blanchard in (4): We in the field did think of the economy as roughly linear, constantly subject to different shocks, constantly fluctuating, but naturally returning to equilibrium over time. [...]. The problem is that we came to believe that this was indeed the way the world worked.

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“…It is also well-known that analysis of chaotic dynamics can be performed by the observation and measurement of dynamics like trace formulas [ 46 , 47 , 48 , 49 ] or inference of control parameters [ 50 , 51 , 52 ], and so forth. Many analysis methods success with additive perturbation [ 46 , 47 , 48 ].…”

Section: Introductionmentioning

confidence: 99%

Novel Models of Image Permutation and Diffusion Based on Perturbed Digital Chaos

Hoang

Assad

2020

Entropy

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Most of chaos-based cryptosystems utilize stationary dynamics of chaos for the permutation and diffusion, and many of those are successfully attacked. In this paper, novel models of the image permutation and diffusion are proposed, in which chaotic map is perturbed at bit level on state variables, on control parameters or on both. Amounts of perturbation are initially the coordinate of pixels in the permutation, the value of ciphered word in the diffusion, and then a value extracted from state variables in every iteration. Under the persistent perturbation, dynamics of chaotic map is nonstationary and dependent on the image content. The simulation results and analyses demonstrate the effectiveness of the proposed models by means of the good statistical properties of transformed image obtained after just only a single round.

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A trace formula for activated escape in noisy maps

Cited by 6 publications

References 39 publications

Confidence collapse in a multihousehold, self-reflexive DSGE model

Confidence collapse in a multihousehold, self-reflexive DSGE model

Confidence Collapse in a Multi-Household, Self-Reflexive DSGE Model

Novel Models of Image Permutation and Diffusion Based on Perturbed Digital Chaos

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