scholarly journals A stochastic-statistical residential burglary model with independent Poisson clocks

2020 ◽  
Vol 32 (1) ◽  
pp. 32-58
Author(s):  
CHUNTIAN WANG ◽  
YUAN ZHANG ◽  
ANDREA L. BERTOZZI ◽  
MARTIN B. SHORT
Keyword(s):  
Pattern Formation ◽  
Statistical Model ◽  
Finite Size ◽  
Residential Burglary ◽  
Time Step ◽  
Finite Size Effects ◽  
Agent Based ◽  
Stochastic Component ◽  
Active Particles ◽  
First Time

Residential burglary is a social problem in every major urban area. As such, progress has been to develop quantitative, informative and applicable models for this type of crime: (1) the Deterministic-time-step (DTS) model [Short, D’Orsogna, Pasour, Tita, Brantingham, Bertozzi & Chayes (2008) Math. Models Methods Appl. Sci.18, 1249–1267], a pioneering agent-based statistical model of residential burglary criminal behaviour, with deterministic time steps assumed for arrivals of events in which the residential burglary aggregate pattern formation is quantitatively studied for the first time; (2) the SSRB model (agent-based stochastic-statistical model of residential burglary crime) [Wang, Zhang, Bertozzi & Short (2019) Active Particles, Vol. 2, Springer Nature Switzerland AG, in press], in which the stochastic component of the model is theoretically analysed by introduction of a Poisson clock with time steps turned into exponentially distributed random variables. To incorporate independence of agents, in this work, five types of Poisson clocks are taken into consideration. Poisson clocks (I), (II) and (III) govern independent agent actions of burglary behaviour, and Poisson clocks (IV) and (V) govern interactions of agents with the environment. All the Poisson clocks are independent. The time increments are independently exponentially distributed, which are more suitable to model individual actions of agents. Applying the method of merging and splitting of Poisson processes, the independent Poisson clocks can be treated as one, making the analysis and simulation similar to the SSRB model. A Martingale formula is derived, which consists of a deterministic and a stochastic component. A scaling property of the Martingale formulation with varying burglar population is found, which provides a theory to the finite size effects. The theory is supported by quantitative numerical simulations using the pattern-formation quantifying statistics. Results presented here will be transformative for both elements of application and analysis of agent-based models for residential burglary or in other domains.

Gravity waves on a rough bottom: experimental evidence of one-dimensional localization

1988 ◽  
Vol 186 ◽  
pp. 539-558 ◽  
Author(s):  
Max Belzons ◽  
Elisabeth Guazzelli ◽  
Olivier Parodi
Keyword(s):  
Experimental Evidence ◽  
Gravity Waves ◽  
Finite Size ◽  
Finite Size Effects ◽  
One Dimensional ◽  
Localization Phenomenon ◽  
Resonant Modes ◽  
Theoretical Predictions ◽  
Rough Bed ◽  
First Time

We present experimental evidence of the localization of linear gravity waves on a rough (i.e. random) bottom in a one-dimensional channel. The localization phenomenon is observed through very precise measurements in a wave tank. Viscous dissipation and rough-bed finite-size effects are examined. The experimental estimation of the localization lengths are compared with the theoretical predictions of Devillard, Dunlop & Souillard (1988). Finally, the resonant modes due to the disorder are directly observed for the first time.

Gluonic excitation of exotic hybrid charmonium from lattice QCD

2007 ◽  
Vol 22 (07n10) ◽  
pp. 573-582
Author(s):  
Yan Liu ◽  
Xiang-Qian Luo
Keyword(s):  
Excited State ◽  
Ground State ◽  
Finite Size ◽  
Finite Size Effects ◽  
Well Control ◽  
Hybrid Mesons ◽  
Quantum Numbers ◽  
Anisotropic Lattice ◽  
First Time ◽  
The Continuum

We give the prediction for the ground and excited state masses of the charmonium hybrid mesons, 1-+, 0+-, 0--, with exotic quantum numbers. We employ improved gluon and quark actions on anisotropic lattice, which reduce greatly the lattice artifacts, and lead to good signals. The data are extrapolated to the continuum limit, with finite size effects under well control. The ground state masses of 1-+, 0+-, 0-- agree with our earlier results, where the mass of 0-- were shown for the first time. And the excited state masses, reported for the first time here, are 6.450(190)GeV, 6.629(138)GeV and 8.487(201)GeV respectively.

Finite size effects in epidemic spreading: the problem of overpopulated systems

Open Physics ◽  
2013 ◽  
Vol 11 (12) ◽  
Author(s):  
Wojciech Ganczarek
Keyword(s):  
Mixing Time ◽  
Finite Size ◽  
Network Size ◽  
Epidemic Spreading ◽  
Epidemic Threshold ◽  
Time Step ◽  
Finite Size Effects ◽  
Sexually Transmitted ◽  
The Impact ◽  
Quasi Stationary Distribution

AbstractIn this paper we analyze the impact of network size on the dynamics of epidemic spreading. In particular, we investigate the pace of infection in overpopulated systems. In order to do that, we design a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step, which can serve as a model for sexually transmitted diseases spreading in some student communes. Because of the highly discrete character of the process, the analysis cannot use the continuous approximation widely exploited for most models. Using a discrete approach, we investigate the epidemic threshold and the quasi-stationary distribution. The main results are two theorems about the mixing time for the process: it scales like the logarithm of the network size and it is proportional to the inverse of the distance from the epidemic threshold.

scholarly journals Novel insights in the Levy–Levy–Solomon agent-based economic market model

2020 ◽  
pp. 2150020
Author(s):  
Maximilian Beikirch ◽  
Torsten Trimborn
Keyword(s):  
Size Effects ◽  
Random Number Generator ◽  
Finite Size ◽  
Market Model ◽  
Economic Market ◽  
Finite Size Effects ◽  
Agent Based ◽  
Huge Impact ◽  
Economic Market Model ◽  
The Impact

The Levy–Levy–Solomon (LLS) model [M. Levy, H. Levy and S. Solomon, Econ. Lett.45, 103 (1994)] is one of the most influential agent-based economic market models. In several publications this model has been discussed and analyzed. Especially Lux and Zschischang [E. Zschischang and T. Lux, Physica A: Stat. Mech. Appl.291, 563 (2001)] have shown that the model exhibits finite-size effects. In this study, we extend existing work in several directions. First, we show simulations which reveal finite-size effects of the model. Second, we shed light on the origin of these finite-size effects. Furthermore, we demonstrate the sensitivity of the LLS model with respect to random numbers. Especially, we can conclude that a low-quality pseudo-random number generator has a huge impact on the simulation results. Finally, we study the impact of the stopping criteria in the market clearance mechanism of the LLS model.

Finite Size Effects on Electroluminescence of Nanoscale Semiconducting Polymer Heterojunctions

1997 ◽  
Vol 9 (2) ◽  
pp. 409-412 ◽  
Author(s):  
Samson A. Jenekhe ◽  
Xuejun Zhang ◽  
X. Linda Chen ◽  
Vi-En Choong ◽  
Yongli Gao ◽  
...  
Keyword(s):  
Size Effects ◽  
Finite Size ◽  
Finite Size Effects ◽  
Semiconducting Polymer

scholarly journals Entanglement, combinatorics and finite-size effects in spin chains

2009 ◽  
Vol 2009 (02) ◽  
pp. P02063 ◽  
Author(s):  
Bernard Nienhuis ◽  
Massimo Campostrini ◽  
Pasquale Calabrese
Keyword(s):  
Size Effects ◽  
Finite Size ◽  
Spin Chains ◽  
Finite Size Effects

scholarly journals An Advance-Tracing Boundary Element Method in the Time Domain for Solving the Radiating Problem of an Arbitrary Obstacle Accelerating Randomly

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Jui-Hsiang Kao
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Time Domain ◽  
Boundary Integral ◽  
Normal Velocity ◽  
Time Step ◽  
Random Acceleration ◽  
The Time Domain ◽  
First Time ◽  
Element Method

This research develops an Advance-Tracing Boundary Element Method in the time domain to calculate the waves that radiate from an immersed obstacle moving with random acceleration. The moving velocity of the immersed obstacle is multifrequency and is projected along the normal direction of every element on the obstacle. The projected normal velocity of every element is presented by the Fourier series and includes the advance-tracing time, which is equal to a quarter period of the moving velocity. The moving velocity is treated as a known boundary condition. The computing scheme is based on the boundary integral equation in the time domain, and the approach process is carried forward in a loop from the first time step to the last. At each time step, the radiated pressure on each element is updated until obtaining a convergent result. The Advance-Tracing Boundary Element Method is suitable for calculating the radiating problem from an arbitrary obstacle moving with random acceleration in the time domain and can be widely applied to the shape design of an immersed obstacle in order to attain security and confidentiality.

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