Towards a General Tool for Studying Threshold Effects Across Diverse Domains

This paper studies the steady-state properties of the join-the-shortest-queue model in the Halfin–Whitt regime. We focus on the process tracking the number of idle servers and the number of servers with nonempty buffers. Recently, Eschenfeldt and Gamarnik proved that a scaled version of this process converges, over finite time intervals, to a two-dimensional diffusion limit as the number of servers goes to infinity. In this paper, we prove that the diffusion limit is exponentially ergodic and that the diffusion scaled sequence of the steady-state number of idle servers and nonempty buffers is tight. Combined with the process-level convergence proved by Eschenfeldt and Gamarnik, our results imply convergence of steady-state distributions. The methodology used is the generator expansion framework based on Stein’s method, also referred to as the drift-based fluid limit Lyapunov function approach in Stolyar. One technical contribution to the framework is to show how it can be used as a general tool to establish exponential ergodicity.

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Propositional Constraint Graphs: An Intuitive, Domain-General Tool for Diagramming Knowledge, Assumptions, and Uncertainties

Proceedings of the Human Factors and Ergonomics Society Annual Meeting ◽

10.1177/1071181320641060 ◽

2020 ◽

Vol 64 (1) ◽

pp. 254-258

Author(s):

Zachary H. Pugh ◽

Douglas J. Gillan

Keyword(s):

Theoretical Models ◽

Modeling Language ◽

Planning And Design ◽

Constraint Structure ◽

General Tool

A diagramming method called Propositional Constraint (PC) graphing was developed as an aid for tasks involving argumentation, planning, and design. Motivated by several AI models of defeasible (or non- monotonic) reasoning, PC graphs were designed to represent knowledge according to an analogical framework in which constraints (e.g., evidence, goals, system constraints) may elicit or deny possibilities (e.g., explanations, decisions, behaviors). In cases of underspecification, an absence of constraints yields uncertainty and competition among plausible outcomes. In cases of overspecification, no plausible outcome is yielded until one of the constraints is amended or forfeited. This framework shares features with theoretical models of reasoning and argumentation, but despite its intuitiveness and applicability, we know of no modeling language or graphical aid that explicitly depicts this defeasible constraint structure. We describe the syntax and semantics for PC graphing and then illustrate potential uses for it.

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Evaluating Threshold Effects in Consumer Sentiment

Southern Economic Journal ◽

10.1002/j.2325-8012.2004.tb00613.x ◽

2004 ◽

Vol 70 (4) ◽

pp. 942-952

Author(s):

Brigitte Desroches ◽

Marc‐André Gosselin

Keyword(s):

Threshold Effects ◽

Consumer Sentiment

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Threshold Effects of Infectious Disease Outbreaks on Livestock Prices: Cases of African Swine Fever and Avian Influenza in South Korea

Applied Sciences ◽

10.3390/app11115114 ◽

2021 ◽

Vol 11 (11) ◽

pp. 5114

Author(s):

Hyung-Chul Rah ◽

Hyeon-Woong Kim ◽

Aziz Nasridinov ◽

Wan-Sup Cho ◽

Seo-Hwa Choi ◽

...

Keyword(s):

Avian Influenza ◽

Infectious Diseases ◽

Disease Outbreaks ◽

African Swine Fever ◽

Threshold Effect ◽

Impact Response ◽

Threshold Effects ◽

Infectious Disease Outbreaks ◽

Retail Prices ◽

The Impact

In this paper we demonstrate the threshold effects of infectious diseases on livestock prices. Daily retail prices of pork and chicken were used as structured data; news and SNS mentions of African Swine Fever (ASF) and Avian Influenza (AI) were used as unstructured data. Models were tested for the threshold effects of disease-related news and SNS frequencies, specifically those related to ASF and AI, on the retail prices of pork and chicken, respectively. The effects were found to exist, and the values of ASF-related news on pork prices were estimated to be −9 and 8, indicating that the threshold autoregressive (TAR) model can be divided into three regimes. The coefficients of the ASF-related SNS frequencies on pork prices were 1.1666, 0.2663 and −0.1035 for regimes 1, 2 and 3, respectively, suggesting that pork prices increased by 1.1666 Korean won in regime 1 when ASF-related SNS frequencies increased. To promote pork consumption by SNS posts, the required SNS frequencies were estimated to have impacts as great as one standard deviation in the pork price. These values were 247.057, 1309.158 and 2817.266 for regimes 1, 2 and 3, respectively. The impact response periods for pork prices were estimated to last 48, 6, and 8 days for regimes 1, 2 and 3, respectively. When the prediction accuracies of the TAR and autoregressive (AR) models with regard to pork prices were compared for the root mean square error, the prediction accuracy of the TAR model was found to be slightly better than that of the AR. When the threshold effect of AI-related news on chicken prices was tested, a linear relationship appeared without a threshold effect. These findings suggest that when infectious diseases such as ASF occur for the first time, the impact on livestock prices is significant, as indicated by the threshold effect and the long impact response period. Our findings also suggest that the impact on livestock prices is not remarkable when infectious diseases occur multiple times, as in the case of AI. To date, this study is the first to suggest the use of SNS to promote meat consumption.

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Threshold effects in heavy quarkonium spectroscopy

10.1063/1.5124595 ◽

2019 ◽

Author(s):

Jacopo Ferretti

Keyword(s):

Heavy Quarkonium ◽

Threshold Effects

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