Robustness, Weak Stability, and Stability in Distribution of Adaptive Filteringalgorithms Under Model Mismatch

This work is concerned with robustness, convergence, and stability of adaptive filtering (AF) type algorithms in the presence of model mismatch. The algorithms under consideration are recursive and have inherent multiscale structure. They can be considered as dynamic systems, in which the `state\u27 changes much more slowly than the perturbing noise. Beyond the existing results on adaptive algorithms, model mismatch significantly affects convergence properties of AF algorithms, raising issues of algorithm robustness. Weak convergence and weak stability (i.e., recurrence) under model mismatch are derived. Based on the limiting stochastic differential equations of suitably scaled iterates, stability in distribution is established. Then algorithms with decreasing step sizes and their convergence properties are examined. When input signals are large, identification bias due to model mismatch will become large and unacceptable. Methods for reducing such bias are introduced when the identified models are used in regulation problems

Stochastic Game Approach to Air Operations

A Command and Control (C2) problem for Military Air Operations is addressed. Specifically, we consider C2 problems for air vehicles against ground based targets and defensive systems. The problem is viewed as a stochastic game. In this paper, we restrict our attention to the C2 level where the problem may consist of a few UCAVs or aircraft (or possibly teams of vehicles); less than say, a half-dozen enemy SAMs; a few enemy assets (viewed as targets from our standpoint); and some enemy decoys (assumed to mimic SAM radar signatures). At this low level, some targets are mapped out and possible SAM sites that are unavoidably part of the situation are known. One may then employ a discrete stochastic game problem formulation to determine which of these SAMs should optimally be engaged (if any), and by what series of air vehicle operations. Since this is a game model, the optimal opponent strategy is also determined. We provide analysis, numerical implementation, and simulation for full state feedback and measurement feedback control within this C2 context

Ecosystem Modeling of College Drinking: Parameter Estimation and Comparing Models to Data

Recently we developed a model composed of five impulsive differential equations that describes the changes in drinking patterns (that persist at epidemic level) amongst college students. Many of the model parameters cannot be measured directly from data; thus, an inverse problem approach, which chooses the set of parameters that results in the “best” model to data fit, is crucial for using this model as a predictive tool. The purpose of this paper is to present the procedure and results of an unconventional approach to parameter estimation that we developed after more common approaches were unsuccessful for our specific problem. The results show that our model provides a good fit to survey data for 32 campuses. Using these parameter estimates, we examined the effect of two hypothetical intervention policies: 1) reducing environmental wetness, and 2) penalizing students who are caught drinking. The results suggest that reducing campus wetness may be a very effective way of reducing heavy episodic (binge) drinking on a college campus, while a policy that penalizes students who drink is not nearly as effective

Parameter Estimation for Gene Regulatory Networks from Microarray Data: Cold Shock Response in Saccharomyces cerevisiae

We investigated the dynamics of a gene regulatory network controlling the cold shock response in budding yeast, Saccharomyces cerevisiae. The medium-scale network, derived from published genome-wide location data, consists of 21 transcription factors that regulate one another through 31 directed edges. The expression levels of the individual transcription factors were modeled using mass balance ordinary differential equations with a sigmoidal production function. Each equation includes a production rate, a degradation rate, weights that denote the magnitude and type of influence of the connected transcription factors (activation or repression), and a threshold of expression. The inverse problem of determining model parameters from observed data is our primary interest. We fit the differential equation model to published microarray data using a penalized nonlinear least squares approach. Model predictions fit the experimental data well, within the 95 % confidence interval. Tests of the model using randomized initial guesses and model-generated data also lend confidence to the fit. The results have revealed activation and repression relationships between the transcription factors. Sensitivity analysis indicates that the model is most sensitive to changes in the production rate parameters, weights, and thresholds of Yap1, Rox1, and Yap6, which form a densely connected core in the network. The modeling results newly suggest that Rap1, Fhl1, Msn4, Rph1, and Hsf1 play an important role in regulating the early response to cold shock in yeast. Our results demonstrate that estimation for a large number of parameters can be successfully performed for nonlinear dynamic gene regulatory networks using sparse, noisy microarray data

GRNsight: a web application and service for visualizing models of small- to medium-scale gene regulatory networks

GRNsight is a web application and service for visualizing models of gene regulatory networks (GRNs). A gene regulatory network (GRN) consists of genes, transcription factors, and the regulatory connections between them which govern the level of expression of mRNA and protein from genes. The original motivation came from our efforts to perform parameter estimation and forward simulation of the dynamics of a differential equations model of a small GRN with 21 nodes and 31 edges. We wanted a quick and easy way to visualize the weight parameters from the model which represent the direction and magnitude of the influence of a transcription factor on its target gene, so we created GRNsight. GRNsight automatically lays out either an unweighted or weighted network graph based on an Excel spreadsheet containing an adjacency matrix where regulators are named in the columns and target genes in the rows, a Simple Interaction Format (SIF) text file, or a GraphML XML file. When a user uploads an input file specifying an unweighted network, GRNsight automatically lays out the graph using black lines and pointed arrowheads. For a weighted network, GRNsight uses pointed and blunt arrowheads, and colors the edges and adjusts their thicknesses based on the sign (positive for activation or negative for repression) and magnitude of the weight parameter. GRNsight is written in JavaScript, with diagrams facilitated by D3.js, a data visualization library. Node.js and the Express framework handle server-side functions. GRNsight’s diagrams are based on D3.js’s force graph layout algorithm, which was then extensively customized to support the specific needs of GRNs. Nodes are rectangular and support gene labels of up to 12 characters. The edges are arcs, which become straight lines when the nodes are close together. Self-regulatory edges are indicated by a loop. When a user mouses over an edge, the numerical value of the weight parameter is displayed. Visualizations can be modified by sliders that adjust the force graph layout parameters and through manual node dragging. GRNsight is best-suited for visualizing networks of fewer than 35 nodes and 70 edges, although it accepts networks of up to 75 nodes or 150 edges. GRNsight has general applicability for displaying any small, unweighted or weighted network with directed edges for systems biology or other application domains. GRNsight serves as an example of following and teaching best practices for scientific computing and complying with FAIR principles, using an open and test-driven development model with rigorous documentation of requirements and issues on GitHub. An exhaustive unit testing framework using Mocha and the Chai assertion library consists of around 160 automated unit tests that examine nearly 530 test files to ensure that the program is running as expected. The GRNsight application (http://dondi.github.io/GRNsight/) and code (https://github.com/dondi/GRNsight) are available under the open source BSD license

Political economy of renewable resource federalism

Author Posting. © Ecological Society of America, 2021. This article is posted here by permission of Ecological Society of America for personal use, not for redistribution. The definitive version was published in Ecological Applications 00 (2021): e2276, doi:10.1002/eap.2276.The authority to manage natural capital often follows political boundaries rather than ecological. This mismatch can lead to unsustainable outcomes, as spillovers from one management area to the next may create adverse incentives for local decision making, even within a single country. At the same time, one‐size‐fits‐all approaches of federal (centralized) authority can fail to respond to state (decentralized) heterogeneity and can result in inefficient economic or detrimental ecological outcomes. Here we utilize a spatially explicit coupled natural–human system model of a fishery to illuminate trade‐offs posed by the choice between federal vs. state control of renewable resources. We solve for the dynamics of fishing effort and fish stocks that result from different approaches to federal management that vary in terms of flexibility. Adapting numerical methods from engineering, we also solve for the open‐loop Nash equilibrium characterizing state management outcomes, where each state anticipates and responds to the choices of the others. We consider traditional federalism questions (state vs. federal management) as well as more contemporary questions about the economic and ecological impacts of shifting regulatory authority from one level to another. The key mechanisms behind the trade‐offs include whether differences in local conditions are driven by biological or economic mechanisms; degree of flexibility embedded in the federal management; the spatial and temporal distribution of economic returns across states; and the status‐quo management type. While simple rules‐of‐thumb are elusive, our analysis reveals the complex political economy dimensions of renewable resource federalism.This work was partially supported through the Ecological Federalism working group of the National Institute for Mathematical and Biological Synthesis, an Institute sponsored by the National Science Foundation through NSF Award (No. DBI‐1300426), with additional support from the Howard H. Baker Jr. Center for Public Policy and The University of Tennessee, Knoxville. M. G. Neubert acknowledges support from the U.S. National Science Foundation (DEB‐1558904) and from the J. Seward Johnson Endowment in support of the Woods Hole Oceanographic Institution’s Marine Policy Center. We would like to thank seminar participants at Oregon State University, Nature Policy Lab at U.C. Davis, and the 2019 Association of Environmental and Resource Economists Summer Conference for valuable comments and suggestions on earlier versions of this research

GRNsight: a web application and service for visualizing models of small- to medium-scale gene regulatory networks

GRNsight is a web application and service for visualizing models of gene regulatory networks (GRNs). A gene regulatory network (GRN) consists of genes, transcription factors, and the regulatory connections between them which govern the level of expression of mRNA and protein from genes. The original motivation came from our efforts to perform parameter estimation and forward simulation of the dynamics of a differential equations model of a small GRN with 21 nodes and 31 edges. We wanted a quick and easy way to visualize the weight parameters from the model which represent the direction and magnitude of the influence of a transcription factor on its target gene, so we created GRNsight. GRNsight automatically lays out either an unweighted or weighted network graph based on an Excel spreadsheet containing an adjacency matrix where regulators are named in the columns and target genes in the rows, a Simple Interaction Format (SIF) text file, or a GraphML XML file. When a user uploads an input file specifying an unweighted network, GRNsight automatically lays out the graph using black lines and pointed arrowheads. For a weighted network, GRNsight uses pointed and blunt arrowheads, and colors the edges and adjusts their thicknesses based on the sign (positive for activation or negative for repression) and magnitude of the weight parameter. GRNsight is written in JavaScript, with diagrams facilitated by D3.js, a data visualization library. Node.js and the Express framework handle server-side functions. GRNsight’s diagrams are based on D3.js’s force graph layout algorithm, which was then extensively customized to support the specific needs of GRNs. Nodes are rectangular and support gene labels of up to 12 characters. The edges are arcs, which become straight lines when the nodes are close together. Self-regulatory edges are indicated by a loop. When a user mouses over an edge, the numerical value of the weight parameter is displayed. Visualizations can be modified by sliders that adjust the force graph layout parameters and through manual node dragging. GRNsight is best-suited for visualizing networks of fewer than 35 nodes and 70 edges, although it accepts networks of up to 75 nodes or 150 edges. GRNsight has general applicability for displaying any small, unweighted or weighted network with directed edges for systems biology or other application domains. GRNsight serves as an example of following and teaching best practices for scientific computing and complying with FAIR principles, using an open and test-driven development model with rigorous documentation of requirements and issues on GitHub. An exhaustive unit testing framework using Mocha and the Chai assertion library consists of around 160 automated unit tests that examine nearly 530 test files to ensure that the program is running as expected. The GRNsight application (http://dondi.github.io/GRNsight/) and code (https://github.com/dondi/GRNsight) are available under the open source BSD license

Simplified Models for LHC New Physics Searches

This document proposes a collection of simplified models relevant to the design of new-physics searches at the LHC and the characterization of their results. Both ATLAS and CMS have already presented some results in terms of simplified models, and we encourage them to continue and expand this effort, which supplements both signature-based results and benchmark model interpretations. A simplified model is defined by an effective Lagrangian describing the interactions of a small number of new particles. Simplified models can equally well be described by a small number of masses and cross-sections. These parameters are directly related to collider physics observables, making simplified models a particularly effective framework for evaluating searches and a useful starting point for characterizing positive signals of new physics. This document serves as an official summary of the results from the "Topologies for Early LHC Searches" workshop, held at SLAC in September of 2010, the purpose of which was to develop a set of representative models that can be used to cover all relevant phase space in experimental searches. Particular emphasis is placed on searches relevant for the first ~50-500 pb-1 of data and those motivated by supersymmetric models. This note largely summarizes material posted at http://lhcnewphysics.org/, which includes simplified model definitions, Monte Carlo material, and supporting contacts within the theory community. We also comment on future developments that may be useful as more data is gathered and analyzed by the experiments.Comment: 40 pages, 2 figures. This document is the official summary of results from "Topologies for Early LHC Searches" workshop (SLAC, September 2010). Supplementary material can be found at http://lhcnewphysics.or