The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.Air Force Office of Scientific Research (90-0128

Accounting for Fluctuations in Social Network Usage and Migration Dynamics

In this paper, we examine network capital usage and migration patterns in a theoretical model. Networks are modeled as impacting the migration decision in many ways. When young, larger networks reduce the time lost moving from one region to another. In addition networks decrease the time spent searching for a job. Finally, when old, migrants receive transfer payments through the network. We show that the number and properties of steady state equilibria as well as the global dynamics depend crucially on whether the returns to network capital accumulation exhibit constant, increasing, or decreasing returns to scales relative to the level of network capital. With constant returns to scale, migration flows and network capital levels are characterized by either a unique steady state equilibria or by a two-period cycle. The fluctuations in network capital usage exhibited by our model are consistent with recent empirical data regarding the usage of networks by Mexican immigrants. In the case of increasing returns to scale, either there exists a unique, stable steady state equilibria or multiple equilibria which are characterized as either sinks or saddles. When the returns to scale are decreasing, there exists a unique, stable steady state equilibrium. Finally, we show that increasing barriers to migration will result in an increase in the flow of immigrants, contrary to the desired effect, in the constant and increasing returns to scale cases

A Dynamic Oligopoly Game of the US Airline Industry: Estimation and Policy Experiments

This paper studies the contribution of demand, costs, and strategic factors to the adoption of hub-and-spoke networks in the US airline industry. Our results are based on the estimation of a dynamic oligopoly game of network competition that incorporates three groups of factors that may explain hub-and-spoke networks: (1) travelers may value the services associated with the scale of operation of an airline in the hub airport; (2) operating costs and entry costs in a route may decline with the airline's scale of operation in the origin and destination airports (e.g., economies of scale and scope); and (3) a hub-and-spoke network may be an effective strategy to deter the entry of other carriers. We estimate the model using data from the Airline Origin and Destination Survey with information on quantities, prices, and entry and exit decisions for every airline company in the routes between the 55 largest US cities. As methodological contributions, we propose and apply a method to reduce the dimension of the state space in dynamic games, and a procedure to deal with the problem of multiple equilibria when using a estimated model to make counterfactual experiments. We find that the most important factor to explain the adoption of hub-and-spoke networks is that the cost of entry in a route declines importantly with the scale of operation of the airline in the airports of the route. For some of the larger carriers, strategic entry deterrence is the second most important factor to explain hub-and-spoke networks.Airline industry; Hub-and-spoke networks; Entry costs; Industry dynamics; Estimation of dynamic games; Counterfactual experiments in models with multiple equilibria.

A Dynamic Oligopoly Game of the US Airline Industry: Estimation and Policy Experiments

This paper studies the contribution of demand, costs, and strategic factors to the adoption of hub-and-spoke networks in the US airline industry. Our results are based on the estimation of a dynamic oligopoly game of network competition that incorporates three groups of factors which may explain the adoption of hub-and-spoke networks: (1) travelers value the services associated with the scale of operation of an airline in the hub airport (e.g., more convenient check-in and landing facilities); (2) operating costs and entry costs in a route may decline with an airline's scale operation in origin and destination airports (e.g., economies of scale and scope); and (3) a hub-and-spoke network may be an effective strategy to deter the entry of other carriers. We estimate the model using data from the Airline Origin and Destination Survey with information on quantities, prices, and entry and exit decisions for every airline company in the routes between the 55 largest US cities. As a methodological contribution, we propose and apply a simple method to deal with the problem of multiple equilibria when using the estimated model to predict the effects of changes in structural parameters. We find that the most important factor to explain the adoption of hub-and-spoke networks is that the cost of entry in a route declines very importantly with the scale of operation of the airline in the airports of the route. For some of the larger carriers, strategic entry deterrence is the second most important factor to explain hub-and-spoke networks.Airline industry; Hub-and-spoke networks; Entry costs; Industry dynamics; Estimation of dynamic games; Counterfactuals with multiple equilibria

On the Design and Analysis of Secure Inference Networks

Parallel-topology inference networks consist of spatially-distributed sensing agents that collect and transmit observations to a central node called the fusion center (FC), so that a global inference is made regarding the phenomenon-of-interest (PoI). In this dissertation, we address two types of statistical inference, namely binary-hypothesis testing and scalar parameter estimation in parallel-topology inference networks. We address three different types of security threats in parallel-topology inference networks, namely Eavesdropping (Data-Confidentiality), Byzantine (Data-Integrity) or Jamming (Data-Availability) attacks. In an attempt to alleviate information leakage to the eavesdropper, we present optimal/near-optimal binary quantizers under two different frameworks, namely differential secrecy where the difference in performances between the FC and Eve is maximized, and constrained secrecy where FC’s performance is maximized in the presence of tolerable secrecy constraints. We also propose near-optimal transmit diversity mechanisms at the sensing agents in detection networks in the presence of tolerable secrecy constraints. In the context of distributed inference networks with M-ary quantized sensing data, we propose a novel Byzantine attack model and find optimal attack strategies that minimize KL Divergence at the FC in the presence of both ideal and non-ideal channels. Furthermore, we also propose a novel deviation-based reputation scheme to detect Byzantine nodes in a distributed inference network. Finally, we investigate optimal jamming attacks in detection networks where the jammer distributes its power across the sensing and the communication channels. We also model the interaction between the jammer and a centralized detection network as a complete information zero-sum game. We find closed-form expressions for pure-strategy Nash equilibria and show that both the players converge to these equilibria in a repeated game. Finally, we show that the jammer finds no incentive to employ pure-strategy equilibria, and causes greater impact on the network performance by employing mixed strategies