Characterization of Information Channels for Asymptotic Mean Stationarity and Stochastic Stability of Non-stationary/Unstable Linear Systems

Stabilization of non-stationary linear systems over noisy communication channels is considered. Stochastically stable sources, and unstable but noise-free or bounded-noise systems have been extensively studied in information theory and control theory literature since 1970s, with a renewed interest in the past decade. There have also been studies on non-causal and causal coding of unstable/non-stationary linear Gaussian sources. In this paper, tight necessary and sufficient conditions for stochastic stabilizability of unstable (non-stationary) possibly multi-dimensional linear systems driven by Gaussian noise over discrete channels (possibly with memory and feedback) are presented. Stochastic stability notions include recurrence, asymptotic mean stationarity and sample path ergodicity, and the existence of finite second moments. Our constructive proof uses random-time state-dependent stochastic drift criteria for stabilization of Markov chains. For asymptotic mean stationarity (and thus sample path ergodicity), it is sufficient that the capacity of a channel is (strictly) greater than the sum of the logarithms of the unstable pole magnitudes for memoryless channels and a class of channels with memory. This condition is also necessary under a mild technical condition. Sufficient conditions for the existence of finite average second moments for such systems driven by unbounded noise are provided.Comment: To appear in IEEE Transactions on Information Theor

Dynamic Heckscher-Ohlin Results from a 2x2x2x2 Overlapping Generations Model with Unequal Population Growth Rates

This paper considers a two-country world where the population in one country grows faster than the other, and investigates the implications of the addition of non-stationary population dynamics to a simple 2- commodity, 2-factor model of international trade within an overlapping- generations framework. The two countries in the world considered are assumed to be identical in every respect except, for their population growth rates initially. The effects of differential speed of population growth on relative factor endowments and patterns of international trade are explored by comparing simulation results obtained from the overlapping-generations general equilibrium model under autarky and trade scenarios. Unequal population growth rates are shown to give rise to differentials in wage rates and rentals for capital under autarky conditions. This, in turn, causes costs of production and relative prices to differ, creating the grounds for trade in the sense of Heckscher-Ohlin (HO). Yet, the results from simulation exercises indicate that static welfare results from the standard 2x2x2 HO model can not be generalized to hold in a dynamic setting with overlapping generations of individuals.Unequal population growth rates, Heckscher-Ohlin model, international trade, overlapping-generations

On Optimal Zero-Delay Coding of Vector Markov Sources

Optimal zero-delay coding (quantization) of a vector-valued Markov source driven by a noise process is considered. Using a stochastic control problem formulation, the existence and structure of optimal quantization policies are studied. For a finite-horizon problem with bounded per-stage distortion measure, the existence of an optimal zero-delay quantization policy is shown provided that the quantizers allowed are ones with convex codecells. The bounded distortion assumption is relaxed to cover cases that include the linear quadratic Gaussian problem. For the infinite horizon problem and a stationary Markov source the optimality of deterministic Markov coding policies is shown. The existence of optimal stationary Markov quantization policies is also shown provided randomization that is shared by the encoder and the decoder is allowed.Comment: IEEE Transactions on Information Theory, accepted for publicatio

Subjective Equilibria under Beliefs of Exogenous Uncertainty

We present a subjective equilibrium notion (called "subjective equilibrium under beliefs of exogenous uncertainty (SEBEU)" for stochastic dynamic games in which each player chooses its decisions under the (incorrect) belief that a stochastic environment process driving the system is exogenous whereas in actuality this process is a solution of closed-loop dynamics affected by each individual player. Players observe past realizations of the environment variables and their local information. At equilibrium, if players are given the full distribution of the stochastic environment process as if it were an exogenous process, they would have no incentive to unilaterally deviate from their strategies. This notion thus generalizes what is known as the price-taking equilibrium in prior literature to a stochastic and dynamic setup. We establish existence of SEBEU, study various properties and present explicit solutions. We obtain the $\epsilon$-Nash equilibrium property of SEBEU when there are many players

Water saturation induced changer in the indirect (Brazilian) tensile strength and the failure mode of some igneous rock materials

The present study concentrates on water induced strength reduction and variation of the failure mode in indirect (Brazilian) tension tests of several igneous rock materials under three moisture cases of oven-dry, air-dry and fully saturated states. In this respect, two andesite and three tuff materials which contain no visible flaws were subjected to indirect tensile strength tests using the Brazilian disc method. Once the tension tests were carried out, photographs of the broken samples were taken to investigate the changes in the failure mode. As a result, it was found that tensile strengths of the samples were highly reduced with the presence of the water and the natural humidity. Additionally, it has been deduced that the failure mode of the samples mainly shifts to central fracturing with the presence of natural moisture and saturation. Although the central crack is the ideal type for the theory of Brazilian tensile strength determination, indefinite contact properties like contact angle and frictions are some notable issues to make only considering failure shapes for the validity of the test results misleading

The Employment Relationship versus Independent Contracting: On the Organizational Choice and Incentives

This paper studies a firm's choice between employing a worker and using an independent contractor to carry out a task. If the firm hires a worker, all residual rights reside with the firm. In contrast, when the firm deals with an independent contractor, it cannot interfere with the way the task is undertaken. The firm's future actions may impose non-pecuniary costs to the worker, and as a result the worker requires an ex-ante compensation. The firm can economize on the up-front cost by hiring an independent contractor. Independent contracting is a commitment device which ensures that the principal will not intervene in the future. However, when the firm has superior private information that is relevant to the execution of the task, the firm faces a trade-off between paying lower costs by hiring an independent contractor and keeping the option of value-enhancing intervention in employment relationship.