In this chapter, we begin with the classic models of partial equilibrium markets. We review the theory, which should be familiar to readers, with a special emphasis on points that are of relevance to an empirical researcher. We emphasize methods for uncovering the parameters of market primitives (demand and cost) that a policy-maker would want to use to analyze alternative policies. The ratio o...

Definition Quantum information processing theory is an alternative mathematical approach for generating theories of how an observer processes information. Typically, quantum information processing models are derived from the axiomatic principles of quantum probability theory. This probability theory may be viewed as a generalization of classic probability. Quantum information processing models ...

Probability theory, and its dynamic aspect stochastic process theory, is both a venerable subject, in that its roots go back to the mid-seventeenth century, and a young one, in that its modern formulation happened comparatively recently – well within living memory. The year 2003 marked the seventieth anniversary of Kolmogorov’s Grundbegriffe der Wahrscheinlichkeitsrechnung, usually regarded as ...

The classic Coupon-Collector Problem (CCP) is generalized. Only basic probability theory is used. Centerpiece rather is an algorithm that efficiently counts all k-element transversals of a set system.

The classic Coupon-Collector Problem (CCP) is generalized. Only basic probability theory is used. Centerpiece rather is an algorithm that efficiently counts all k-element transversals of a set system.

The lore is that standard information theory provides an analysis of information quantity, but not of information content. I argue this lore is incorrect, that there is an adequate informational semantics latent in standard theory. The roots of this notion of content can be traced to the secret parallel development of an information theory equivalent to Shannon’s by Turing at Bletchley Park, an...

This paper builds a general mathematical and algorithmic theory for balloon-twisting structures by modeling their underlying edge skeleta, evolving classic balloon animals into the new world of balloon polyhedra. What if Euler were a clown?

Following the Gauss-Markov theorem the generalized lest-squares estimator is the best linear unbiased estimator but following the kriging theory its use is limited. This paper shows the kriging constraint on the classic generalized least-squares estimator.

This paper introduces basic notions of classic computational complexity theory and probabilistically checkable proof. It sketches the proof of the PCP theorem, and discusses its applications to the hardness of approximation of various problems.