Towards Divine Economics: Some Testable Propositions

Some Propositions Equivalent to the Continuum Hypothesis

Let 8 denote the real line. If TQ& and r £ 8 , we set {t+r: / £ J H } = r [ r ] . In [ l ] we have proved these two theorems: (BK) Let S C S , T C 8 , S be at most enumerable and T be of first category. Then 8 contains a residual subset R such that SC\T\r\ is empty for every rÇzR. (BM) Let S C S , 2"C8, S be at most enumerable and T be of measure zero. Then 8 contains a subset R such that 8— Ri...

Towards testable neuromechanical control architectures for running.

Some Value Propositions of Online Communities

Online communities are an integral part of the Internet. However, it is not entirely clear exactly what the value propositions of online communities are, and how firms should leverage them. This paper is an attempt to describe some of the value propositions of online communities and to suggest control structures that firms should employ to maximize community value. The general trend that emerge...

Some properties are not even partially testable

For a property P and a sub-property P , we say that P is P -partially testable with q queries if there exists an algorithm that distinguishes, with high probability, inputs in P ′ from inputs ǫ-far from P by using q queries. There are natural properties that require many queries to test, but can be partitioned into a small number of subsets for which they are partially testable with very few qu...

Towards Lower Bounds on Locally Testable Codes

1 Abbreviations and Notations 3 1 General Introduction 4 1.1 PCP theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Property Testing . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Locally Testable Codes . . . . . . . . . . . . . . . . . . . . . . 6 1.3.1 Random locally testable codes . . . . . . . . . . . . . 6 1.3.2 Algebraic Construction of LTCs . . . . . . . . . . ....