Stratification and enumeration of Boolean functions by canalizing depth

Boolean network models have gained popularity in computational systems biology over the last dozen years. Many of these networks use canalizing Boolean functions, which has led to increased interest in the study of these functions. The canalizing depth of a function describes how many canalizing variables can be recursively picked off, until a non-canalizing function remains. In this paper, we show how every Boolean function has a unique algebraic form involving extended monomial layers and a well-defined core polynomial. This generalizes recent work on the algebraic structure of nested canalizing functions, and it yields a stratification of all Boolean functions by their canalizing depth. As a result, we obtain closed formulas for the number of n-variable Boolean functions with depth k, which simultaneously generalizes enumeration formulas for canalizing, and nested canalizing functions

EFFICIENCY OF FOREST COMMODITY FUTURES MARKETS

Market efficiency and unbiasedness tests are performed for the first time for three forest commodity futures markets: softwood lumber, oriented strand board (OSB), and northern bleached softwood kraft pulp (NBSK). The Johansen cointegration procedure is applied to test long-term market efficiency, while the standard error correction models (ECM) and ECM with GQARCH-in-mean process are also used to examine short-term market efficiency and unbiasedness. Results show that these markets are inefficient and biased in both the long-term and short-term. Results also indicate that no short-term time-varying risk premiums are found in these commodity futures markets.Marketing,

Divergence in credit ratings

During the recent credit crisis credit rating agencies (CRAs) became increas- ingly lax in their rating of structured products, yet increasingly stringent in their rating of corporate bonds. We examine a model in which a CRA operates in both the market for structured products and for corporate debt, and shares a common reputation across the two markets. We find that, as a CRA s reputation becomes good enough, it can be optimal for it to infl ate its ratings with probability one in the structured products market, but in flate its ratings with a probability zero in the corporate bond market

Exceptional and Anisotropic Transport Properties of Photocarriers in Black Phosphorus

We show that black phosphorus has room-temperature charge mobilities on the order of 10$^4$ cm$^2$V$^{-1}$s$^{-1}$, which are about one order of magnitude larger than silicon. We also demonstrate strong anisotropic transport in black phosphorus, where the mobilities along the armchair direction are about one order of magnitude larger than zigzag direction. A photocarrier lifetime as long as 100 ps is also determined. These results illustrate that black phosphorus is a promising candidate for future electronic and optoelectronic applications.Comment: 5 pages, 4 figure