Temperature discrimination, behavioral thermoregulation and related measures in the rat Final report

Hyperthermia, dietary, and desalivation effects on thermoregulation in rat

Polynomials that Sign Represent Parity and Descartes' Rule of Signs

A real polynomial $P(X_1,..., X_n)$ sign represents $f: A^n \to \{0,1\}$ if for every $(a_1, ..., a_n) \in A^n$, the sign of $P(a_1,...,a_n)$ equals $(-1)^{f(a_1,...,a_n)}$. Such sign representations are well-studied in computer science and have applications to computational complexity and computational learning theory. In this work, we present a systematic study of tradeoffs between degree and sparsity of sign representations through the lens of the parity function. We attempt to prove bounds that hold for any choice of set $A$. We show that sign representing parity over $\{0,...,m-1\}^n$ with the degree in each variable at most $m-1$ requires sparsity at least $m^n$. We show that a tradeoff exists between sparsity and degree, by exhibiting a sign representation that has higher degree but lower sparsity. We show a lower bound of $n(m -2) + 1$ on the sparsity of polynomials of any degree representing parity over $\{0,..., m-1\}^n$. We prove exact bounds on the sparsity of such polynomials for any two element subset $A$. The main tool used is Descartes' Rule of Signs, a classical result in algebra, relating the sparsity of a polynomial to its number of real roots. As an application, we use bounds on sparsity to derive circuit lower bounds for depth-two AND-OR-NOT circuits with a Threshold Gate at the top. We use this to give a simple proof that such circuits need size $1.5^n$ to compute parity, which improves the previous bound of ${4/3}^{n/2}$ due to Goldmann (1997). We show a tight lower bound of $2^n$ for the inner product function over $\{0,1\}^n \times \{0, 1\}^n$.Comment: To appear in Computational Complexit

Copyright, Plagiarism, and Emerging Norms in Digital Publishing

Today\u27s copyright law derives from the needs of the publishing industry in centuries past. The digital world creates even more significant concerns for authors and publishers than those that arose with the advent of the printing press. Digital technology enables easy, fast, and inexpensive global copying and distribution of digital texts. Other digitized industries--such as the music, movie, and video-game industries--have faced these challenges with a higher apparent success rate, at least in the courts, than the publishing industry. This Article considers why publishing has been less successful in protecting its online copyrights and examines the extent to which copyright law might work more effectively within the industry. Drawing on evidence of emerging norms in the self-publishing community, the Author suggests that the answers for e-publishing may lie outside formal legal regulation; rather, the answers reside in market-based solutions, social norms, and grassroots antipiracy campaigns, augmented by currently available digital technologies such as encryption and plagiarism-detection software