14,280 research outputs found
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 sign represents if
for every , the sign of equals
. 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
. We show that sign representing parity over with the
degree in each variable at most requires sparsity at least . 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 on the sparsity of polynomials of any degree representing
parity over . We prove exact bounds on the sparsity of such
polynomials for any two element subset . 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 to compute parity, which improves the previous bound
of due to Goldmann (1997). We show a tight lower bound of
for the inner product function over .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
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