Ding, G., Monotone clutters, Discrete Mathematics 119 (1993) 67-77. A clutter is k-monotone, completely monotone or threshold if the corresponding Boolean function is k-monotone, completely monotone or threshold, respectively. A characterization of k-monotone clutters in terms ofexcluded minors is presented here. This result is used to derive a characterization of 2-monotone matroids and of 3-m...

Although integral and differential nonlinearity may not be the most important parameters for high-speed, high dynamic performance data converters, they gain significance when it comes to highresolution imaging applications. The following application note serves as a refresher course for their definitions and details two different, yet commonly used techniques to measure INL and DNL in highspeed...

‎In this paper‎, ‎we generalize the proximal point algorithm to complete CAT(0) spaces and show‎ ‎that the sequence generated by the proximal point algorithm‎ $w$-converges to a zero of the maximal‎ ‎monotone operator‎. ‎Also‎, ‎we prove that if $f‎: ‎Xrightarrow‎ ‎]-infty‎, +‎infty]$ is a proper‎, ‎convex and lower semicontinuous‎ ‎function on the complete CAT(0) space $X$‎, ‎then the proximal...

1. Overview This paper talks about that monotone circuit is P-Complete. Decision problem that include P-Complete is mapping that classify input with a similar property. Therefore equivalence relation of input value is important for computation. But monotone circuit cannot compute the equivalence relation of the value because monotone circuit can compute only monotone function. Therefore, I make...

ENERGY METHODS FOR REACTION-DIFFUSION PROBLEMS by Xing Zhong Nonlinear reaction-diffusion equations arise in many areas of applied sciences such as combustion modeling, population dynamics, chemical kinetics, etc. A fundamental problem in the studies of these equations is to understand the long time behavior of solutions of the associated Cauchy problem. These kinds of questions were originally...

We characterize the size of monotone span programs computing certain “structured” boolean functions by the Nullstellensatz degree of a related unsatisfiable Boolean formula. This yields the first exponential lower bounds for monotone span programs over arbitrary fields, the first exponential separations between monotone span programs over fields of different characteristic, and the first expone...

Compressed sensing posits that, within limits, one can undersample a sparse signal and yet reconstruct it accurately. Knowing the precise limits to such undersampling is important both for theory and practice. We present a formula precisely delineating the allowable degree of of undersampling of generalized sparse objects. The formula applies to Approximate Message Passing (AMP) algorithms for ...

This paper deals with monotone relaxation iterates for solving nonlinear monotone difference schemes of elliptic type. The monotone ω-Jacobi and SUR (Successive Under-Relaxation) methods are constructed. The monotone methods solve only linear discrete systems at each iterative step and converge monotonically to the exact solution of the nonlinear monotone difference schemes. Convergent rates of...

We provide sufficient conditions for a monotone function with finite set of outcomes to be cyclically monotone. Using these conditions, we show that any defined on the domain gross substitutes is The result also extends generalized and complements.