We show that the monotone analogue of logspace computation is more powerful than monotone log-depth circuits: monotone bounded fanin circuits for a certain function in monotone logspace require depth (lg 2 n).

Manski (1997) and Manski and Pepper (2000) gave sharp bounds on causal effects under the assumptions of monotone treatment response (MTR) and monotone treatment selection (MTS). VanderWeele (2008) provided bounds for binary treatment under an assumption of monotone confounding (MC). We discuss the relation between MC and MTS and provide bounds under various combinations of these assumptions. We...

We investigate whether circuit lower bounds for monotone circuits can be used to derandomize randomized monotone circuits. We show that, in fact, any derandomization of randomized monotone computations would derandomize all randomized computations, whether monotone or not. We prove similar results in the settings of pseudorandom generators and average-case hard functions – that a pseudorandom g...

Several approaches to the product of non-additive monotone measures (or capacities) are discussed and a new approach is proposed. It starts with the M obius product [E. Hendon, H.J. Jacobsen, B. Sloth, T. Tranñs, The product of capacities and belief functions, Mathematical Social Sciences 32 (1996) 95±108] of totally monotone measures and extends it by means of a supremum to general monotone m...

In this paper we show several results about monotone planar circuits. We show that monotone planar circuits of bounded width, with access to negated input variables, compute exactly the functions in non-uniform AC0. This provides a striking contrast to the non-planar case, where exactly NC1 is computed. We show that the circuit value problem for monotone planar circuits, with inputs on the oute...

in this paper, a vector version of the intermediate value theorem is established. the main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{on fixed point theorems for monotone increasing vector valued mappings via scalarizing}, positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

In this paper we study some monotone behavior of the residual (past) entropy of order . We prove that, under some relation between the hazard rates (reversed hazard rates) of two distributions functions F and G, when the residual (past) entropy of order of F is decreasing (increasing) then the residual (past) entropy of G is decreasing (increasing). Using this, several conclusions regarding mo...

semilinear stochastic evolution equations with multiplicative l'evy noise are considered‎. ‎the drift term is assumed to be monotone nonlinear and with linear growth‎. ‎unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎we establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎as corollaries of ...

in this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in f(t,x(t))dt +g(t,x(t))dw_t$ in which the multifunction $f$ is semimonotone and hemicontinuous and the operator-valued multifunction $g$ satisfies a lipschitz condition. we define the it^{o} stochastic integral of operator set-valued stochastic pr...