The Experts below are selected from a list of 57594 Experts worldwide ranked by ideXlab platform

J M L Bernard - One of the best experts on this subject based on the ideXlab platform.

Ryan Williams - One of the best experts on this subject based on the ideXlab platform.

  • nonuniform acc circuit lower bounds
    Journal of the ACM, 2014
    Co-Authors: Ryan Williams
    Abstract:

    The class ACC consists of circuit families with Constant depth over unbounded fan-in AND, OR, NOT, and MODm gates, where m > 1 is an Arbitrary Constant. We prove the following. ---NEXP, the class of languages accepted in nondeterministic exponential time, does not have nonuniform ACC circuits of polynomial size. The size lower bound can be slightly strengthened to quasipolynomials and other less natural functions. ---ENP, the class of languages recognized in 2O(n) time with an NP oracle, doesn’t have nonuniform ACC circuits of 2no(1) size. The lower bound gives an exponential size-depth tradeoff: for every d, m there is a Δ > 0 such that ENP doesn’t have depth-d ACC circuits of size 2nΔ with MODm gates. Previously, it was not known whether EXPNP had depth-3 polynomial-size circuits made out of only MOD6 gates. The high-level strategy is to design faster algorithms for the circuit satisfiability problem over ACC circuits, then prove that such algorithms entail these lower bounds. The algorithms combine known properties of ACC with fast rectangular matrix multiplication and dynamic programming, while the second step requires a strengthening of the author’s prior work.

  • non uniform acc circuit lower bounds
    Conference on Computational Complexity, 2011
    Co-Authors: Ryan Williams
    Abstract:

    The class ACC consists of circuit families with Constant depth over unbounded fan-in AND, OR, NOT, and MOD$m$ gates, where $m > 1$ is an Arbitrary Constant. We prove:- $NTIME[2^n]$ does not have non-uniform ACC circuits of polynomial size. The size lower bound can be strengthened to quasi-polynomials and other less natural functions.- $E^{NP}$, the class of languages recognized in $2^{O(n)}$ time with an $NP$ oracle, doesn't have non-uniform ACC circuits of $2^{n^{o(1)}}$ size. The lower bound gives a size-depth tradeoff: for every $d$, $m$ there is a $\delta > 0$ such that $E^{NP}$ doesn't have depth-$d$ ACC circuits of size $2^{n^{\delta}}$ with MOD$m$ gates.Previously, it was not known whether $EXP^{NP}$ had depth-3 polynomial size circuits made out of only MOD6 gates. The high-level strategy is to design faster algorithms for the circuit satisfiability problem over ACC circuits, then prove that such algorithms can be applied to obtain the above lower bounds.

D S Shirokov - One of the best experts on this subject based on the ideXlab platform.

Abimbola Abolarinwa - One of the best experts on this subject based on the ideXlab platform.

  • elliptic gradient estimates and liouville theorems for a weighted nonlinear parabolic equation
    Journal of Mathematical Analysis and Applications, 2019
    Co-Authors: Abimbola Abolarinwa
    Abstract:

    Abstract Let ( M N , g , e − f d v ) be a complete smooth metric measure space with ∞-Bakry–Emery Ricci tensor bounded from below. We derive elliptic gradient estimates for positive solutions of a weighted nonlinear parabolic equation ( Δ f − ∂ ∂ t ) u ( x , t ) + q ( x , t ) u α ( x , t ) = 0 , where ( x , t ) ∈ M N × ( − ∞ , ∞ ) and α is an Arbitrary Constant. As Applications we prove a Liouville-type theorem for positive ancient solutions and Harnack-type inequalities for positive bounded solutions.

  • elliptic gradient estimates and liouville theorems for a weighted nonlinear parabolic equation
    arXiv: Differential Geometry, 2018
    Co-Authors: Abimbola Abolarinwa
    Abstract:

    Let $(M^N, g, e^{-f}dv)$ be a complete smooth metric measure space with $\infty$-Bakry-\'Emery Ricci tensor bounded from below. We derive elliptic gradient estimates for positive solutions of a weighted nonlinear parabolic equation \begin{align*} \displaystyle \Big(\Delta_f - \frac{\partial}{\partial t}\Big) u(x,t) +q(x,t)u^\alpha(x,t) = 0, \end{align*} where $(x,t) \in M^N \times (-\infty, \infty)$ and $\alpha$ is an Arbitrary Constant. As Applications we prove a Liouville-type theorem for positive ancient solutions and Harnack-type inequalities for positive bounded solutions.

Panayiotis Vafeas - One of the best experts on this subject based on the ideXlab platform.

  • The 3D Happel model for complete isotropic Stokes flow
    Hindawi Limited, 2004
    Co-Authors: George Dassios, Panayiotis Vafeas
    Abstract:

    The creeping flow through a swarm of spherical particles that move with Constant velocity in an Arbitrary direction and rotate with an Arbitrary Constant angular velocity in a quiescent Newtonian fluid is analyzed with a 3D sphere-in-cell model. The mathematical treatment is based on the two-concentric-spheres model. The inner sphere comprises one of the particles in the swarm and the outer sphere consists of a fluid envelope. The appropriate boundary conditions of this non-axisymmetric formulation are similar to those of the 2D sphere-in-cell Happel model, namely, nonslip flow condition on the surface of the solid sphere and nil normal velocity component and shear stress on the external spherical surface. The boundary value problem is solved with the aim of the complete Papkovich-Neuber differential representation of the solutions for Stokes flow, which is valid in non-axisymmetric geometries and provides us with the velocity and total pressure fields in terms of harmonic spherical eigenfunctions. The solution of this 3D model, which is self-sufficient in mechanical energy, is obtained in closed form and analytical expressions for the velocity, the total pressure, the angular velocity, and the stress tensor fields are provided

  • © Hindawi Publishing Corp. THE 3D HAPPEL MODEL FOR COMPLETE ISOTROPIC STOKES FLOW
    2003
    Co-Authors: George Dassios, Panayiotis Vafeas
    Abstract:

    The creeping flow through a swarm of spherical particles that move with Constant velocity in an Arbitrary direction and rotate with an Arbitrary Constant angular velocity in a quiescent Newtonian fluid is analyzed with a 3D sphere-in-cell model. The mathematical treatment is based on the two-concentric-spheres model. The inner sphere comprises one of the particles in the swarm and the outer sphere consists of a fluid envelope. The appropriate boundary conditions of this non-axisymmetric formulation are similar to those of the 2D sphere-in-cell Happel model, namely, nonslip flow condition on the surface of the solid sphere and nil normal velocity component and shear stress on the external spherical surface. The boundary value problem is solved with the aim of the complete Papkovich-Neuber differential repre-sentation of the solutions for Stokes flow, which is valid in non-axisymmetric geometries and provides us with the velocity and total pressure fields in terms of harmonic spherical eigenfunctions. The solution of this 3D model, which is self-sufficient in mechanical energy, is obtained in closed form and analytical expressions for the velocity, the total pressure, the angular velocity, and the stress tensor fields are provided