We consider the solution of large linear systems with multiple right-hand sides using a block GMRES approach. We introduce a new algorithm that effectively handles the situation of almost rank deficient block generated by the block Arnoldi procedure and that enables the recycling of spectral information at restart. The first feature is inherited from an algorithm introduced by Robbé and Sadkane...

The variety DQD of semi-Heyting algebras with a weak negation, called dually quasi-De Morgan operation, and several of its subvarieties were investigated in the series [31], [32], [33], and [34]. In this paper we define and investigate a new subvariety JID of DQD, called “JI-distributive, dually quasi-De Morgan semi-Heyting algebras”, defined by the identity: x ∨ (y → z) ≈ (x ∨ y) → (x ∨ z), as...

The algebra of truth values for fuzzy sets of type-2 consists of all mappings from the unit interval into itself, with operations certain convolutions of these mappings with respect to pointwise max and min. This algebra generalizes the truth-value algebras of both type-1 and of interval-valued fuzzy sets, and has been studied rather extensively both from a theoretical and applied point of view...

We show a connection between the De Morgan formula size of a Boolean function f : {0, 1}n → {0, 1} and the noise stability of the function. Specifically, we prove that for 0 < p ≤ 1/2 it holds that NSp(f) ≥ 1− 2p √ L(f) · ‖f‖2 · (1− ‖f‖2) where NSp(f) is the noise stability of f with noise parameter p, ‖f‖ is the L2 norm of f , and L(f) is the De Morgan formula size of f . This result stems fro...

Detecting patterns in strings and images is a fundamental and well studied problem. We study the circuit complexity of the string matching problem under two popular choices of gates: De Morgan and threshold gates. For strings of length n and patterns of length log n k ≤ n− o(n), we prove super polynomial lower bounds for De Morgan circuits of depth 2, and nearly linear lower bounds for depth 2 ...

Detecting patterns in strings and images is a fundamental and widely studied problem. Motivated by the proliferation of specialized circuits in pattern recognition tasks, we study the circuit complexity of pattern matching under two popular choices of gates: De Morgan and threshold gates. For strings of length n and patterns of length log n k ≤ n− o(n), we prove super polynomial lower bounds fo...

Akhil Kapur, MBCHB, MD,* Roger J. Hall, MD,†‡ Iqbal S. Malik, MMBCHIR, PHD,† Ayesha C. Qureshi, MBBS,* Jeremy Butts, MBBS,† Mark de Belder, MD,§ Andreas Baumbach, MS, Gianni Angelini, MD, MCH, Adam de Belder, MBBS, MD,¶ Keith G. Oldroyd, MBCHB, MD,# Marcus Flather, MBBS,†** Michael Roughton, MSC,** Petros Nihoyannopoulos, MD,† Jens Peder Bagger, MBBS, DSC,† Kenneth Morgan, MBCHB, BSC,† Kevin J....

Rogelio Hasimoto-Beltrán and Ashfaq A. Khokhar 1 Centro de Investigación en Matemáticas – CIMAT Jalisco s/n, Col. Mineral de Valenciana, Guanajuato, Gto., México 36240 Tel: +52-(473)-732-7155 ext. 49636, Fax: +52-(473)-732-5749 [email protected] 2 University of Illinois at Chicago, Departments of Computer Sciences and Electrical and Computer Engineering, 851 South Morgan Street, Chicago, IL 606...