The key issue affecting Cognitive Diagnostic Models (CDMs) is how to specify attributes and the Q-matrix. In this paper, we first attempt to use the Boolean Matrix Factorization (BMF) method to express conjunctive models in CDMs. Because BMF is an NPhard problem [2], we propose a recursive method that updates the attribute matrix (its rank equals to one) in each step. As Boolean algebra is irre...

We study the Cauchy problem for integrable nonlocal focusing nonlinear Schr\"odinger (NNLS) equation $ iq_{t}(x,t)+q_{xx}(x,t)+2 q^{2}(x,t)\bar{q}(-x,t)=0 with step-like initial data close to ``shifted step function'' $\chi_R(x)=AH(x-R)$, where $H(x)$ is Heaviside function, and $A>0$ $R>0$ are arbitrary constants. Our main aim large-$t$ behavior of solution this problem. show that $R\in\left(\f...

We present a finite difference method for discretizing a Heaviside function H(u(~x)), where u is a level set function u : Rn 7→ R that is positive on a bounded region Ω ⊂ R. There are two variants of our algorithm, both of which are adapted from finite difference methods that we proposed for discretizing delta functions in [13–15]. We consider our approximate Heaviside functions as they are use...

In this paper, we consider a neural field model comprised of two distinct populations of neurons, excitatory and inhibitory, for which both the velocities of action potential propagation and the time courses of synaptic processing are different. Using recently-developed techniques, we construct the Evans function characterising the stability of both stationary and travelling wave solutions, und...

A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously nonhomogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for ...

A subdomain variational inequality and its meshless linear complementary formulation are developed in the present paper for solving two-dimensional contact problems. The subdomain variational inequality will be defined in detail. The meshless method is based on a local weighted residual method with the Heaviside step function as the weighting function over a local subdomain and radial basis fun...

This paper presents two new analytical equations, the Two Exponent Phenomenological Percolation Equation (TEPPE) and Single (SEPPE) which, for proper choice of parameters, approximate widely used Heaviside Step Function. The plots equations presented in figures this show some, but by no means all, step, ramp, delta, differentiable activation functions that can be obtained using percolation equa...

It is shown that feedforward neural nets of constant depth with piecewise polynomial activation functions and arbitrary real weights can be simulated for boolean inputs and outputs by neural nets of a somewhat larger size and depth with heaviside gates and weights from f0; 1g. This provides the rst known upper bound for the computational power and VC-dimension of such neural nets. It is also sh...