Image super-resolution is a process to enhance image resolution. It is widely used in medical imaging, satellite imaging, target recognition, etc. In this paper, we conduct continuous modeling and assume that the unknown image intensity function is defined on a continuous domain and belongs to a space with a redundant basis. We propose a new iterative model for single image super-resolution bas...

Zipf’s law predicts a power-law relationship between word rank and frequency in language communication systems, and is widely reported in texts yet remains enigmatic as to its origins. Computer simulations have shown that language communication systems emerge at an abrupt phase transition in the fidelity of mappings between symbols and objects. Since the phase transition approximates the Heavis...

We analyze radially symmetric bumps in a two-dimensional piecewise-smooth neural field model with synaptic depression. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synaptic weights between populations of neurons whose mean firing rate is taken to be a Heaviside function of local activ...

in Gaussian units and in spherical coordinates where a(t) is the radius of the shell, Q is the total surface charge, and H(x, x0) = ∫ x −∞ δ(x ′ − x0) dx′ is the Heaviside step function. However, magnetic charges do not exist, so we cannot have a radial magnetic field of the form (1). That is, the magnetic field is zero, B = 0 everywhere, no matter what is the time dependence a(t) of the radius...

In this paper we construct a stochastic particle method for the Burgers equation with a monotone initial condition; we prove that the convergence rate is O(1= p N + p t) for the L 1 (IR)-norm of the error. To obtain that result, we link the PDE and the algorithm to a system of weakly interacting stochastic particles; the diiculty of the analysis comes from the discontinuity of the interaction k...

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...

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The set of interval Hausdorff continuous functions constitutes the largest space preserving basic algebraic and topological structural properties of continuous functions, such as linearity, ring structure, Dedekind order completeness, etc. Spaces of interval functions have important applications not only in the construction of numerical methods and algorithms, but to problems in abstract areas ...

We present an algorithm to reduce the computational complexity for plane-wave codes used in electronic structure calculations. The proposed algorithm avoids the diagonalization of large Hermitian matrices arising in such problems. The computational time for the diagonalization procedure typically grows as the cube of the number of atoms, or the number of eigenvalues required. To reduce this com...

An extended isogeometric analysis (XIGA) approach is proposed for modeling fracturing in a fluid-saturated porous material. XIGA provides definition of the discontinuity independent underlying mesh layout, which obviates need knowing crack extension direction priori. Unlike Lagrange shape functions used standard finite element approach, non-uniform rational B-splines (NURBS) provide higher-orde...