We define a “mock theta” function

We propose a new solver for the sparse spikes deconvolution problem over the space of Radon measures. A common approach to off-the-grid deconvolution considers semidefinite (SDP) relaxations of the total variation (the total mass of the absolute value of the measure) minimization problem. The direct resolution of this SDP is however intractable for large scale settings, since the problem size g...

Pattern contrast discrimination is typically studied with simultaneous onset of the base contrast (C) and added contrast (delta C) patterns. I measured contrast discrimination functions at pattern offset. A brief (30 msec) localized, spatially narrow-band D6 test stimulus was delta C. The onset of delta C was simultaneous with the offset of a large, 500 msec cosine pattern (the base contrast C)...

We explore the Hamiltonian operator H = − d2 dx2 + z δ(x) where x ∈ R, δ(x) is the Dirac delta function, and z is an arbitrary complex coupling constant. For a purely imaginary z, H has a spectral singularity at E = −z2/4 ∈ R+. For R(z) < 0, H has an eigenvalue at E = −z2/4. For the case that R(z) > 0, H has a real, positive, continuous spectrum that is free from spectral singularities. For thi...

We explore the Hamiltonian operator H = − d2 dx2 + z δ(x) where x ∈ R, δ(x) is the Dirac delta function, and z is an arbitrary complex coupling constant. For a purely imaginary z, H has a spectral singularity at E = −z2/4 ∈ R+. For R(z) < 0, H has an eigenvalue at E = −z2/4. For the case that R(z) > 0, H has a real, positive, continuous spectrum that is free from spectral singularities. For thi...

BACKGROUND Opioid receptors regulate a diverse array of physiological functions. Mu opioid receptor agonists are well-known analgesics for treating acute pain. In contrast, animal models suggest that chronic pain is more effectively relieved by delta opioid receptor agonists. A number of studies have shown that chronic pain results in increased function of delta opioid receptors. This is propos...

The backpropagation learning algorithm for feedforward networks (Rumelhart et al. 1986) has recently been generalized to recurrent networks (Pineda 1989). The algorithm has been further generalized by Pearlmutter (1989) to recurrent networks that produce time-dependent trajectories. The latter method requires much more training time than the feedforward or static recurrent algorithms. Furthermo...

Let X be a compact Riemann surface of genus g X ≥ 1. In [7], G. Falt-ings introduced a new invariant δ Fal (X) associated to X. In this paper we give explicit bounds for δ Fal (X) in terms of fundamental differential geometric invariants arising from X, when g X > 1. As an application, we are able to give bounds for Faltings's delta function for the family of modular curves X 0 (N) in terms of ...

This article is devoted to nonlinear ordinary differential equations with additive or multiplicative terms consisting of Dirac delta functions or derivatives thereof. Regularizing the delta function terms produces a family of smooth solutions. Conditions on the nonlinear terms, relating to the order of the derivatives of the delta function part, are established so that the regularized solutions...

In this paper, we discuss some interesting applications of Dirac's delta function in Statistics. We have tried to extend some of the existing results to the more than one variable case. While doing that, we particularly concentrate on the bivariate case.