The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

The secant method is one of the most popular methods for root finding. Standard text books in numerical analysis state that the secant method is super linear: the rate of convergence is set by the gold number. Nevertheless, this property holds only for simple roots. If the multiplicity of the root is larger than one, the convergence of the secant method becomes linear. This communication includ...

J-Y. Park, M. Garwood Center for Magnetic Resonance Research and Department of Radiology, University of Minnesota, Minneapolis, MN, United States Synopsis: Frequency-swept pulses, like the hyperbolic secant (HS1) pulse, are not typically employed for excitation in MRI. When used for excitation in gradient-echo imaging, the HS1 pulse does not produce a proper echo because the magnetization phase...

Adiabatic radio frequency (RF) pulses are in widespread use in biomedical magnetic resonance imaging and spectroscopy. The primary advantage of adiabatic pulses is that provided the condition for adiabaticity is satisfied they can be made insensitive to inhomogeneities in the RF field. In this pedagogical article the principles of adiabatic fast passage (AFP) are explained, and the use of AFP t...

Introduction Rotating frame relaxation rates (R1ρ and R2ρ) measured during continuous-wave spin-lock pulse depend on the frequency offset (ΔΩ) between the pulse and the isochromat of interest [1]. This characteristic impairs a time-efficient utilization of this method for MRS applications in vivo, since data need to be acquired separately for each metabolite of interest. The present work invest...

We study curves with linear series that are exceptional with regard to their secant planes. Working in the framework of an extension of Brill-Noether theory to pairs of linear series, we prove that a general curve of genus g has no exceptional secant planes, in a very precise sense. We also address the problem of computing the number of linear series with exceptional secant planes in a one-para...

Let X ⊆ PN be a non-degenerate projective variety of dimension d. Then the sth secant variety of X, denoted σs(X), is the Zariski closure of the union of linear spans of s-tuples of points lying on X. The study of secant varieties has a long history. The interest in this subject goes back to the Italian school at the turn of the 20th century. This topic has received renewed interest over the pa...

This paper studies a novel recurrent neural network (RNN) with hyperbolic secant (sech) in the gate for specific medical application task of Parkinson’s disease (PD) detection. In detail, it focuses on fact that patients PD have motor speech disorders, by converting voice data into black-and-white images recurrence plot (RP) at time intervals and constructing detection model combines RNN convol...