Spitzer 70-micron Confusion Level

Spitzer 70μm confusion measurements are presented based on ultra-deep MIPS-70μm observations of GOODS Hubble Deep Field North (HDFN). The instrument noise for the MIPS-70μm band integrates down with nearly t^(−0.5) for the low background HDF-N field. The estimated confusion level is σ_c = 0.30 ± 0.15mJy for a limiting flux density of 1.5mJy (q = 5)

Second-order accurate nonoscillatory schemes for scalar conservation laws

Explicit finite difference schemes for the computation of weak solutions of nonlinear scalar conservation laws is presented and analyzed. These schemes are uniformly second-order accurate and nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time

What makes external financial supporters engage in university spin-off seed investments:entrepreneurs' capabilities or social networks?

This study aims to enrich our knowledge of the influences of social networks and capabilities of entrepreneurial teams have on the engagement of external seed investors by exploring academic entrepreneurial teams. This paper studies the capabilities and characteristics of social networks of entrepreneurial teams based upon resource-based view and the conceptual model of social networks. The results from an examination of the sample of 181 Spanish university spin-offs demonstrate that by exploiting social networks an entrepreneurial team can shape its capabilities which, in turn, improve its ability to access various types of external seed capital sources. Thus, the paper has implications for universities in training and policy development to support spin-off’s activity, especially to build entrepreneurial teams with capabilities to pitch for external seed capital

Modeling Power Systems Dynamics with Symbolic Physics-Informed Neural Networks

In recent years, scientific machine learning, particularly physic-informed neural networks (PINNs), has introduced new innovative methods to understanding the differential equations that describe power system dynamics, providing a more efficient alternative to traditional methods. However, using a single neural network to capture patterns of all variables requires a large enough size of networks, leading to a long time of training and still high computational costs. In this paper, we utilize the interfacing of PINNs with symbolic techniques to construct multiple single-output neural networks by taking the loss function apart and integrating it over the relevant domain. Also, we reweigh the factors of the components in the loss function to improve the performance of the network for instability systems. Our results show that the symbolic PINNs provide higher accuracy with significantly fewer parameters and faster training time. By using the adaptive weight method, the symbolic PINNs can avoid the vanishing gradient problem and numerical instability

A Reconstruction Approach to High-Order Schemes Including Discontinuous Galerkin for Diffusion

We introduce a new approach to high-order accuracy for the numerical solution of diffusion problems by solving the equations in differential form using a reconstruction technique. The approach has the advantages of simplicity and economy. It results in several new high-order methods including a simplified version of discontinuous Galerkin (DG). It also leads to new definitions of common value and common gradient quantities at each interface shared by the two adjacent cells. In addition, the new approach clarifies the relations among the various choices of new and existing common quantities. Fourier stability and accuracy analyses are carried out for the resulting schemes. Extensions to the case of quadrilateral meshes are obtained via tensor products. For the two-point boundary value problem (steady state), it is shown that these schemes, which include most popular DG methods, yield exact common interface quantities as well as exact cell average solutions for nearly all cases

A finite difference scheme for three-dimensional steady laminar incompressible flow

A finite difference scheme for three-dimensional steady laminar incompressible flows is presented. The Navier-Stokes equations are expressed conservatively in terms of velocity and pressure increments (delta form). First order upwind differences are used for first order partial derivatives of velocity increments resulting in a diagonally dominant matrix system. Central differences are applied to all other terms for second order accuracy. The SIMPLE pressure correction algorithm is used to satisfy the continuity equation. Numerical results are presented for cubic cavity flow problems for Reynolds numbers up to 2000 and are in good agreement with other numerical results

A nonoscillatory, characteristically convected, finite volume scheme for multidimensional convection problems

A new, nonoscillatory upwind scheme is developed for the multidimensional convection equation. The scheme consists of an upwind, nonoscillatory interpolation of data to the surfaces of an intermediate finite volume; a characteristic convection of surface data to a midpoint time level; and a conservative time integration based on the midpoint rule. This procedure results in a convection scheme capable of resolving discontinuities neither aligned with, nor convected along, grid lines

Deciding the inequivalence of context-free grammars with 1-letter terminal alphabet is ΣP2-complete

AbstractThis paper deals with the complexity of context-free grammars with 1-letter terminal alphabet. We study the complexity of the membership problem and the inequivalence problem. We show that the first problem is NP-complete and the second one is ΣP2-complete with respect to log-space reduction. The second result also implies that the inequivalence problem is in Pspace, solving an open problem stated by Hunt, Rosenkrantz and Szymanski (1976)