Spectral Solution with a Subtraction Method to Improve Accuracy

This work addresses the solution to a Dirichlet boundary value problem for the Poisson equation in 1-D, d2u/dx2 = f using a numerical Fourier collocation approach. The order of accuracy of this approach can be increased by modifying f so the periodic extension of the right hand side is suffciently smooth. A proof for the order is given by Sköllermo. This work introduces a subtraction technique to modify the function\u27s right hand side to reduce the discontinuities or improve the smoothness of its periodic extension. This subtraction technique consists of cosine polynomials found by using boundary derivatives. We subtract cosine polynomials to match boundary values and derivatives of f. The derivatives need only be calculated numerically and approximately represent derivatives at the boundaries. Increasing the number of cosine polynomials in the subtraction technique increases the order of accuracy of the solution. The use of cosine polynomials matches well with the Fourier transform approach and is computationally efficient. Implementation of this technique results in a solution with variable accuracy depending on the number of collocation points and approximated boundary derivatives. Results show that the technique can be up to 14th order accurate

Vagueness as Cost Reduction : An Empirical Test

This work was funded in part by an EPSRC Platform Grant awarded to the NLG group at Aberdeen.Publisher PD

KeyForge: Mitigating Email Breaches with Forward-Forgeable Signatures

Email breaches are commonplace, and they expose a wealth of personal, business, and political data that may have devastating consequences. The current email system allows any attacker who gains access to your email to prove the authenticity of the stolen messages to third parties -- a property arising from a necessary anti-spam / anti-spoofing protocol called DKIM. This exacerbates the problem of email breaches by greatly increasing the potential for attackers to damage the users' reputation, blackmail them, or sell the stolen information to third parties. In this paper, we introduce "non-attributable email", which guarantees that a wide class of adversaries are unable to convince any third party of the authenticity of stolen emails. We formally define non-attributability, and present two practical system proposals -- KeyForge and TimeForge -- that provably achieve non-attributability while maintaining the important protection against spam and spoofing that is currently provided by DKIM. Moreover, we implement KeyForge and demonstrate that that scheme is practical, achieving competitive verification and signing speed while also requiring 42% less bandwidth per email than RSA2048

Augmented Biracks and their Homology

We introduce augmented biracks and define a (co)homology theory associated to augmented biracks. The new homology theory extends the previously studied Yang-Baxter homology with a combinatorial formulation for the boundary map and specializes to $N$-reduced rack homology when the birack is a rack. We introduce augmented birack 2-cocycle invariants of classical and virtual knots and links and provide examples.Comment: 16 page

John Boehner is not the first Speaker to be forced from his post unwillingly, and likely will not be the last.

On Friday last week, the Republican House Speaker, John Boehner, announced that he would resign at the end of October. Matthew Green writes that Boehner’s forthcoming departure is symptomatic of larger forces that have made the job of Speaker extremely challenging