Algorithm-assisted discovery of an intrinsic order among mathematical constants.

In recent decades, a growing number of discoveries in mathematics have been assisted by computer algorithms, primarily for exploring large parameter spaces. As computers become more powerful, an intriguing possibility arises-the interplay between human intuition and computer algorithms can lead to discoveries of mathematical structures that would otherwise remain elusive. Here, we demonstrate computer-assisted discovery of a previously unknown mathematical structure, the conservative matrix field. In the spirit of the Ramanujan Machine project, we developed a massively parallel computer algorithm that found a large number of formulas, in the form of continued fractions, for numerous mathematical constants. The patterns arising from those formulas enabled the construction of the first conservative matrix fields and revealed their overarching properties. Conservative matrix fields unveil unexpected relations between different mathematical constants, such as π and ln(2), or e and the Gompertz constant. The importance of these matrix fields is further realized by their ability to connect formulas that do not have any apparent relation, thus unifying hundreds of existing formulas and generating infinitely many new formulas. We exemplify these implications on values of the Riemann zeta function ζ (n), studied for centuries across mathematics and physics. Matrix fields also enable new mathematical proofs of irrationality. For example, we use them to generalize the celebrated proof by Apéry of the irrationality of ζ (3). Utilizing thousands of personal computers worldwide, our research strategy demonstrates the power of large-scale computational approaches to tackle longstanding open problems and discover unexpected connections across diverse fields of science.

A system for exact and approximate genetic linkage analysis of SNP data in large pedigrees.

MOTIVATION: The use of dense single nucleotide polymorphism (SNP) data in genetic linkage analysis of large pedigrees is impeded by significant technical, methodological and computational challenges. Here we describe Superlink-Online SNP, a new powerful online system that streamlines the linkage analysis of SNP data. It features a fully integrated flexible processing workflow comprising both well-known and novel data analysis tools, including SNP clustering, erroneous data filtering, exact and approximate LOD calculations and maximum-likelihood haplotyping. The system draws its power from thousands of CPUs, performing data analysis tasks orders of magnitude faster than a single computer. By providing an intuitive interface to sophisticated state-of-the-art analysis tools coupled with high computing capacity, Superlink-Online SNP helps geneticists unleash the potential of SNP data for detecting disease genes. RESULTS: Computations performed by Superlink-Online SNP are automatically parallelized using novel paradigms, and executed on unlimited number of private or public CPUs. One novel service is large-scale approximate Markov Chain-Monte Carlo (MCMC) analysis. The accuracy of the results is reliably estimated by running the same computation on multiple CPUs and evaluating the Gelman-Rubin Score to set aside unreliable results. Another service within the workflow is a novel parallelized exact algorithm for inferring maximum-likelihood haplotyping. The reported system enables genetic analyses that were previously infeasible. We demonstrate the system capabilities through a study of a large complex pedigree affected with metabolic syndrome. AVAILABILITY: Superlink-Online SNP is freely available for researchers at http://cbl-hap.cs.technion.ac.il/superlink-snp. The system source code can also be downloaded from the system website. CONTACT: omerw@cs.technion.ac.il SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Eternal Sunshine of the Spotless Machine: Protecting Privacy with Ephemeral Channels.

Modern systems keep long memories. As we show in this paper, an adversary who gains access to a Linux system, even one that implements secure deallocation, can recover the contents of applications' windows, audio buffers, and data remaining in device drivers-long after the applications have terminated. We design and implement Lacuna, a system that allows users to run programs in "private sessions." After the session is over, all memories of its execution are erased. The key abstraction in Lacuna is an ephemeral channel, which allows the protected program to talk to peripheral devices while making it possible to delete the memories of this communication from the host. Lacuna can run unmodified applications that use graphics, sound, USB input devices, and the network, with only 20 percentage points of additional CPU utilization.