Asymptotic enumeration of correlation-immune boolean functions

A boolean function of $n$ boolean variables is {correlation-immune} of order $k$ if the function value is uncorrelated with the values of any $k$ of the arguments. Such functions are of considerable interest due to their cryptographic properties, and are also related to the orthogonal arrays of statistics and the balanced hypercube colourings of combinatorics. The {weight} of a boolean function is the number of argument values that produce a function value of 1. If this is exactly half the argument values, that is, $2^{n-1}$ values, a correlation-immune function is called {resilient}. An asymptotic estimate of the number $N(n,k)$ of $n$-variable correlation-immune boolean functions of order $k$ was obtained in 1992 by Denisov for constant $k$. Denisov repudiated that estimate in 2000, but we will show that the repudiation was a mistake. The main contribution of this paper is an asymptotic estimate of $N(n,k)$ which holds if $k$ increases with $n$ within generous limits and specialises to functions with a given weight, including the resilient functions. In the case of $k=1$, our estimates are valid for all weights.Comment: 18 page

Multi-parameter approach to R-parity violating SUSY couplings

We introduce and implement a new, extended approach to placing bounds on trilinear R-parity violating couplings. We focus on a limited set of leptonic and semi-leptonic processes involving neutrinos, combining multidimensional plotting and cross-checking constraints from different experiments. This allows us to explore new regions of parameter space and to relax a number of bounds given in the literature. We look for qualitatively different results compared to those obtained previously using the assumption that a single coupling dominates the R-parity violating contributions to a process (SCD). By combining results from several experiments, we identify regions in parameter space where two or more parameters approach their maximally allowed values. In the same vein, we show a circumstance where consistency between independent bounds on the same combinations of trilinear coupling parameters implies mass constraints among slepton or squark masses. Though our new bounds are in most cases weaker than the SCD bounds, the largest deviations we find on individual parameters are factors of two, thus indicating that a conservative, order of magnitude bound on an individual coupling is reliably estimated by making the SCD assumption.Comment: 30 pages, 8 figures, 2 tables. Typos fixed, two references added and references updated. Eq. (41) removed, Eq. (40) and text modified. Published versio

Workshop on Mars Sample Return Science

Martian magnetic history; quarantine issues; surface modifying processes; climate and atmosphere; sampling sites and strategies; and life sciences were among the topics discussed

Asymptotic behavior of the number of Eulerian orientations of graphs

We consider the class of simple graphs with large algebraic connectivity (the second-smallest eigenvalue of the Laplacian matrix). For this class of graphs we determine the asymptotic behavior of the number of Eulerian orientations. In addition, we establish some new properties of the Laplacian matrix, as well as an estimate of a conditionality of matrices with the asymptotic diagonal predominanceComment: arXiv admin note: text overlap with arXiv:1104.304

Comparative study of radio pulses from simulated hadron-, electron-, and neutrino-initiated showers in ice in the GeV-PeV range

High energy particle showers produce coherent Cherenkov radio emission in dense, radio-transparent media such as cold ice. Using PYTHIA and GEANT simulation tools, we make a comparative study among electromagnetic (EM) and hadronic showers initiated by single particles and neutrino showers initiated by multiple particles produced at the neutrino-nucleon event vertex. We include all the physics processes and do a complete 3-D simulation up to 100 TeV for all showers and to 1 PeV for electron and neutrino induced showers. We calculate the radio pulses for energies between 100 GeV and 1 PeV and find hadron showers, and consequently neutrino showers, are not as efficient below 1 PeV at producing radio pulses as the electromagnetic showers. The agreement improves as energy increases, however, and by a PeV and above the difference disappears. By looking at the 3-D structure of the showers in time, we show that the hadronic showers are not as compact as the EM showers and hence the radiation is not as coherent as EM shower emission at the same frequency. We show that the ratio of emitted pulse strength to shower tracklength is a function only of a single, coherence parameter, independent of species and energy of initiating particle.Comment: a few comments added, to bo published in PRD Nov. issue, 10 pages, 3 figures in tex file, 3 jpg figures in separate files, and 1 tabl

Peak reduction technique in commutative algebra

The "peak reduction" method is a powerful combinatorial technique with applications in many different areas of mathematics as well as theoretical computer science. It was introduced by Whitehead, a famous topologist and group theorist, who used it to solve an important algorithmic problem concerning automorphisms of a free group. Since then, this method was used to solve numerous problems in group theory, topology, combinatorics, and probably in some other areas as well. In this paper, we give a survey of what seems to be the first applications of the peak reduction technique in commutative algebra and affine algebraic geometry.Comment: survey; 10 page