Fast Gr\"obner Basis Computation for Boolean Polynomials

We introduce the Macaulay2 package BooleanGB, which computes a Gr\"obner basis for Boolean polynomials using a binary representation rather than symbolic. We compare the runtime of several Boolean models from systems in biology and give an application to Sudoku

Inferring Biologically Relevant Models: Nested Canalyzing Functions

Inferring dynamic biochemical networks is one of the main challenges in systems biology. Given experimental data, the objective is to identify the rules of interaction among the different entities of the network. However, the number of possible models fitting the available data is huge and identifying a biologically relevant model is of great interest. Nested canalyzing functions, where variables in a given order dominate the function, have recently been proposed as a framework for modeling gene regulatory networks. Previously we described this class of functions as an algebraic toric variety. In this paper, we present an algorithm that identifies all nested canalyzing models that fit the given data. We demonstrate our methods using a well-known Boolean model of the cell cycle in budding yeast

Statistical support for the ATL program

Statistical experimental designs are presented for various numbers of organisms and agar solutions pertinent to the experiment, ""colony growth in zero gravity''. Missions lasting 7 and 30 days are considered. For the designs listed, the statistical analysis of the observations obtained on the space shuttle are outlined

The Evangelical Movement in Austria from 1945 to the Present: A Critical Appraisal

This essay examines the development of the Evangelical Movement in Austria from 1945 to the present. The history of the Evangelical Movement can be divided into four phases: The beginnings (1945-1961), which can be characterized above all by missionary work among ethnic German refugees of the World War II, a second phase from 1961-1981, which can be described as an internationalization of the Evangelical Movement especially through the work of North American missionaries. During this time new ways of evangelism were sought and also church planting projects were started. A third phase is characterized by a growing confessionalization and institutionalization of the Evangelical Movement. While free church congregation were increasingly taking on denominational contours, the evangelical movement as a whole began to increasingly establish its own institutions. The last phase since 1998 is characterized by the Evangelical Movement breaking out of isolation towards social and political acceptance

Compact and efficient sub-10 ps pump sources at 2 µm for the generation of coherent mid-infrared radiation

Ultrashort pulse laser systems in the 2 µm wavelength region featuring high pulse energies are powerful tools for driving a multitude of different applications in industry, medicine, and fundamental science. The implementation of such laser sources remains challenging and usually relies on the chirped-pulse amplification (CPA) in regenerative amplifiers. Here, a much more simplified concept based on a CPA-free multipass amplification scheme operating at room temperature has been investigated. I show that optical pulses with moderate sub-10 ps duration can be amplified up to the millijoule energy level without the onset of nonlinear effects in holmium-doped crystals. The laser system consists of an ultrafast all-fiber mode-locked oscillator and power amplifier based on holmium-doped silica fiber. It has been spectrally tailored to efficiently seed subsequent amplifiers based on holmium-doped YLiF4 crystals. A multipass amplification concept was used to amplify the nJ-level seed pulses from the fiber front-end up to 100 µJ of pulse energy at a pulse repetition frequency of 50 kHz. The maximum pulse energy was limited only by the laser-induced damage threshold of the amplifier crystals. Further pulse energy scaling has been achieved in a final single-pass booster amplifier generating 1.2 mJ at 1 kHz. The overall gain in the Ho:YLF crystals amounts to > 51 dB. Taking into account a measured pulse duration of 8.3 ps, this yields a pulse peak power of 136 MW. These results have been supported by numerical simulations based on a modified Frantz-Nodvik formalism, which is capable of modeling chromatic effects as well as a detailed description of the energy built-up in such amplifiers. Up to 50 µJ at 100 kHz from the multipass amplifier have been used to pump an optical parametric generator/amplifier tandem configuration based on the highly nonlinear non-oxide crystal ZnGeP2. The phase-matching condition has been set to achieve a signal and idler center wavelength of 3 µm and 6.5 µm, respectively. The maximum signal and idler pulse energy was 7.7 µJ and 2.5 µJ. Considering a measured pulse duration of 4 ps for both wavelengths, a peak intensity of about 2 MW (signal) and 0.5 MW (idler) was reached. The mid-IR coherent source is wavelength tunable covering the spectral range from 2.5 to 8 µm under appropriate phase-matching conditions and has shown long-term stability of less than 1.25%rms low-frequency power noise

Computing cost estimates for proof strategies

In this paper we extend work of Treitel and Genesereth for calculating cost estimates for alternative proof methods of logic programs. We consider four methods: (1) forward chaining by semi-naive bottom-up evaluation, (2) goal-directed forward chaining by semi-naive bottom-up evaluation after Generalized Magic-Sets rewriting, (3) backward chaining by OLD resolution, and (4) memoing backward chaining by OLDT resolution. The methods can interact during a proof. After motivating the advantages of each of the proof methods, we show how the effort for the proof can be estimated. The calculation is based on indirect domain knowledge like the number of initial facts and the number of possible values for variables. From this information we can estimate the probability that facts are derived multiple times. An important valuation factor for a proof strategy is whether these duplicates are eliminated. For systematic analysis we distinguish between in costs and out costs of a rule. The out costs correspond to the number of calls of a rule. In costs are the costs for proving the premises of a clause. Then we show how the selection of a proof method for one rule influences the effort of other rules. Finally we discuss problems of estimating costs for recursive rules and propose a solution for a restricted case