Torsion in the cohomology of congruence subgroups of SL(4,Z) and Galois representations

We report on the computation of torsion in certain homology theories of congruence subgroups of SL(4,Z). Among these are the usual group cohomology, the Tate-Farrell cohomology, and the homology of the sharbly complex. All of these theories yield Hecke modules. We conjecture that the Hecke eigenclasses in these theories have attached Galois representations. The interpretation of our computations at the torsion primes 2,3,5 is explained. We provide evidence for our conjecture in the 15 cases of odd torsion that we found in levels up to 31

Mod 2 homology for GL(4) and Galois representations

We extend the computations in [AGM4] to find the mod 2 homology in degree 1 of a congruence subgroup Gamma of SL(4,Z) with coefficients in the sharbly complex, along with the action of the Hecke algebra. This homology group is closely related to the cohomology of Gamma with F_2 coefficients in the top cuspidal degree. These computations require a modification of the algorithm to compute the action of the Hecke operators, whose previous versions required division by 2. We verify experimentally that every mod 2 Hecke eigenclass found appears to have an attached Galois representation, giving evidence for a conjecture in [AGM4]. Our method of computation was justified in [AGM5]

Resolutions of the Steinberg module for GL(n)

We give several resolutions of the Steinberg representation St_n for the general linear group over a principal ideal domain, in particular over Z. We compare them, and use these results to prove that the computations in [AGM4] are definitive. In particular, in [AGM4] we use two complexes to compute certain cohomology groups of congruence subgroups of SL(4,Z). One complex is based on Voronoi's polyhedral decomposition of the symmetric space for SL(n,R), whereas the other is a larger complex that has an action of the Hecke operators. We prove that both complexes allow us to compute the relevant cohomology groups, and that the use of the Voronoi complex does not introduce any spurious Hecke eigenclasses

Monte Carlo simulations of pulse propagation in massive multichannel optical fiber communication systems

We study the combined effect of delayed Raman response and bit pattern randomness on pulse propagation in massive multichannel optical fiber communication systems. The propagation is described by a perturbed stochastic nonlinear Schr\"odinger equation, which takes into account changes in pulse amplitude and frequency as well as emission of continuous radiation. We perform extensive numerical simulations with the model, and analyze the dynamics of the frequency moments, the bit-error-rate, and the mutual distribution of amplitude and position. The results of our numerical simulations are in good agreement with theoretical predictions based on the adiabatic perturbation approach.Comment: Submitted to Physical Review E. 8 pages, 5 figure

Natively Unstructured Loops Differ from Other Loops

Natively unstructured or disordered protein regions may increase the functional complexity of an organism; they are particularly abundant in eukaryotes and often evade structure determination. Many computational methods predict unstructured regions by training on outliers in otherwise well-ordered structures. Here, we introduce an approach that uses a neural network in a very different and novel way. We hypothesize that very long contiguous segments with nonregular secondary structure (NORS regions) differ significantly from regular, well-structured loops, and that a method detecting such features could predict natively unstructured regions. Training our new method, NORSnet, on predicted information rather than on experimental data yielded three major advantages: it removed the overlap between testing and training, it systematically covered entire proteomes, and it explicitly focused on one particular aspect of unstructured regions with a simple structural interpretation, namely that they are loops. Our hypothesis was correct: well-structured and unstructured loops differ so substantially that NORSnet succeeded in their distinction. Benchmarks on previously used and new experimental data of unstructured regions revealed that NORSnet performed very well. Although it was not the best single prediction method, NORSnet was sufficiently accurate to flag unstructured regions in proteins that were previously not annotated. In one application, NORSnet revealed previously undetected unstructured regions in putative targets for structural genomics and may thereby contribute to increasing structural coverage of large eukaryotic families. NORSnet found unstructured regions more often in domain boundaries than expected at random. In another application, we estimated that 50%–70% of all worm proteins observed to have more than seven protein–protein interaction partners have unstructured regions. The comparative analysis between NORSnet and DISOPRED2 suggested that long unstructured loops are a major part of unstructured regions in molecular networks

Surveillance of gastrointestinal disease in France using drug sales data

AbstractDrug sales data have increasingly been used for disease surveillance during recent years. Our objective was to assess the value of drug sales data as an operational early detection tool for gastroenteritis epidemics at national and regional level in France. For the period 2008–2013, we compared temporal trends of drug sales for the treatment of gastroenteritis with trends of cases reported by a Sentinel Network of general practitioners. We benchmarked detection models to select the one with the best sensitivity, false alert proportion and timeliness, and developed a prospective framework to assess the operational performance of the system. Drug sales data allowed the detection of seasonal gastrointestinal epidemics occurring in winter with a distinction between prescribed and non-prescribed drugs. Sales of non-prescribed drugs allowed epidemic detection on average 2.25 weeks earlier than Sentinel data. These results confirm the value of drug sales data for real-time monitoring of gastroenteritis epidemic activity