Permutation groups, simple groups and sieve methods

We show that the number of integers n ≤ x which occur as indices of subgroups of nonabelian finite simple groups, excluding that of An-1 in An, is ∼ hx/log x, for some given constant h. This might be regarded as a noncommutative analogue of the Prime Number Theorem (which counts indices n ≤ x of subgroups of abelian simple groups). We conclude that for most positive integers n, the only quasiprimitive permutation groups of degree n are Sn and An in their natural action. This extends a similar result for primitive permutation groups obtained by Cameron, Neumann and Teague in 1982. Our proof combines group-theoretic and number-theoretic methods. In particular, we use the classification of finite simple groups, and we also apply sieve methods to estimate the size of some interesting sets of primes

Spectral Sparsification and Regret Minimization Beyond Matrix Multiplicative Updates

In this paper, we provide a novel construction of the linear-sized spectral sparsifiers of Batson, Spielman and Srivastava [BSS14]. While previous constructions required $\Omega(n^4)$ running time [BSS14, Zou12], our sparsification routine can be implemented in almost-quadratic running time $O(n^{2+\varepsilon})$. The fundamental conceptual novelty of our work is the leveraging of a strong connection between sparsification and a regret minimization problem over density matrices. This connection was known to provide an interpretation of the randomized sparsifiers of Spielman and Srivastava [SS11] via the application of matrix multiplicative weight updates (MWU) [CHS11, Vis14]. In this paper, we explain how matrix MWU naturally arises as an instance of the Follow-the-Regularized-Leader framework and generalize this approach to yield a larger class of updates. This new class allows us to accelerate the construction of linear-sized spectral sparsifiers, and give novel insights on the motivation behind Batson, Spielman and Srivastava [BSS14]

The Computational Power of Optimization in Online Learning

We consider the fundamental problem of prediction with expert advice where the experts are "optimizable": there is a black-box optimization oracle that can be used to compute, in constant time, the leading expert in retrospect at any point in time. In this setting, we give a novel online algorithm that attains vanishing regret with respect to $N$ experts in total $\widetilde{O}(\sqrt{N})$ computation time. We also give a lower bound showing that this running time cannot be improved (up to log factors) in the oracle model, thereby exhibiting a quadratic speedup as compared to the standard, oracle-free setting where the required time for vanishing regret is $\widetilde{\Theta}(N)$. These results demonstrate an exponential gap between the power of optimization in online learning and its power in statistical learning: in the latter, an optimization oracle---i.e., an efficient empirical risk minimizer---allows to learn a finite hypothesis class of size $N$ in time $O(\log{N})$. We also study the implications of our results to learning in repeated zero-sum games, in a setting where the players have access to oracles that compute, in constant time, their best-response to any mixed strategy of their opponent. We show that the runtime required for approximating the minimax value of the game in this setting is $\widetilde{\Theta}(\sqrt{N})$, yielding again a quadratic improvement upon the oracle-free setting, where $\widetilde{\Theta}(N)$ is known to be tight

Final Report DOE Contract No. DE-FG36-04G014294 ICEKAP 2004: A Collaborative Joint Geophysical Imaging Project at Krafla and IDDP P.E. Malin, S.A. Onacha, E. Shalev Division of Earth and Ocean Sciences Nicholas School of the Environment Duke University Durham, NC 27708

In this final report, we discuss both theoretical and applied research resulting from our DOE project, ICEKAP 2004: A Collaborative Joint Geophysical Imaging Project at Krafla and IDDP. The abstract below begins with a general discussion of the problem we addressed: the location and characterization of “blind” geothermal resources using microearthquake and magnetotelluric measurements. The abstract then describes the scientific results and their application to the Krafla geothermal area in Iceland. The text following this abstract presents the full discussion of this work, in the form of the PhD thesis of Stephen A. Onacha. The work presented here was awarded the “Best Geophysics Paper” at the 2005 Geothermal Resources Council meeting, Reno. This study presents the modeling of buried fault zones using microearthquake and electrical resistivity data based on the assumptions that fluid-filled fractures cause electrical and seismic anisotropy and polarization. In this study, joint imaging of electrical and seismic data is used to characterize the fracture porosity of the fracture zones. P-wave velocity models are generated from resistivity data and used in locating microearthquakes. Fracture porosity controls fluid circulation in the hydrothermal systems and the intersections of fracture zones close to the heat source form important upwelling zones for hydrothermal fluids. High fracture porosity sites occur along fault terminations, fault-intersection areas and fault traces. Hydrothermal fault zone imaging using resistivity and microearthquake data combines high-resolution multi-station seismic and electromagnetic data to locate rock fractures and the likely presence fluids in high temperature hydrothermal systems. The depths and locations of structural features and fracture porosity common in both the MT and MEQ data is incorporated into a joint imaging scheme to constrain resistivity, seismic velocities, and locations of fracture systems. The imaging of the fault zones is constrained by geological, drilling, and geothermal production data. The objective is to determine interpretation techniques for evaluating structural controls of fluid circulation in hydrothermal systems. The conclusions are: • directions of MT polarization and anisotropy and MEQ S-splitting correlate. Polarization and anisotropy are caused by fluid filled fractures at the base of the clay cap. •Microearthquakes occur mainly on the boundary of low resistivity within the fracture zone and high resistivity in the host rock. Resistivity is lowest within the core of the fracture zone and increases towards the margins of the fracture zone. The heat source and the clay cap for the hydrothermal have very low resistivity of less than 5Ωm. •Fracture porosity imaged by resistivity indicates that it varies between 45-5% with most between 10-20%, comparable to values from core samples in volcanic areas in Kenya and Iceland. For resistivity values above 60Ωm, the porosity reduces drastically and therefore this might be used as the upper limit for modeling fracture porosity from resistivity. When resistivity is lower than 5Ωm, the modeled fracture porosity increases drastically indicating that this is the low resistivity limit. This is because at very low resistivity in the heat source and the clay cap, the resistivity is dominated by ionic conduction rather than fracture porosity. •Microearthquakes occur mainly above the heat source which is defined by low resistivity at a depth of 3-4.5 km at the Krafla hydrothermal system and 4-7 km in the Longonot hydrothermal system. •Conversions of S to P waves occur for microearthquakes located above the heat source within the hydrothermal system. Shallow microearthquakes occur mainly in areas that show both MT and S-wave anisotropy. •S-wave splitting and MT anisotropy occurs at the base of the clay cap and therefore reflects the variations in fracture porosity on top of the hydrothermal system. •In the Krafla hydrothermal system in Iceland, both MT polarization and MEQ splitting directions align with zones that have high fracture porosity below the clay cap. These zones coincide with fault zones trending in the NNE-SSW and NW-SE directions in otherwise uniform volcanic rocks and laterally continuous geology. The NW-SE orientation is parallel to the regional shear fractures while the NNE-SSW trending polarizations align parallel to rift zone fracture swarms. This suggest that correlations between MT polarizations and MEQ splitting may be related to fluid filled fractures. •In areas of high resistivity (60Ωm), the P-wave velocity approaches that of the rock matrix. •S-wave splitting polarization is determined from measurements of angles of rotation to get the optimum direction of polarization. •The use of MEQ and resistivity for imaging fractures requires that the MEQ data acquisition system be located close to the fracture zone

Premise Selection for Mathematics by Corpus Analysis and Kernel Methods

Smart premise selection is essential when using automated reasoning as a tool for large-theory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large corpora of proofs. This work develops learning-based premise selection in two ways. First, a newly available minimal dependency analysis of existing high-level formal mathematical proofs is used to build a large knowledge base of proof dependencies, providing precise data for ATP-based re-verification and for training premise selection algorithms. Second, a new machine learning algorithm for premise selection based on kernel methods is proposed and implemented. To evaluate the impact of both techniques, a benchmark consisting of 2078 large-theory mathematical problems is constructed,extending the older MPTP Challenge benchmark. The combined effect of the techniques results in a 50% improvement on the benchmark over the Vampire/SInE state-of-the-art system for automated reasoning in large theories.Comment: 26 page

Single-molecule transcript counting of stem-cell markers in the mouse intestine

available in PMC 2012 July 1.Determining the molecular identities of adult stem cells requires technologies for sensitive transcript detection in tissues. In mouse intestinal crypts, lineage-tracing studies indicated that different genes uniquely mark spatially distinct stem-cell populations, residing either at crypt bases or at position +4, but a detailed analysis of their spatial co-expression has not been feasible. Here we apply three-colour single-molecule fluorescent in situ hybridization to study a comprehensive panel of intestinal stem-cell markers during homeostasis, ageing and regeneration. We find that the expression of all markers overlaps at crypt-base cells. This co-expression includes Lgr5, Bmi1 and mTert, genes previously suggested to mark distinct stem cells. Strikingly, Dcamkl1 tuft cells, distributed throughout the crypt axis, co-express Lgr5 and other stem-cell markers that are otherwise confined to crypt bases. We also detect significant changes in the expression of some of the markers following irradiation, indicating their potential role in the regeneration process. Our approach can enable the sensitive detection of putative stem cells in other tissues and in tumours, guiding complementary functional studies to evaluate their stem-cell properties.National Institutes of Health (U.S.) (U54CA143874)National Cancer Institute (U.S.) (Physical Sciences Oncology Center at MIT (U54CA143874))National Institutes of Health (U.S.) (NIH Pioneer award (1DP1OD003936))National Cancer Institute (U.S.) (Cancer Center Support (core) grant P30-CA14051)European Molecular Biology Organization (postdoctoral fellowship)Human Frontier Science Program (Strasbourg, France)Machiah FoundationHoward Hughes Medical Institute (Gilliam fellowship

‘Together … for only a moment’ British newspaper constructions of altruistic non-commercial surrogate motherhood

Objectives: To explore how national altruistic surrogacy is framed in a representative selection of the British press. Methods: A study of 90 British national newspaper articles was carried out using the Lexis-Nexis data base to search for articles on altruistic surrogacy. Content analysis of gain, loss, neutral frames and high or low alarm and vulnerability frames in the titles and the body of the text was carried out. The type of construction used in the article content was also analysed. Data were coded and consensus reached using a coding strategy specifically developed for the purposes of this study. Results: Titles and content were predominantly loss, high alarm and high vulnerability framed. The content was also gain framed, and written with a focus on the social and legal aspects differentially between the newspaper types. Discussion: The tabloid press emphasizes social issues, and the middle market and serious press focus on legal issues of altruistic surrogacy. Selectively framed and reinforced information provided by the different newspapers, reflect the different readership, with Tabloid readers likely to be, surrogates (mostly from lower socioeconomic strata) and serious/ middle-market readers likely to be commissioning parents (mostly professionals)

Adaptive Stochastic Primal-Dual Coordinate Descent for Separable Saddle Point Problems

We consider a generic convex-concave saddle point problem with separable structure, a form that covers a wide-ranged machine learning applications. Under this problem structure, we follow the framework of primal-dual updates for saddle point problems, and incorporate stochastic block coordinate descent with adaptive stepsize into this framework. We theoretically show that our proposal of adaptive stepsize potentially achieves a sharper linear convergence rate compared with the existing methods. Additionally, since we can select "mini-batch" of block coordinates to update, our method is also amenable to parallel processing for large-scale data. We apply the proposed method to regularized empirical risk minimization and show that it performs comparably or, more often, better than state-of-the-art methods on both synthetic and real-world data sets.Comment: Accepted by ECML/PKDD201