Search results for " Set theory"
showing 10 items of 113 documents
Random Walks on Weighted Graphs of Groups
2019
Let X be a locally finite simplicial tree without terminal vertices, and let X = ∣X∣1 be its geometric realisation. Let Γ be a nonelementary discrete subgroup of Aut(X).
Tally languages accepted by alternating multitape finite automata
1997
We consider k-tape 1-way alternating finite automata (k-tape lafa). We say that an alternating automaton accepts a language L\(\subseteq\)(Σ*)k with f(n)-bounded maximal (respectively, minimal) leaf-size if arbitrary (respectively, at least one) accepting tree for any (w1, w2,..., wk) ∈ L has no more than $$f\mathop {(\max }\limits_{1 \leqslant i \leqslant k} \left| {w_i } \right|)$$ leaves. The main results of the paper are the following. If k-tape lafa accepts language L over one-letter alphabet with o(log n)-bounded maximal leaf-size or o(log log n)-bounded minimal leaf-size then the language L is semilinear. Moreover, if a language L is accepted with o(log log(n))-bounded minimal (respe…
Least-squares community extraction in feature-rich networks using similarity data
2021
We explore a doubly-greedy approach to the issue of community detection in feature-rich networks. According to this approach, both the network and feature data are straightforwardly recovered from the underlying unknown non-overlapping communities, supplied with a center in the feature space and intensity weight(s) over the network each. Our least-squares additive criterion allows us to search for communities one-by-one and to find each community by adding entities one by one. A focus of this paper is that the feature-space data part is converted into a similarity matrix format. The similarity/link values can be used in either of two modes: (a) as measured in the same scale so that one may …
Set similarity joins on mapreduce
2018
Set similarity joins, which compute pairs of similar sets, constitute an important operator primitive in a variety of applications, including applications that must process large amounts of data. To handle these data volumes, several distributed set similarity join algorithms have been proposed. Unfortunately, little is known about the relative performance, strengths and weaknesses of these techniques. Previous comparisons are limited to a small subset of relevant algorithms, and the large differences in the various test setups make it hard to draw overall conclusions. In this paper we survey ten recent, distributed set similarity join algorithms, all based on the MapReduce paradigm. We emp…
A Large-Scale Empirical Evaluation of Cross-Validation and External Test Set Validation in (Q)SAR.
2013
(Q)SAR model validation is essential to ensure the quality of inferred models and to indicate future model predictivity on unseen compounds. Proper validation is also one of the requirements of regulatory authorities in order to accept the (Q)SAR model, and to approve its use in real world scenarios as alternative testing method. However, at the same time, the question of how to validate a (Q)SAR model, in particular whether to employ variants of cross-validation or external test set validation, is still under discussion. In this paper, we empirically compare a k-fold cross-validation with external test set validation. To this end we introduce a workflow allowing to realistically simulate t…
Glass transition of hard spheres in high dimensions
2009
We have investigated analytically and numerically the liquid-glass transition of hard spheres for dimensions $d\to \infty $ in the framework of mode-coupling theory. The numerical results for the critical collective and self nonergodicity parameters $f_{c}(k;d) $ and $f_{c}^{(s)}(k;d) $ exhibit non-Gaussian $k$ -dependence even up to $d=800$. $f_{c}^{(s)}(k;d) $ and $f_{c}(k;d) $ differ for $k\sim d^{1/2}$, but become identical on a scale $k\sim d$, which is proven analytically. The critical packing fraction $\phi_{c}(d) \sim d^{2}2^{-d}$ is above the corresponding Kauzmann packing fraction $\phi_{K}(d)$ derived by a small cage expansion. Its quadratic pre-exponential factor is different fr…
Large time behavior for a porous medium equation in a nonhomogeneous medium with critical density
2014
Abstract We study the large time behavior of solutions to the Cauchy problem for the porous medium equation in nonhomogeneous media with critical singular density | x | − 2 ∂ t u = Δ u m , in R N × ( 0 , ∞ ) , where m > 1 and N ≥ 3 , with nonnegative initial condition u ( x , 0 ) = u 0 ( x ) ≥ 0 . The asymptotic behavior proves to have some interesting and striking properties. We show that there are different asymptotic profiles for the solutions, depending on whether the continuous initial data u 0 vanishes at x = 0 or not. Moreover, when u 0 ( 0 ) = 0 , we show the convergence towards a peak-type profile presenting a jump discontinuity, coming from an interesting asymptotic simplification…
Evolution of small-scale magnetic elements in the vicinity of granular-size swirl convective motions
2014
Advances in solar instrumentation have led to a widespread usage of time series to study the dynamics of solar features, specially at small spatial scales and at very fast cadences. Physical processes at such scales are determinant as building blocks for many others occurring from the lower to the upper layers of the solar atmosphere and beyond, ultimately for understanding the bigger picture of solar activity. Ground-based (SST) and space-borne (Hinode) high-resolution solar data are analyzed in a quiet Sun region displaying negative polarity small-scale magnetic concentrations and a cluster of bright points observed in G-band and Ca II H images. The studied region is characterized by the …
The barrier height of the F+H2 reaction revisited: coupled-cluster and multireference configuration-interaction benchmark calculations.
2008
Large scale coupled-cluster benchmark calculations have been carried out to determine the barrier height of the F+H2 reaction as accurately as possible. The best estimates for the barrier height of the linear and bent transition states amount to 2.16 and 1.63 kcal/mol, respectively. These values include corrections for core correlation, scalar-relativistic effects, spin-orbit effects, as well as the diagonal Born-Oppenheimer correction. The CCSD(T) basis-set limits are estimated using extrapolation techniques with augmented quintuple and sextuple-zeta basis sets, and remaining N-electron errors are determined using coupled-cluster singles, doubles, triples, quadruples calculations with up t…
Type designation of the name of the conifer Araâr-tree Tetraclinis articulata (Cupressaceae)
2018
The typification of the name Tetraclinis articulata (Cupressaceae) is discussed. Previous type designation is considered ineffective. Original material conserved in the herbarium of the Natural History Museum of Denmark at C is designated as the lectotype.