In this section we fix F⊆FF,n and E, and we suppose that we are in exactly the same setting as in §5.1. In particular, we have (5.2) and (5.3), with a multiplicative function δe that satisfies 1≪Fδp≤1 if p∉E and δp=0 if p∈E. Furthermore, we set

For all positive integers $\ell$, we prove non-trivial bounds for the $\ell$-torsion in the class group of $K$, which hold for almost all number fiel…

Paul Mätzig was funded by the Studienstiftung des deutschen Volkes. This research was partly funded by the Volkswagen Foundation grant 89 953 to Shravan Vasishth.

We present a computational evaluation of three hypotheses about sources of deficit in sentence comprehension in aphasia: slowed processing, intermitt…

We prove our main result in this section.

We show that a minimal counter example to the Cherlin-Zilber Algebraicity Conjecture for simple groups of finite Morley rank has normal 2-rank at mos…

Adaptive-network models are typically studied using deterministic differential equations which approximately describe their dynamics. In simulations,…

Following the pioneering observations with COBE in the early 1990s, studies of the cosmic microwave background (CMB) have focused on temperature and …

We present a weak lensing analysis of the 3 GHz JVLA radio survey of the COSMOS field, which we correlate with overlapping HST-ACS optical observatio…

Written language is a complex communication signal capable of conveying information encoded in the form of ordered sequences of words. Beyond the loc…

Markov chain Monte Carlo methods are a commonly used and powerful family of numerical methods for sampling from complex probability distributions. As…

Artificial Intelligence models are becoming increasingly more powerful and accurate, supporting or even replacing humans' decision making. But with i…

We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the couplin…

Low frequency radio waves, while challenging to observe, are a rich source of information about pulsars. The LOw Frequency ARray (LOFAR) is a new rad…

We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the method…

Measurements of cosmic microwave background spectral distortions have profound implications for our understanding of physical processes taking place …

We present a new perturbative formulation of non-equilibrium thermal field theory, based upon non-homogeneous free propagators and time-dependent ver…

The explosion of Big Data was followed by the proliferation of numerous complex parallel software stacks whose aim is to tackle the challenges of dat…

Several different methods exist for efficient approximation of paths in multiscale stochastic chemical systems. Another approach is to use bursts of …

The joint spectral radius of a finite set of real d x d matrices is defined to be the maximum possible exponential rate of growth of products of matr…

The joint spectral radius of a finite set of real $d \times d$ matrices is defined to be the maximum possible exponential rate of growth of long prod…

Decentralised optimisation tasks are important components of multi-agent systems. These tasks can be interpreted as n-player potential games: therefo…

We extend a previous work by Reischke et al., 2016 by studying the effects of tidal shear on clustering dark energy models within the framework of th…

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