TopologyNet: Topology based deep convolutional neural networks for biomolecular property predictions

Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered by the entangled geometric complexity and biological complexity. We introduce topology, i.e., element specific persistent homology (ESPH), to untangle geometric complexity and biological complexity. ESPH represents 3D complex geometry by one-dimensional (1D) topological invariants and retains crucial biological information via a multichannel image representation. It is able to reveal hidden structure-function relationships in biomolecules. We further integrate ESPH and convolutional neural networks to construct a multichannel topological neural network (TopologyNet) for the predictions of protein-ligand binding affinities and protein stability changes upon mutation. To overcome the limitations to deep learning arising from small and noisy training sets, we present a multitask topological convolutional neural network (MT-TCNN). We demonstrate that the present TopologyNet architectures outperform other state-of-the-art methods in the predictions of protein-ligand binding affinities, globular protein mutation impacts, and membrane protein mutation impacts.Comment: 20 pages, 8 figures, 5 table

Emergent spacetime and empirical (in)coherence

Numerous approaches to a quantum theory of gravity posit fundamental ontologies that exclude spacetime, either partially or wholly. This situation raises deep questions about how such theories could relate to the empirical realm, since arguably only entities localized in spacetime can ever be observed. Are such entities even possible in a theory without fundamental spacetime? How might they be derived, formally speaking? Moreover, since by assumption the fundamental entities can't be smaller than the derived (since relative size is a spatiotemporal notion) and so can't 'compose' them in any ordinary sense, would a formal derivation actually show the physical reality of localized entities? We address these questions via a survey of a range of theories of quantum gravity, and generally sketch how they may be answered positively.Comment: 18 pages, 1 figure, accepted for publication in Studies in History and Philosophy of Modern Physic

What is the best spatial distribution to model base station density? A deep dive into two european mobile networks

This paper studies the base station (BS) spatial distributions across different scenarios in urban, rural, and coastal zones, based on real BS deployment data sets obtained from two European countries (i.e., Italy and Croatia). Basically, this paper takes into account different representative statistical distributions to characterize the probability density function of the BS spatial density, including Poisson, generalized Pareto, Weibull, lognormal, and \alpha -Stable. Based on a thorough comparison with real data sets, our results clearly assess that the \alpha -Stable distribution is the most accurate one among the other candidates in urban scenarios. This finding is confirmed across different sample area sizes, operators, and cellular technologies (GSM/UMTS/LTE). On the other hand, the lognormal and Weibull distributions tend to fit better the real ones in rural and coastal scenarios. We believe that the results of this paper can be exploited to derive fruitful guidelines for BS deployment in a cellular network design, providing various network performance metrics, such as coverage probability, transmission success probability, throughput, and delay