Toward Fast and Reliable Potential Energy Surfaces for Metallic Pt Clusters by Hierarchical Delta Neural Networks.

Data-driven machine learning force fields (MLFs) are more and more popular in atomistic simulations and exploit machine learning methods to predict energies and forces for unknown structures based on the knowledge learned from an existing reference database. The latter usually comes from density functional theory calculations. One main drawback of MLFs is that physical laws are not incorporated in the machine learning models, and instead, MLFs are designed to be very flexible to simulate complex quantum chemistry potential energy surface (PES). In general, MLFs have poor transferability, and hence, a very large trainset is required to span all the target feature space to get a reliable MLF. This procedure becomes more troublesome when the PES is complicated, with a large number of degrees of freedom, in which building a large database is inevitable and very expensive, especially when accurate but costly exchange-correlation functionals have to be used. In this manuscript, we exploit a high-dimensional neural network potential (HDNNP) on Pt clusters of sizes from 6 to 20 as one example. Our standard level of energy calculation is DFT GGA (PBE) using a plane wave basis set. We introduce an approximate but fast level with the PBE functional and a minimal atomic orbital basis set, and then, a more accurate but expensive level, using a hybrid functional or nonlocal vdW functional and a plane wave basis set, is reliably predicted by learning the difference with HDNNP. The results show that such a differential approach (named ΔHDNNP) can deliver very accurate predictions (error <10 meV/atom) in reference to converged basis set energies as well as more accurate but expensive xc functionals. The overall speedup can be as large as 900 for a 20 atom Pt cluster. More importantly, ΔHDNNP shows much better transferability due to the intrinsic smoothness of the delta potential energy surface, and accordingly, one can use much smaller trainset data to obtain better accuracy than the conventional HDNNP. A multilayer ΔHDNNP is thus proposed to obtain very accurate predictions versus expensive nonlocal vdW functional calculations in which the required trainset is further reduced. The approach can be easily generalized to any other machine learning methods and opens a path to study the structure and dynamics of Pt clusters and nanoparticles

Analysis of Large Urn Models with Local Mean-Field Interactions

The stochastic models investigated in this paper describe the evolution of a set of $F_N$ identical balls scattered into $N$ urns connected by an underlying symmetrical graph with constant degree $h_N$. After some random amount of time {\em all the balls} of any urn are redistributed locally, among the $h_N$ urns of its neighborhood. The allocation of balls is done at random according to a set of weights which depend on the state of the system. The main original features of this context is that the cardinality $h_N$ of the range of interaction is not necessarily linear with respect to $N$ as in a classical mean-field context and, also, that the number of simultaneous jumps of the process is not bounded due to the redistribution of all balls of an urn at the same time. The approach relies on the analysis of the evolution of the local empirical distributions associated to the state of urns located in the neighborhood of a given urn. Under convenient conditions, by taking an appropriate Wasserstein distance and by establishing several technical estimates for local empirical distributions, we are able to prove mean-field convergence results. When the load per node goes to infinity, a convergence result for the invariant distribution of the associated McKean-Vlasov process is obtained for several allocation policies. For the class of power of $d$ choices policies, we show that the associated invariant measure has an asymptotic finite support property under this regime. This result differs somewhat from the classical double exponential decay property usually encountered in the literature for power of $d$ choices policies

Analysis of Large Unreliable Stochastic Networks

In this paper a stochastic model of a large distributed system where users' files are duplicated on unreliable data servers is investigated. Due to a server breakdown, a copy of a file can be lost, it can be retrieved if another copy of the same file is stored on other servers. In the case where no other copy of a given file is present in the network, it is definitively lost. In order to have multiple copies of a given file, it is assumed that each server can devote a fraction of its processing capacity to duplicate files on other servers to enhance the durability of the system. A simplified stochastic model of this network is analyzed. It is assumed that a copy of a given file is lost at some fixed rate and that the initial state is optimal: each file has the maximum number $d$ of copies located on the servers of the network. Due to random losses, the state of the network is transient and all files will be eventually lost. As a consequence, a transient $d$-dimensional Markov process $(X(t))$ with a unique absorbing state describes the evolution this network. By taking a scaling parameter $N$ related to the number of nodes of the network. a scaling analysis of this process is developed. The asymptotic behavior of $(X(t))$ is analyzed on time scales of the type $t\mapsto N^p t$ for $0\leq p\leq d{-}1$. The paper derives asymptotic results on the decay of the network: Under a stability assumption, the main results state that the critical time scale for the decay of the system is given by $t\mapsto N^{d-1}t$. When the stability condition is not satisfied, it is shown that the state of the network converges to an interesting local equilibrium which is investigated. As a consequence it sheds some light on the role of the key parameters $\lambda$, the duplication rate and $d$, the maximal number of copies, in the design of these systems

Beneficial influence of nanocarbon on the aryliminopyridylnickel chloride catalyzed ethylene polymerization

A series of 1-aryliminoethylpyridine ligands (L1―L3) was synthesized by condensation of 2-acetylpyridine with 1-aminonaphthalene, 2-aminoanthracene or 1-aminopyrene, respectively. Reaction with nickel dichloride afforded the corresponding nickel (II) chloride complexes (Ni1–Ni3). All compounds were fully characterized and the molecular structures of Ni1 and Ni3 are reported. Upon activation with methylaluminoxane (MAO), all nickel complexes exhibit high activities for ethylene polymerization, producing waxes of low molecular weight and narrow polydispersity. The presence of multi-walled carbon nanotubes (MWCNTs) or few layer graphene (FLG) in the catalytic medium can lead to an increase of productivity associated to a modification of the polymer structure

Four not six: revealing culturally common facial expressions of emotion

As a highly social species, humans generate complex facial expressions to communicate a diverse range of emotions. Since Darwin’s work, identifying amongst these complex patterns which are common across cultures and which are culture-specific has remained a central question in psychology, anthropology, philosophy, and more recently machine vision and social robotics. Classic approaches to addressing this question typically tested the cross-cultural recognition of theoretically motivated facial expressions representing six emotions, and reported universality. Yet, variable recognition accuracy across cultures suggests a narrower cross-cultural communication, supported by sets of simpler expressive patterns embedded in more complex facial expressions. We explore this hypothesis by modelling the facial expressions of over 60 emotions across two cultures, and segregating out the latent expressive patterns. Using a multi-disciplinary approach, we first map the conceptual organization of a broad spectrum of emotion words by building semantic networks in two cultures. For each emotion word in each culture, we then model and validate its corresponding dynamic facial expression, producing over 60 culturally valid facial expression models. We then apply to the pooled models a multivariate data reduction technique, revealing four latent and culturally common facial expression patterns that each communicates specific combinations of valence, arousal and dominance. We then reveal the face movements that accentuate each latent expressive pattern to create complex facial expressions. Our data questions the widely held view that six facial expression patterns are universal, instead suggesting four latent expressive patterns with direct implications for emotion communication, social psychology, cognitive neuroscience, and social robotics

Advanced Silicon Avalanche Photodiodes on NASA's Global Ecosystem Dynamics Investigation (GEDI) Mission

Silicon Avalanche Photodiodes (APDs) are used in NASAs Global Ecosystem Dynamics Investigation (GEDI) which was launched in December 2018 and is currently measuring the Earths vegetation vertical structure from the International Space Station. The APDs were specially made for space lidar with a much lower hole-to-electron ionization coefficient ratio (k-factor ~0.008) than that of commercially available silicon APDs in order to reduce the APD excess noise from the randomness of the avalanche gain. A silicon heater resistor was used under the APD chip to heat the device up to 70C and improve its quantum efficiency at 1064 nm laser wavelength while maintaining a low dark current such that the overall signal to noise ratio is improved. Special APD protection circuits were used to raise the overload damage threshold to prevent device damage from strong laser return by specular surfaces, such as still water bodies, and space radiation events. The APD and a hybrid transimpedance amplifier circuit were hermetically sealed in a package with a sufficiently low leak rate to ensure multi-year operation lifetime in space. The detector assemblies underwent a series of pre-launch tests per NASA Goddard Environmental Verification Standard for space qualification. They have performed exactly as expected with GEDI in orbit. A detailed description of the GEDI detector design, signal and noise model, and test results are presented in this paper