A statistical MMN reflects the magnitude of transitional probabilities in auditory sequences

Within the framework of statistical learning, many behavioural studies investigated the processing of unpredicted events. However, surprisingly few neurophysiological studies are available on this topic, and no statistical learning experiment has investigated electroencephalographic (EEG) correlates of processing events with different transition probabilities. We carried out an EEG study with a novel variant of the established statistical learning paradigm. Timbres were presented in isochronous sequences of triplets. The first two sounds of all triplets were equiprobable, while the third sound occurred with either low (10%), intermediate (30%), or high (60%) probability. Thus, the occurrence probability of the third item of each triplet (given the first two items) was varied. Compared to high-probability triplet endings, endings with low and intermediate probability elicited an early anterior negativity that had an onset around 100 ms and was maximal at around 180 ms. This effect was larger for events with low than for events with intermediate probability. Our results reveal that, when predictions are based on statistical learning, events that do not match a prediction evoke an early anterior negativity, with the amplitude of this mismatch response being inversely related to the probability of such events. Thus, we report a statistical mismatch negativity (sMMN) that reflects statistical learning of transitional probability distributions that go beyond auditory sensory memory capabilities

Testing statistical hypothesis on random trees and applications to the protein classification problem

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov--Smirnov-type goodness-of-fit test proposed by Balding et al. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford--Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton--Watson related processes.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS218 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A robust comparison of dynamical scenarios in a glass-forming liquid

We use Bayesian inference methods to provide fresh insights into the sub-nanosecond dynamics of glycerol, a prototypical glass-forming liquid. To this end, quasielastic neutron scattering data as a function of temperature have been analyzed using a minimal set of underlying physical assumptions. On the basis of this analysis, we establish the unambiguous presence of three distinct dynamical processes in glycerol, namely, translational diffusion of the molecular centre of mass and two additional localized and temperature-independent modes. The neutron data also provide access to the characteristic length scales associated with these motions in a model-independent manner, from which we conclude that the faster (slower) localized motions probe longer (shorter) length scales. Careful Bayesian analysis of the entire scattering law favors a heterogeneous scenario for the microscopic dynamics of glycerol, where molecules undergo either the faster and longer or the slower and shorter localized motions.Peer ReviewedPostprint (author's final draft

Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit

A remarkable feature of quantum many-body systems is the orthogonality catastrophe that describes their extensively growing sensitivity to local perturbations and plays an important role in condensed matter physics. Here we show that the dynamics of the orthogonality catastrophe can be fully characterized by the quantum speed limit and, more specifically, that any quenched quantum many-body system, whose variance in ground state energy scales with the system size, exhibits the orthogonality catastrophe. Our rigorous findings are demonstrated by two paradigmatic classes of many-body systems—the trapped Fermi gas and the long-range interacting Lipkin-Meshkov-Glick spin model

Between impact and returns: Private investors and the sustainable development goals

We investigate the expectations of wealthy private investors regarding the impact and financial return of sustainable investments. Our paper focuses on the sustainable development goals (SDGs) as a framework for investors' attempts to create impact. We analyze the behavior of 60 high-net-worth individuals (HNWIs), a powerful yet overlooked investor segment. Our results show large allocations in line with the SDGs, which demonstrates these investors' aim of achieving real-word changes. Furthermore, we show that these “impact investors” have a clear preference for SDGs that are associated with high financial returns. As such, we confirm that both impact and attractive financial returns are expected. Our findings provide rich, deep insights into how HNWIs practice impact investing and their underlying motivations. We outline practical implications for different stakeholders, notably regarding the fact that financially attractive SDGs are likely to attract substantial amounts of capital, with other SDGs remaining underfunded